JP2004265381A - Feasibility handling of constraint and limit in process control system optimizer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To allow an optimization technique used for driving a process plant controller, such as a model prediction controller, to create a solution that is used by the controller and achievable by using a method that is organized and systematized, and simple in terms of a computer for relaxing or redefining the constraint in operation variables/constant variables/auxiliary variables, when no feasible, optimum solution exists within a preset constraint. <P>SOLUTION: An optimization routine uses a slack variable given penalty, or redefines a constraint model along with the use of the penalty variable for creating a new object function, and determines a control solution for fully satisfying the initial constraint limit by using the new object function. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

  No. 10 / 241,350, filed Sep. 11, 2002, entitled "Integrated Model Predictive Control and Optimization Within a Process Control System." )) ", The disclosure of which is expressly incorporated herein by reference.

  The present invention relates generally to process control systems, and more particularly to addressing the feasibility of constraints and limitations in a process control system optimizer when used, for example, in a model predictive controller for controlling a process plant. About.

  Process control systems, such as those used for chemical, petroleum or other processes, such as distributed or large-scale process control systems, typically include one or more process controllers, which are controlled by communication means. It is interconnected with each other and with at least one host or operator workstation and with one or more field devices via an analog, digital, or combined analog / digital bus. Field devices include, for example, valves, valve positioners, switches, and transmitters (temperature, pressure, flow rate sensors, etc.), and perform functions in the process, such as opening and closing valves and measuring process parameters. The process controller receives signals indicating process measurements generated by the field device and / or other information about the field device and uses this information to execute control routines and generate control signals. This control signal is transmitted to the field device through the bus and controls the operation of the process. Information from field devices and controllers is typically made available to one or more applications executed by an operator workstation, and the operator performs desired functions for the process, such as viewing the current state of the process, modifying process operation, and the like. be able to.

  A process controller typically has different algorithms, subroutines, or control loops (such as flow control loops, temperature control loops, pressure control loops, etc.) for each of a plurality of different loops defined for or included within a process. Are all control routines). In general, each of these control loops can include one or more input blocks, such as an analog input (AI) function block, a single output control block, such as a proportional-integral-derivative (PID) or fuzzy logic control function block, and an analog Includes a single output block, such as an output (AO) function block. These control loops typically provide single input / single output control. The reason is that the control block produces a single control output that is used to control a single process input, such as the position of a valve. However, in some cases, using multiple single-input / single-output control loops that operate independently may not be very effective. This is because the controlled process variables are affected by more than just a single process input, and in fact, each process input can affect the state of multiple process outputs. As an example, for example, in a process having tanks filled by two input lines and discharged by a single output line, each line is controlled by a different valve and the temperature, pressure and flow rate of the tank at or near the desired values Such situations can occur when controlled. As mentioned above, the control of the flow, temperature and pressure of the tank is considered to be performed using a separate flow control loop, a separate temperature control loop, and a separate pressure control loop. However, in such a situation, when the temperature control loop is activated to change the setting of one of the input valves to control the temperature in the tank, the pressure in the tank will increase, thereby causing the pressure loop to increase the pressure, for example. The drain valve may be opened to lower it. This action then causes the flow control loop to close one of the input valves, which affects the temperature, so that the temperature control loop may perform another action. As can be seen from this example, a single-input / single-output control loop is an unacceptable way of oscillating the process output (in this case, flow, temperature and pressure) without the output reaching a steady state. To act on.

  Thus, model predictive control (MPC) or other types of advanced control are used to perform process control in situations where changes to a particular control process variable affect multiple process variables or outputs. Since the late 1970s, numerous successful examples of implementing model predictive control have been reported, making MPC the dominant form of advanced multivariable control in the process industry. Further, MPC is implemented as distributed control system layer software in a distributed control system.

  In general, MPCs measure the effect of each change in a plurality of process inputs on each of a plurality of process outputs, and use this measured response to create a control matrix or model of the process. Control strategy. The process model or control matrix (which generally defines the steady state behavior of the process) is mathematically inverted and used as or in a multiple-input / multiple-output controller and changes introduced to process inputs Control the process output based on In some cases, the process model is represented as a process output response curve (typically a step response curve) for each process input, and these curves are created, for example, based on a series of pseudo-random step changes provided to each process input. Sometimes. These response curves can be used to model the process in a known manner. Since MPC is well known in the art, a detailed description thereof will be omitted in this specification, but "An Overview of Industrial Model Predictive Control Technology," by AI, Conference, 1996. US Pat. Nos. 4,616,308 and 4,349,869 also outline MPC controllers that can be used in process control systems.

  MPC has proven to be a very effective and useful control technology and is being used in conjunction with process optimization. To optimize a process using MPC, the optimizer runs the process at an optimal point by minimizing or maximizing one or more process input variables determined by the MPC routine. Although this technique is computationally feasible, optimizing the process from an economic point of view requires processes that have a significant effect on, for example, improving the economic operation of the process (such as process flow rate or quality). You need to select a variable. Operating a process at an optimal point from a financial or economic point of view typically requires controlling not only a single process variable but also many other process variables.

  As a solution for performing dynamic optimization by MPC, optimization using a more modern technique such as a quadratic programming technique or an interior point method has been proposed. With these methods, the optimal solution is determined, and the optimizer provides the controller with motion at the controller output (ie, the manipulated variables of the process), taking into account process dynamics, current constraints and optimization goals. However, this approach places an enormous load on the computer and is not practically feasible with the current state of the art.

  In many cases using MPC, the number of manipulated variables available in the process (ie, the control output of the MPC routine) is determined by the number of control variables in the process (ie, the number of process variables to be controlled to a particular set point). ). As a result, there are often many degrees of freedom available for optimization and constraint handling. Theoretically, to perform such optimization, one must calculate values that represent process variables, constraints, limits, and economic factors that define the optimal operating point of the process. In many cases, these process variables are constrained variables. This is because there is a limit as to the physical properties of the process associated with them and in which these variables must be kept. For example, process variables representing tank levels are limited to the maximum and minimum levels physically reachable in the actual tank. The optimization function may calculate costs and / or benefits in relation to each of the constraint or auxiliary variables to operate at a level that maximizes benefits and minimizes costs. The measured values of these auxiliary variables are then provided as input to the MPC routine and can be treated by the MPC routine as control variables with set points equal to the operating points of the auxiliary variables defined by the optimization routine.

  No. 10 / 241,350, filed Sep. 11, 2002, entitled "Integrated Model Predictive Control and Optimization Within a Process Control System" Accordingly, applications that are assigned to the assignee of the present application and whose disclosures are cited and hereby expressly incorporated herein use advanced control blocks, such as MPC blocks, in which optimization is integral with multivariable model predictive control. A method and apparatus for providing improved online optimization is disclosed. This technique has been quite successful. The reason is that in normal operation, the MPC controller provides a future prediction of the process output up to a steady state, thereby creating the necessary conditions for the optimizer to operate reliably. However, this optimization approach to finding a solution does not always work. The reason is that, depending on the circumstances, these variables may appear in the controller output or predicted controller output (herein referred to as manipulated variable) or process output (herein referred to as control variable) associated with the possible optimal solution. Because it may fall outside of the predicted constraints or limits preset for, and therefore the solution falls within a predefined, unrealizable range. Whenever the optimizer is integrated with an MPC or other controller, it is desirable to find a solution that avoids operating as far as possible to the extent that is not feasible, and in many control situations that There is.

  At this time, if the optimizer determines that there is an optimal solution that is not feasible, but that any process control output or input will maintain preset constraints or limits, the optimizer will generally obtain an acceptable solution To relax one or more constraints or limitations. This recovery technique typically uses priorities associated with each of the manipulated and control variables to determine which constraints or limits to relax first. Here, as a simple approach, there is a method in which the optimizer removes the lowest priority constraint in order to obtain a solution that can satisfy the higher priority constraint. However, this technique is not always the most rational way to handle constraints on unrealizable solutions. The reason is that removing lower priority constraints to make minimal adjustments to one or more higher priority constraints can cause these lower priority constraints to deviate significantly from scope. Because there is. Also, it is usually necessary to guess the number of constraints that must be removed to obtain a feasible solution. Naturally, it is desirable to minimize the number of constraints that are removed to satisfy the higher priority constraints. However, to determine the appropriate number of constraints to drop, either make an offline calculation based on the available degrees of freedom in the system, or else have the optimizer repeatedly remove the constraints one by one, It is necessary to determine whether or not a feasible solution can be obtained with the new combination in which the feasibility is reduced until a feasible solution is obtained. Unfortunately, offline calculations do not work well with real-time or online optimization systems, and iterative approaches are generally borderless. This can result in an unacceptable delay before a feasible solution is obtained. In other words, the process of creating an optimal solution by sequentially removing constraints must be repeated until a solution is obtained, and such an open-ended iterative process is often used in real-time optimization applications. Not desirable.

Several other well-known approaches have been proposed to achieve optimization when there are unfeasible solutions. For example, prioritize "Propositional Logic in Control and Monitoring Problems," by Tyler, ML and Morari M., Proceedings of European Control Conference '97, pp. 623-238, Brussels, Belgium, June 1997. The use of integer variables has been disclosed to minimize the magnitude of infringement by solving the sequence of mixed integer optimization problems. On the other hand, Vada, J., Slupphaug, O. , Foss, BA, due to "Infeasibility Handling in Linear MPC subject to Prioritized Constraints," Preprints IFCA'99 14 th World Congress, China, Beijing, July 1999, in the, Algorithms are described that can be used to solve a sequence of linear programming (LP) or quadratic programming (QP) problems to minimize violations of unsatisfiable constraints. However, neither of these approaches is computationally rigorous and generally not suitable or acceptable for fast and real-time applications. On the other hand, "Efficient Infeasibility Handling in Linear MPC subject to Prioritized Constraints," by Vada. J., Slupphaug, O., and Johansen, TA, ACC2002 Proceedings, Anchorage, Alaska, May 2002 An off-line algorithm for calculating LP weights to optimize infringement is disclosed. Although this technique reduces the excessive computational burden on the offline environment, it requires addressing additional offline optimization problems and is not as useful for online or real-time optimization procedures.
U.S. Pat.No. 4,616,308 U.S. Pat.No. 4,349,869 U.S. Patent Application No. 10 / 241,350 U.S. Patent No. 6,445,963 Qin, S. Joe, Thomas A. Badgwell, `` An Overview of Industrial Model Predictive Control Technology '' AIChE Conference, 1996 Tyler, ML, Morari M. Propositional Logic in Control and Monitoring Problems, Proceedings of European Control Conference '97, pp.623-628, June 1997. Vada, J., Slupphaug, O., Foss, BA, `` Infeasibility Handling in Linear MPC subject to Prioritized Constraints, '' Preprints IFCA'99 14th World Congress, July 1999. Vada. J., Slupphaug, O, Johansen, TA, "Efficient Infeasibility Handling in Linear MPC subject to Prioritized Constraints," ACC2002 Proceedings, May 2002.

  Integrated optimization techniques that can be used to optimize advanced control procedures, such as model predictive control procedures, require that the operating or control variables be controlled when no feasible optimal solution exists within preset constraints or limits Search for achievable optimal solutions for use in control procedures by using an organized, systematic, and computationally simple method that relaxes or redefines the constraints or limits of In particular, the optimization routine may redefine the constraint model based on penalized slack variables and / or if it encounters an optimizer solution that is not feasible within preset constraint limits. Systematically selects the optimal solution using powerful and reliable techniques. Because the technique disclosed herein is computationally simple, it is suitable for online implementation of a real-time optimizer.

  In one embodiment, the optimizer uses an objective function that includes a penalized slack variable to find an optimal solution in the presence of one or more manipulated or controlled variables that are outside preset limits. May be. In another embodiment, the optimizer redefines the acceptable limits of out-of-bound manipulated or control variables by redefining the constraint model, and replaces the objective function with the penalty variables defined in the new constraint model. It may be used to push higher priority constraints out of bounds toward a preset limit without further violation of lower priority constraints. In yet another embodiment, the optimizer may integrate the use of penalized slack variables with the redefinition of constraint models to provide flexible and effective constraint handling techniques.

Referring now to FIG. 1, a process control system 10 includes a process controller 11, which includes a data historian 12, and one or more host workstations or computers 13, each having a display screen 14, Type of personal computer, workstation, etc.). The controller 11 is also connected to field devices 15-22 via input / output (I / O) cards 26,28. The data historian 12 may be a desired type of data collection unit having a desired type of memory for storing data and desired or well-known software, hardware, or firmware; It may be separate from one (as shown in FIG. 1) or a part thereof. The controller 11 is, for example, a DeltaV ^™ controller sold by Emerson Process Management, for example, with the host computer 13 and the data historian 12 through an Ethernet connection or other desired communication network 29. May be communicably connected to The communication network 29 has a form such as a local area network (LAN), a wide area network (WAN), and a telecommunications network, and is realized by using a wired or wireless technology. The controller 11 may include the desired hardware and software associated with, for example, a standard 4-20 mA device and / or associated with a smart communication protocol such as the FOUNDATION ^™ fieldbus protocol (Fieldbus), HART ^™ protocol. And is communicably connected to the field device 15-22.

  Field devices 15-22 may be any type of device, such as sensors, valves, transmitters, positioners, etc., and I / O cards 26, 28 may be any type of I / O device that follows a desired communication or controller protocol. In the embodiment shown in FIG. 1, the field devices 15-18 are standard 4-20 mA devices that communicate with the I / O card 26 through an analog line, and the field devices 19-22 use fieldbus protocol communication. A smart device, such as a fieldbus field device, that communicates with the I / O card 28 over a digital bus. Of course, field devices 15-22 may conform to any other standards or protocols desired, including any standards or protocols developed in the future.

  A controller 11 that is one of many distributed controllers in the plant 10 and includes at least one processor therein executes or monitors one or more process processing routines, which are stored therein. Or it may include a control loop associated therewith. Controller 11 also communicates with devices 15-22, host computer 13, and data historian 12, and controls the process in a desired manner. It should be noted that any of the control routines or elements described herein may be implemented or performed by another controller or other device, if desired. Similarly, the control routines or elements described herein, implemented within process control system 10, may be in any form, including software, firmware, or hardware. In this regard, a process control element may be any part of a process control system that includes, for example, a routine, block, or module stored on a computer-readable medium. A control routine, which is part of a control procedure such as a module or subroutine, parts of a subroutine (strings of code, etc.), ladder logic, sequential function charts, function block diagrams, purpose-based programming, or any other software It may be implemented in any desired software format using a programming language or design paradigm. Similarly, the control routines may be hard-coded, for example, in one or more EPROMs, EEPROMs, dedicated integrated circuits (ASICs), or other hardware or firmware elements. Further, the control routines may be designed using any design tool, including graphic design tools or other types of software / hardware / firmware programming tools or design tools. Thus, the controller 11 may be configured to execute a control strategy or control routine in a desired manner.

  In one embodiment, the controller 11 executes the control strategy using what is commonly referred to as a functional block. In this strategy, each functional block is part or subject of an overall control routine, operates in conjunction with other functional blocks (by communication called links), and executes a process control loop within the process control system 10. I do. Functional blocks are typically input functions such as those associated with transmitters, sensors or other process parameter measurement devices, control functions such as those associated with control routines that perform PID control, fuzzy logic control, etc., or valves such as valves. It performs one of the output functions that control the operation of the various devices, and performs some physical function within the process control system 10. Of course, there are hybrid functional blocks and other types of functional blocks. The function blocks may be stored in and executed by the controller 11, but this is typically the case when these function blocks are standard 4-20 mA devices, and some type of smart field device such as a HART device. Or associated therewith, or may be stored and executed within the field device itself, as in the case of a fieldbus device. Although the control system is described here using a functional block control strategy using a purpose-based programming paradigm, the control strategy or control loop or control module uses other conventions such as ladder logic, sequential function charts, etc. Or may be implemented or designed using any other desired programming language or programming paradigm.

  As shown in expanded block 30 of FIG. 1, controller 11 may include a plurality of single loop control routines, shown as routines 32, 34, and one or more advanced control loops shown as control loop 36. May be executed. Each such loop is commonly referred to as a control module. The single-loop control routines 32, 34 are respectively a single-input / single-output fuzzy logic control block and a single-input / single-output block connected to the appropriate analog input (AI) and analog output (AO) function blocks. Shown as performing signal loop control using an output PID control block, the functional block may be associated with a process control device such as a valve, or associated with a measurement device such as a temperature transmitter and a pressure transmitter. And may be associated with other devices in the process control system 10. The advanced control loop 36 is shown as including an advanced control block 38 having an input communicatively connected to a number of AI function blocks and an output communicatively connected to a number of AO function blocks, but the advanced control The inputs and outputs of block 38 may be communicatively connected to other desired functional blocks or control elements to receive other types of inputs and provide other types of control outputs. As will be described later, the advanced control block 38 may be a control block that integrates a model predictive control routine and an optimizer to execute optimal control of a process or a part of the process. Although the advanced control blocks are described herein as including model predictive control (MPC) blocks, other multi-input / multi-output control routines, such as neural network modeling or control routines, multi-variable fuzzy logic control routines, or the like. It may be a procedure. The functional blocks shown in FIG. 1, including the advanced control block 38, are executed by the controller 11 or in other processing units, such as one of the workstations 13 or one of the field devices 19-22. It will be appreciated that this is implemented by

  As shown in FIG. 1, one of the workstations 13 includes an advanced control block generation routine 40, which is used to create, download, and execute the advanced control block 38. The advanced control block generation routine 40 may be stored in memory within the workstation 13 and executed by a processor, but the routine (or a portion thereof) may additionally or alternatively include, if desired, the process control system 10. May be stored in and executed by other devices within. In general, the advanced control block generation routine 40 includes a control block generation routine 42 that generates an advanced control block and connects the advanced control block into the process control system, and a process control process based on the data collected by the advanced control block. A process modeling routine 44 for creating a process model or a part thereof, and control logic parameters for an advanced control block from the process model, and an advanced control block for using these control logic parameters for process control. It includes a control logic parameter creation routine 46 to be stored or downloaded within, and an optimizer routine 48 to create an optimizer for use with the advanced control block. These routines 42, 44, 46, 48 can be comprised of a series of different routines. The series of routines includes a first routine for creating an advanced control element having a control input adapted to receive process output and a control output adapted to provide control signals to the process input, and a process control routine (desired). A second routine that allows a user to download and communicatively connect the advanced control element within the control routine, and a third routine that uses the advanced control element to provide an excitation waveform for each process input. A routine and a fourth routine to collect data reflecting the response of each process output to the excitation waveform using the advanced control element, and to select or allow the user to select a set of inputs for the advanced control block. A fifth routine to create a process model, A seventh routine for creating advanced control logic parameters from the process model, and an eighth routine for placing the advanced control logic and, if necessary, the process model within the advanced control element so that the advanced control element can control the process. There are routines and a ninth routine that selects or allows the user to select an optimizer for use within the advanced control block 38.

FIG. 2 is a block diagram illustrating one embodiment of the advanced control block 38 communicatively coupled to the process 50 in further detail. It can be seen from this figure that the advanced control block 38 generates a set of manipulated variables MV to provide to the other function blocks, while these other function blocks are connected to the control inputs of the process 50. As shown in FIG. 2, the advanced control block 38 includes an MPC controller block 52, an optimizer 54, a target transform block 55, a step response model or control matrix 56, and an input processing / filter block 58. The MPC controller 52 is a standard M × M square (M can be any number greater than 1) MPC routine or procedure, with as many inputs as outputs. The MPC controller 52 receives as input a set of N control variables CV and auxiliary variables AV (vectors of values) measured in the process 50 and a known or expected value provided to the process 50 at some time in the future. receiving a set of disturbance variables DV is changed or disturbances is, and a set of steady state target control variable CV _T and the auxiliary variables AV _T provided from the target conversion block 55. The MPC controller 52 uses these inputs to create a set of M manipulated variables MV (in the form of control signals) and supply manipulated variable MV signals to control the process 50.

In addition, the MPC controller 52 calculates a set of predicted steady state control variables CV _SS and auxiliary variables AV _SS using the predicted values of the control variables CV, auxiliary variables AV (each at the predicted horizontal line) and manipulated variables MV (at the control horizontal line). represents a set of calculated along with the predicted steady state manipulated variables MV _SS, provided to the input processing / filter block 58. Input processing / filter block 58 processes the determined predicted steady state values of control variable CV _SS , auxiliary variable AV _SS , and manipulated variable MV _SS to reduce the effects of noise and unpredictable disturbances on these variables. . The input processing / filter block 58 may include a low-pass filter or any other input processing that reduces the effects of noise, modeling errors, and disturbances on these values, and may include a filtered control variable CV _SSfil , It will be appreciated that the auxiliary variable AV _SSfil and the manipulated variable MV _SSfil are provided to the optimizer 54.

  The optimizer 54 is a linear programming (LP) optimizer in this example, and performs a process optimization using an objective function (OF) that may be provided from a selection block 62. Alternatively, the optimizer 54 may be a quadratic programming optimizer, that is, an optimizer having a linear model and a quadratic objective function. In general, the objective function OF specifies a cost or benefit associated with each of a plurality of control, auxiliary, and manipulated variables (collectively referred to as process variables), and the optimizer 54 maximizes or reduces this objective function. A set of process variables to be minimized is searched to determine target values for these variables. The selection block 62 also selects the objective function OF provided to the optimizer 54 as one of a set of pre-stored objective functions 64 that mathematically represent various ways of determining the optimal operation of the process 50. Good. For example, one pre-stored objective function 64 is configured to maximize plant benefits, another objective function 64 is configured to minimize the use of certain raw materials that are in short supply, and Another objective function 64 may be configured to maximize the quality of the product manufactured in the process 50. In general, the objective function is defined by the set point or range of the control variable CV and the limits of the auxiliary variable AV and the manipulated variable MV, using the cost or benefit associated with the movement of each of the control, auxiliary and manipulated variables. Determine the most optimal process operating point within an acceptable set of points. Of course, any desired objective function may be used instead of, or in addition to, those described herein, including an objective function that optimizes each of several concerns, such as raw material usage and profit margins.

  The user or operator may select an objective function 64 by presenting an objective function 64 to be used on the operator or user's terminal (such as one of the workstations 13 of FIG. 1), the selection being made by input 66 Is provided to the selection block 62 via In response to input 66, selection block 62 provides the selected objective function OF to optimizer 54. Of course, the user or operator can change the objective function used during the operation of the process. If desired, a default objective function may be used if the user does not provide or select an objective function. One of the possible default objective functions is described in detail below. Although the operator terminal 13 in FIG. 1 stores various objective functions, which are shown as a part of the advanced control block 38, one of these objective functions is changed during the creation of the advanced control block 38. Alternatively, it may be provided to the block during generation.

  In addition to the objective function OF, the optimizer 54 takes as inputs a set of control variable set points (usually an operator specified set point for the control variable CV of the process 50, which can be changed by the operator or another user). , And the range and weight or priority associated with each control variable CV. In addition, the optimizer 54 receives a set of range or constraint limits for the auxiliary variable AV and a set of weights or priorities and a set of limits for the manipulated variable MV used to control the process 50. Optimizer 54 may also receive set points, preferred operating ranges, ideal rest values, and other limits associated with one or more process variables. In general, the ranges of the auxiliary and manipulated variables define the limits of the auxiliary and manipulated variables (usually based on the physical characteristics of the plant), and the range of the control variables is used by the control variables to control the process well. Provide the range you can. The weights of the control, auxiliary and manipulated variables may specify the relative importance of the control, auxiliary and manipulated variables during the optimization process and, depending on the situation, the constraints or constraints associated with these variables. If a limit needs to be violated, it may be used to enable the optimizer 54 to generate a control target solution.

  During operation, the optimizer 54 may perform optimization using linear programming (LP) techniques. As is well known, linear programming is a mathematical technique for solving a set of linear equations and inequalities that maximize or minimize certain additional functions, called objective functions. As described above, the objective function may represent an economic value such as cost or profit, or may represent other objectives instead of or in addition to the economic objective. In addition, as described below, the objective function is adjusted to include the cost or penalty associated with violating the constraint or limit if none of the CVs, AVs, and MVs fall within preset limits. And may make it available to determine acceptable solutions.

  As will be appreciated, the steady state gain matrix defines the steady state gain for each possible pair of manipulated and control or auxiliary variables. In other words, the steady state gain matrix defines the steady state gain in each control variable and auxiliary variable for each unit change of the manipulated variable and disturbance variable. This steady state gain matrix is typically an N × M matrix, where N is the number of control and auxiliary variables, and M is the number of manipulated variables used in the optimizer routine. In general, N may be greater than, equal to, or less than M, and in the most general case N is greater than M.

Using well-known or standard LP algorithm or technique, the optimizer 54 is generally from a set of to determine the target manipulated variables MV _T (steady state gain matrix to maximize or minimize the objective function OF selected (Determined) iteratively, and if possible, perform process actions that meet or do not meet within the control variable CV setpoint range limits, auxiliary variable AV constraint limits, and manipulated variable MV limits. In one embodiment, the optimizer 54 actually determines the change of the manipulated variable and uses the display of the predicted steady state control variable CV _SSfil , the auxiliary variable AV _SSfil and the manipulated variable MV _SSfil to change the process behavior from the current behavior. Determine to make a change, that is, determine the dynamic behavior of the MPC control routine during the process to reach the target or optimal process operating point. This dynamic operation is important because it is desirable to ensure that no constraint limits are violated during the transition from the current operating point to the target operating point.

  In some embodiments, LP optimizer 54 may be designed to minimize an objective function of the form

Here, the vector for calculating Q = total cost / profit, P = AV _S, benefits vectors associated with CV _S, cost vector associated with the C = MV _S, A = gain matrix, the change in .DELTA.MV = MV _S ,.

  The profit value is generally a positive number, and the cost value is generally a negative number, indicating each influence on the purpose. Using this or another objective function, the LP optimizer 54 determines that the control variable CV falls within the range from the target set point, the auxiliary variable AV falls within its own upper and lower bound constraints, and the manipulated variable MV The change in the manipulated variable MV that minimizes the objective function is calculated while keeping the value within the upper limit and the lower limit.

  In one available optimization procedure, the manipulated variable increment is used at the current time (t), and the sum of the manipulated variable increments is determined by the control variable and an Used across the prediction horizon in conjunction with the variable increment. This is common in LP applications. Of course, the LP algorithm may be modified appropriately for this variation. In any case, the LP optimizer 54 may use a steady state model, so that the application generally requires a steady state. Predictive horizon commonly used in MPC design ensures future steady state for self-regulatory processes. Assuming that the prediction horizon is p and the control horizon is c, one possible prediction process steady state equation for an m × n input / output process expressed in incremental form is:

The vector ΔMV (t + c) represents the total change over the control horizon caused by all controller outputs mv _i , so that:

  These changes desirably satisfy the limits for both the manipulated variable MV and the control variable CV (where the auxiliary variables are treated as control variables), and thus:

  In this case, an objective function that maximizes product value and minimizes raw material costs can be determined together as follows.

  Here, UCV is a cost vector for changing the unit in the control variable CV process value, and UMV is a cost vector for changing the unit in the operation variable MV process value.

  Applying the above equation (1), the objective function can be expressed as follows with respect to the manipulated variable MV.

The LP algorithm calculates the objective function for the initial vertex in the area defined by equation (7) in order to search for the optimal solution, and the vertex having the maximum value (minimum value) of the objective function is determined as the optimal solution. Improve the solution at each step until the algorithm determines that The determined optimal manipulated variable values are applied or provided to the controller as the target manipulated variables MV _T is achieved in the control horizon.

In general, when the LP algorithm is run on the created matrix, three results can be assumed. First, the unique solution for the target manipulated variables MV _T is obtained. Second, the solution has no boundaries. However, this does not occur when the control variable and the auxiliary variable each have an upper limit and a lower limit. Third, there is no solution that meets the limits of the process variables. In other words, this means that the boundaries or constraints of the process variables are too tight. To address the third case, the overall constraint may be relaxed and the optimizer run again with the relaxed constraint to obtain a solution. Basically, it is assumed that the limits (upper / lower) of the manipulated variables cannot be changed by the optimizer, but this assumption need not be true. Similar assumptions can be used for auxiliary variable constraints or limits (upper / lower). However, the optimizer may run from running to a specific setpoint of the control variable CV (CV setpoint control) to running to any value within or around the setpoint of the control variable CV (CV range control). Can be changed to In this case, the value of the control variable is not within a specific set point but within a certain range. If there are some auxiliary variables AV that violate your own constraints and the transition from CV set point control to CV range control does not result in a solution, the auxiliary variable based on the provided weight or priority specification Can be relaxed or ignored. In one embodiment, the solution is determined by sequentially minimizing the square error of the auxiliary variables, each allowing violation of that constraint, or abandoning the constraint of the lowest priority auxiliary variable. You. As will be described in more detail below, other methods of addressing out-of-bound solutions include slack or penalty variables that evaluate the cost or penalty for each process variable that violates preset limits or constraints. How to change the objective function and rerun the optimizer with the new objective function, and / or redefine the limits for one or more process variables that exceed the limits, including penalties for process variables within the new limits There is a way to change the objective function, run these variables towards the original limits, rerun the optimizer with the new objective function, and search for optimal solutions within these redefined limits . First, a method of selecting an objective function will be described.

  As described above, the objective function OF is selected or set by default by the control block generation program 40. While it is desirable to provide the ability to optimize, there are many situations where the set point of the control variable only needs to be maintained in such a way as to monitor the operational constraints of the auxiliary and manipulated variables. For these applications, block 38 may be configured as a simple MPC function block. To enable such simple use, a default "action" objective function may be automatically created with default auxiliary variable AV weights, as well as default costs assigned to various variables. These defaults may set any costs for the auxiliary variable AV and the manipulated variable MV that are equal to the auxiliary variable AV or the manipulated variable MV, or that result in another predetermined cost assignment. Once the expert option is selected, the user may create additional optimization choices and define costs associated with various objective functions 64. Also, the expert user can modify the default auxiliary variable AV and control variable CV weights of the default objective function, as well as the constraint limits or setpoint range infringement costs. This can be used by the optimizer, as described in more detail below, if the optimizer does not initially obtain a feasible solution.

  In one embodiment, the objective function may be automatically configured from the MPC configuration, for example, if no economic factors are defined for the process configuration. In general, the objective function can be constructed using the following equation.

Variables C _j and P _j can be defined from configuration settings. In particular, assuming that the control variable CV set point is defined only by the lower limit (LL) or the upper limit (HL), the P _j value can be defined as follows.

P _j = -1 if the set point is defined by LL or a minimum is chosen
P _j = 1 if set point is defined by HL or maximum is chosen
Assuming that no configuration information about the auxiliary variable AV is input, P _j = 0 for all auxiliary variables AV. Similarly, for the manipulated variable MV, the C _j value differs depending on whether or not a desirable manipulated variable target MV _T is defined. As it follows if the preferred operating target MV _T is defined.

If MV _T is HL or maximum is chosen, C _j = 1
If MV _T is selected to be LL or minimum, C _j = -1
If MV _T is not defined, C _j = 0
If desired, the choice of using optimizer 54 in conjunction with MPC controller 52 may be adjustable, thereby providing a degree of optimization. To execute this function, the operation variable MV used by the controller 52 can be changed by applying various weights to the change of the operation variable MV determined by the MPC controller 52 and the optimizer 54. Such a combination of the weights of the manipulated variable MV is referred to as an effective MV (MV _eff ) here. The effective MV _eff can be determined as follows.

  S is arbitrarily or heuristically selected. Typically, S is likely to be greater than 1 and in the range of 10. Here, when α = 1, the optimizer contributes to the effective output as in the case where it is set to the generation point. If α = 0, the controller provides only MPC dynamic control. Of course, ranges between 0 and 1 make various contributions to the optimizer and MPC control.

  The default objective function described above may be used to establish the optimizer's operation during various possible modes of operation of the optimizer. In particular, if the number of control variables CV matches the number of manipulated variables MV, the behavior expected with the default setting is that the control variable CV set point is such that the auxiliary variable AV and the manipulated variable MV fall within their limits. It can be maintained as long as it is planned. If the auxiliary or manipulated variable is expected to exceed the limits, the control variable actuation set point can be varied, if possible, within its limits so as not to violate these limits. In this case, if the optimizer 54 cannot obtain a solution that satisfies the limits of the auxiliary and manipulated variables and maintains the control variable within that range, the control variable is maintained within that range and the auxiliary and / or manipulated variable Is allowed to deviate from its constraint limits. To find the optimal solution, these auxiliary variables AV and manipulated variables MV that are designed to violate the bounds are treated equally, and their mean marginal deviation is minimized. To achieve this behavior, the default cost / benefit used by the objective function is such that the control variable CV is assigned a benefit of 1 if the range is defined such that the deviation is below the set point, and that the deviation is If the range is defined to exceed the set point, it may be automatically set so that a profit of -1 is assigned to the control variable CV. A profit 0 may be assigned to the auxiliary variable AV within the limit, and a cost 0 may be assigned to the manipulated variable MV. In addition, profit 1 or -1 may be assigned to the auxiliary variable, and cost 0.1 may be assigned to the manipulated variable.

  If the number of control variables CV is less than the number of manipulated variables MV, the extra degrees of freedom can be used to indicate the requirements associated with the final pause of the configured manipulated variable MV. Here, the control variable set point (if the control variable CV set point is defined) can be maintained as long as the auxiliary and manipulated variables are planned to fall within their limits. The average value of the manipulated variables deviating from the configured final rest position is minimized. If one or more auxiliary and manipulated variables are predicted to violate its limits, the control variable actuation set point is changed within those limits so that these limits are not violated. If there are multiple solutions under this condition, the solution used for control will be the one that minimizes the average of the deviation of the manipulated variable from the configured final rest position.

  Under normal conditions, the target setpoints generated by the optimizer 54 in the above manner are within acceptable ranges, and the manipulated variables, auxiliary variables, and control variables are maintained within current limits or ranges. However, if the disturbance is so severe that it cannot be compensated within the constraints, some constraints will be violated. In that case, the optimizer 54 may not be able to obtain a feasible solution (ie a solution that does not violate any constraints or limits) using the default or selected objective function in conjunction with the setpoint mitigation techniques described above. Possible ways to provide optimization in such situations include abandoning any optimization operations and removing lower priority constraints.

  Abandoning optimization is the easiest and possible way to deal with unfeasible solutions, but it is not the best way to handle constraints. The reason is that even if there are no feasible solutions within the bounds, it is often possible to minimize the violation of constraints, taking into account the goal of the optimization. In addition, removing lower-priority constraints is the ultimate action, which helps in meeting higher-priority constraints, but can unduly deviate from the limits of removed constraints. Because of this, it may not be acceptable. Another problem with removing lower-priority constraints is to predict how many lower-priority constraints must be removed to get a solution. Such predictions are based on the degrees of freedom available in the system and must be calculated before or determined during the optimization procedure. In the latter case, it may be necessary to repeat the process of sequentially removing constraints and generating an optimal solution until a solution is obtained, and such an open-ended iterative process is not desirable in many real-time optimization applications. Absent.

  However, in some situations, even if an objective function for which no feasible solution exists is initially configured, a penalty is assigned in the objective function for each constraint violation according to the priority of the variable and the magnitude of the constraint violation ( (Commonly referred to as using slack variables in the objective function), redefining the constraint limits for one or more process variables, and using the redefined limits to move the process variables to a previous limit. On the other hand, it may be possible to obtain an acceptable solution by redefining the objective function so that other process variables do not deviate from the original constraints or limits, or by combining both techniques. found.

  More specifically, an unrealizable optimizer solution can be dealt with using a well-known concept of slack variables. This technique assigns a penalty according to one or both of the priority of the infringing constraint and the magnitude of the marginal infringement. In general, the prior art states that it is possible to use slack variables in optimization in the presence of controller constraint margin violations, but the present inventor has specified a method for implementing this. It is recognized that it is not publicly disclosed. Therefore, the technique described below allows the present inventor to redefine the objective function used by the optimizer using slack variables when there is necessarily a constraint violation in the solution generated using the original objective function. It was developed in order to

  Generally, a slack variable is defined as a value or degree that exceeds (above or below) the limit at which a predicted process variable is violated. To minimize slack variables (and thereby minimize marginal violations), the objective function used by the optimizer is redefined to include a non-zero slack variable value penalty, so that the optimizer Search for a solution that minimizes slack variables, along with other objectives such as the economic objective defined by the objective function. According to this technique, even when the optimizer can provide only an unrealizable solution, the objective function is associated with a violation of the limit of each process variable (such as an operation variable, an auxiliary variable, or a control variable), or It is redefined, including the cost or penalty, associated with each process variable that is planned to exceed at least a preset limit. If desired, define the same or different penalties for each process variable so that the objective function includes a slack variable that defines the cost or penalty arising from each limit violation for each process variable that violates the associated limit. You may. The cost or penalty of the slack variable in the redefined objective function varies depending on the magnitude of the marginal violation and the process variable in which the marginal violation occurs. The unit cost or penalty is, for example, higher for higher priority process variable limits and lower for lower priority process variable limits. In any case, the redefined objective function will be based on both the predefined economic factors (benefits and costs) and the cost or penalty associated with the presence of a non-zero slack variable in one or more process variables. In existence, it is used to search for the optimal solution by minimizing (or maximizing) the redefined objective function.

More specifically, the slack variable vectors S _max · 0 and S _min · 0 can be used in the linear programming as follows.

Here, it will be appreciated that AV is included in the CV term in these equations (ie, the CV variable includes all outputs, regardless of whether the control variable is an auxiliary variable). Equations (10) and (11) require equality in linear programming models, and the slack variables S _min and S _max serve only as supporting formal parameters that have no meaning for a particular application . In this application, additional slack variables S ⁺ and S ^- are used to expand the limits on the slack vector, S ⁺ · 0 are used to increase the upper limit, S ^- · 0 are used to decrease the lower limit Can be Equations (10) and (11) are effective if redefined or rewritten as follows.

Here, the values S ⁺ and S ⁻ are the values at which the predicted process variables violate the low and high constraint limits, respectively. By this definition, a new slack variables S ⁺ and S ^- defines the factor penalize in the objective function, used to obtain the LP solution with minimal overrun from within or range range. As an example, the objective function term PS ^{T _-} * S _- is extended by adding and PS ^{T ₊} * S _+, as follows.

Where PS _- is a slack variable penalty vector violating the lower bound, PS ₊ is a slack variable penalty vector violating the upper bound, and PS _- >> UCV and PS ₊ >> UCV (sign >> is a very large Means).

Then, the objective function, which is newly defined, the value S by minimizing an objective function that is newly defined ^- as these values as defined by the costs associated with and S ⁺ is minimized , May be used in a standard way to obtain an optimal solution in the sense of optimally reducing the overrun of the limit with respect to other objectives of the objective function.

In general, the penalty associated with the slack variables S ^- and S ⁺ should be much higher than the economic cost or benefit optimized within or in relation to the objective function. Thus, the vectors PS _- and PS ₊ (which define the penalties associated with the different slack variables) should have any elements much larger than the economic cost / benefit vector used in the objective function. In general, it is reasonable to assume that the smallest element of the vectors PS _- and PS ₊ is several times larger than the largest element of the UCV vector. Thus, as described herein, slack variables should be subject to high penalties in the objective function compared to economic costs, benefits, etc.

FIG. 5 illustrates the use of slack variables to address constraint violations of process variables (without associated set points). In particular, FIG. 5 illustrates (1) the case where the predicted process variable is within preset constraint limits (defined by lines 202 and 204), as shown at point 206; The values of S _max (i) and S _min (i) for the case where the predicted process variable is below the maximum constraint limit 202 and the case where the predicted process variable is below the minimum constraint limit 204 as shown at (3) point 210. Is shown. In the first case (related to the point 206), since the limitations of high constraints and low constraints are not violated, S ⁺ (i) and S ^- the value of (i) is zero. In this case, no penalty is given or associated with the process variable in the objective function. However, in the second case (represented by point 208), the value of S ⁺ (i) is not zero because point 208 exceeds upper limit 202. The bold dashed line indicates the value of the slack variable S ⁺ (i), which is multiplied by the unit cost associated with violating the upper bound of this process variable in the objective function. Similarly, in the third case (indicated by point 210), S for the point 210 is greater than the lower limit 204 ^- the value of (i) is not zero. Thick dotted line here is slack variables S ^- indicates the values of (i), This value unit cost associated with the lower limit violation of the process variable is multiplied in the objective function. Of course, FIG. 5 shows a single time associated with a signal process variable, and it will be appreciated that the redefined objective function gradually minimizes constraint violations up to the control horizon.

  In addition to (or in lieu of) minimizing the bounds violation as described above, the optimizer may be able to obtain an unrealistic solution or optimize the setpoint for other reasons, Penalized slack variables can also be used to effect setpoint optimization. In particular, the penalized slack variable may be a pre-selected set point (eg, a set point provided by an operator or other source) in response to an unrealizable solution or for any other desired reason. May be used to relax the set point within an acceptable range defined around and to cause other process variables to meet or approach the limits that are associated with them. The set point range includes a high range (set points can deviate within a range above a preselected set point), a low range (set points can deviate within a range below a preselected set point), or both. The set point range used in the present technology may be one side or both sides. The one-sided range defines a penalty in the objective function to deviate outside the preselected setpoint range, but provides only the economic cost in the objective function to deviate from the setpoint within the setpoint range, minimization It may be associated with an objective function or a maximizing objective function. On the other hand, a two-sided range usually has no economic objective, but within the preferred range extended with slack variables that are penalized high outside the range, to obtain an optimal solution as close as possible to the preselected set point Used. If the preferred set point range is equal to zero, this situation is substantially equal to the set point with a slack variable penalized around.

6 and 7 respectively show the use of slack variables with and without the extension range. In FIG. 6, point 215 indicates the set point of the process variable within the range defined by lines 217 and 219. There is no slack variable penalty associated with departure from the set point within the limits defined by lines 217 and 219. However, if the process variable exceeds the high range limit 217 of the range, as shown by point 221, to evaluate the penalty for this deviation in the objective function, similar to using the slack variable in the case of the constraint violation described above The penalty slack variable S ⁺ (i) is used. Similarly, if the process variable exceeds the low range limit 219 as shown at point 223, the penalty for this deviation in the objective function can be evaluated in the same way as using the slack variable in the case of constraint violations described above. , slack variables S were penalized ^- (i) is used.

FIG. 7 illustrates the use of slack variables in the context of an extended range. Here, the first slack variable penalty is evaluated for deviations from the set point in the first range, and the high penalty slack variable (with the high penalty cost) is in the first range Used to extend the possible range of outside set points. In particular, point 230 illustrates the situation where the predicted process variable is above the pre-selected set point 231 but within the preset tolerance defined by lines 232 and 234. Here, the variable S (i) _above is used to determine the penalty associated with the departure of point 230 from preset set point 231. As shown by the dotted line, non-zero values of the S (i) _above variable are penalized in the objective function. Point 236, on the other hand, illustrates the use of a high penalized slack variable when the manipulated variable associated with the set point exceeds the preset high range limit 232 by an S ⁺ (i) value. Here, the large bold dashed line indicates that the S ⁺ (i) value is penalized higher in the objective function compared to the S (i) _above variable, so that deviations outside the range limit 232 A far greater penalty than departure from set point 231 at.

Similarly, point 238 illustrates a situation where the predicted process variable is below the preselected set point 231 but within a preset tolerance defined by lines 232 and 234. Here, the variable S (i) _below is used to determine the penalty associated with the departure of point 238 from the preselected set point 231. As shown by the dotted line, non-zero values of the S (i) _below variable are penalized in the objective function. Furthermore, the point 240, the process variables associated with setpoint limit 234 preset low range S ^- shows the use of a case, the slack variables imposed a high penalty in excess (i) value by. Here, large thick dotted line, S ^- (i) value, imposed a higher penalty than the _S (i) below variable in the objective function, whereby the range limit 234 out of deviations, range limit 234 A far greater penalty than departure from set point 231 at.

  The equation for set point control with a two-sided range can be expressed as:

Where S _below and S _above are vectors of the slack variables of the solutions located _below and _above the set point, and the terms PSP ^T _below * S _below + PSP ^T _above * S _above should be added to the objective function _Yes , where PSP ^T _below is the unit penalty for solutions located _below the set point, and PSP ^T _above is the unit penalty for solutions located _above the set point. The objective function S defined above ^- it would also comprise and slack variables penalties S ⁺ variables are understood.

  This technique for addressing constraints with penalized slack variables provides significant flexibility in dealing with unfeasible situations. In particular, by applying a penalized slack variable, the optimizer finds an optimal solution that minimizes the overall constraint violation cost, defined by the objective function, even if the solution falls outside the preselection bounds or constraints. You can always search. However, some of the process variable outputs were within limits before running the redefined optimizer with penalized slack variables, but exceeded the limits as a result of solutions using slack variables. is there. Furthermore, the amount by which the limit is overrun for a particular process variable is not quantitatively defined before generating a solution. These two features are not desirable in many applications. This is because some applications require that lower-priority process variables that were initially within the range limits be not out of bounds in order to bring higher-priority process variables into the range. Also, some applications require well-defined solution limits for all process variables. In some cases, these two objectives can be met by redefining the constraint model in response to unrealizable situations or solutions.

  In particular, the constraint model itself may be redefined to address the infeasibility to fulfill a tightly defined degree of marginal infringement. Of course, this redefinition was the first optimization action, where the penalized slack variable was not used and there was no solution within the original bounds, or the penalized slack variable was used Is followed if the solution with the penalized slack variable is not acceptable. Generally, the redefined limit is set as the value of a predictive process variable (ie, control variable CV) that violates the original limit and the original limit minus some nominal value. These newly defined limits are used in a second optimization run to find a solution that minimizes or maximizes the objective function without violating the newly redefined limits. Redefining this limit prevents process variables that violate the original limit from deteriorating, while other process variables that did not violate the original preset limit violate it in the second optimization run To prevent However, the process variable is optimal within the original limits (if the predicted values of the process variables do not violate the original limits) or within the newly defined limits (if the predicted values of the process variables violate the original limits) And provide a limited optimal solution in the presence of marginal infringement.

This technique can also be mathematically defined for the control variable CV as follows. If there is no solution and the high limit CV ^HL is exceeded, the new limit of CV is defined as:

CV ^{HL '} = CV ^prediction
CV ^{LL '} = CV ^HL -D
Here, to avoid that the solution becomes the same as the original limit, D = 1-3%.

Similarly, above the low limit CV ^LL , the new limit is defined as:

CV ^{LL '} = CV ^prediction
CV ^{HL '} = CV ^LL + D
Of course, similar limits can be defined for other process variables, such as manipulated variable MV and auxiliary variable AV.

FIG. 8 outlines these newly defined limits. In particular, the original constraints CV ^HL and CV ^LL are shown on the left side of FIG. 8 by lines 250 and 252, and two CV predictions that violate these constraints (by the first pass of the optimizer using the original objective function) Generated) are shown by points 254 and 256. The two sets of redefined limits CV ^{HL '} and CV ^LL' are shown by the sets of lines 258 and 260 and lines 262 and 264. As can be seen, the redefined set of limits 258 and 260 corresponds to the new limit at point 254, limited by point 254 on the upper side and lower by the delta function from the original limit 250 on the lower side. . Similarly, the redefined set of limits 262 and 264 corresponds to the new limit of point 256, with the upper limit being point 256 (the most positive side) and the lower being the initial limit 252 plus the delta function. (Minimum positive side), limited. These new sets of limits are used in the objective function as new limits for points 254 or 256 (whichever is appropriate), and it is acknowledged that the new objective function will yield solutions outside these limits. Absent. Also, based on the distance between the new limit 260 (for point 254) or the new limit 262 (for point 256) and the new CV value, a high penalized coefficient is assigned and A new CV with a new limit may be used to advance to a new lower limit 260 or to a new upper limit 262. More specifically, after redefining the constraint correspondence model or limits, the penalty vectors for all CVs that exceed the range or limit may be recalculated to force the CVs toward the excess limit. To this end, the penalty for marginal infringement should override the economic valuation and the penalty associated with the new margin should be a highly penalized variable.

  Thus, for each process variable (e.g., CV) that is predicted to exceed the limit, a new limit is established to give the process variable space, but the process variable in the second pass of the optimizer is replaced by the original Penalties are used in the objective function to push to the limit. This optimizes the process variables without violating any limits (newly defined limits for process variables exceeding the limits, and initial limits for process variables that do not violate the original limits). However, in this case, the limit (the initial limit of a process variable that did not violate the initial limit in the first pass of the objective function, or the process variable that violated the initial limit in the first pass of the objective function is redefined) Are limited, and the optimizer can search for solutions within these limits.

  The general form of the LP objective function with the redefined limits and penalty factors for the limits is expressed as:

  If the cost of the process output is represented by a vector:

  As a result, the vector becomes:

In order to make the constraints correspond to priorities, the additional penalty for violating constraint outputs, v _i, is defined as a negative value if the process variable (eg, CV) is above the upper limit, and a negative value if the process variable is above the lower limit. It can be defined as a positive value. Contribution to the cost vector of additional penalty v _i is expressed as follows.

Constraints in order to respond to priority than economic factors, this vector is any element must be larger than the vector CM ^T. Thus:

Where r _i is the priority / rank number of the redefined CV, r _max is the maximum priority / rank number for the lowest priority / rank, and r _min is the minimum priority / rank for the highest priority / rank. Is a number.

The calculation can be simplified by using the high prediction | v _i |.

For practical purposes, assume | a _ij |> .05 to exclude very low process gains from the calculations. After calculating the v penalty for all process variables (eg, CVs) that exceed a preset limit or range, the penalties may be adjusted according to the priority of the process variables as follows.

After calculating the cost of a particular process variable that exceeds each constraint according to equation (23), the total cost of all constraints for all manipulated variables may be calculated from equation (19). The procedure for calculating the penalty is based on equation (22) for all CVs that violate the constraint.
Apply the should be applied sequentially from the lowest compromised precedence constraint (r _i maximum value) to the highest compromised precedence constraint. For practical purposes, the effective penalty vector may be normalized. One possible normalization technique is to divide all vector elements by the largest element and multiply by 100.

  If desired, the concept of constraint correspondence can be extended to situations that combine the above two approaches, especially those that combine penalized slack variables and model redefinition. In this integrated approach, only penalized slack variables are used if there are no constraint violations, or if the optimal solution calculated using the penalized slack variables is acceptable. However, if the constraints violated and the penalized slack variable solution is unacceptable, the process output limits are redefined. In this case, the new power limit is equal to the prediction for the predicted process output that violates the limit, as shown in FIG. However, the original limits are still used to define penalized slack variables, as in the slack variable application described above.

FIG. 9 shows the combined use of slack variables and limit redefinition. In particular, point 270 indicates the predicted process variable or CV within the initial limits CV ^HL and CV ^LL indicated by lines 272 and 274. Point 276 indicates a predicted process variable or CV that violates the upper bound CV ^HL 272. In this case, the limits are redefined as CV ^{HL '} and CV ^LL', as outlined above with respect to the limit redefinition of FIG. Also, the slack variables S ^′ _max and S ⁺ (i) are used to evaluate the penalty for infringing the initial margin using the slack variable penalty as described above. Similarly, point 280 indicates a predicted process variable or CV that violates the lower bound CV ^LL 274. In this case, the limits are redefined as CV ^{HL '} and CV ^LL', as outlined above with respect to the limit redefinition of FIG. Also, the slack variables S ^′ _min and S ⁻ (i) are used to evaluate the penalty for infringing the initial margin using the slack variable penalty as described above.

  This technique can be represented using the following equation:

Here, the redefined limit values CV ^{LL ′} and CV ^{HL ′} are lower and upper limits that the optimizer must not exceed. The limit value is set as an out-of-limit CV predicted value or an out-of-limit value that is wider than the initial limit. Integrated equations for CV range control and double sided CV range control can be created as well. Also, the integration equation for one-sided control is the same as equations (25) through (28). Bilateral range control can also be realized by the following equation:

  This is the same as equation (15).

  As can be appreciated, this integrated approach allows constraint handling to be managed in a more flexible way. Currently, the inputs have only hard or fixed defined constraint limits. However, by using this approach, it is possible to define soft constraints that are included in the hard constraints for some inputs. By incorporating penalized slack variables for soft constraints, the MV penalized range can be easily defined. The equations for these soft ranges can be expressed as:

Finally, a similar approach may be used to cause the optimizer to advance a process variable, such as the manipulated variable MV, to a preferred input value, the so-called "ideal rest value." This approach is illustrated in FIG. 9, where the ideal rest value is represented by line 290, and the upper and lower limits of the MV limit are represented by lines 292 and 294, respectively. Points 296 and 298 indicate situations where the predicted value is above or below the ideal pause value 290. In these cases, the penalized slack variables S (i) _above and S (i) _below are used to determine the cost or penalty in the objective function related to the deviation from the ideal rest value. The equation for the MV with the ideal rest value is expressed as:

As will be appreciated, the slack variables S imposed a penalty ^-, S ^+, S _Below, components such as S _Above, unit cost or penalty, priority variables, the unit cost and / or limit violations variables It is set or selected within the objective function as a function of other coefficients, such as degree.

  In tests using these techniques, marginal violations have been achieved by applying high-level disturbances or by setting the lower and upper limits for inputs and outputs to be violated. These tests confirm the benefits of the technique. In particular, during these tests, the optimizer worked properly and effectively, improving the violation of higher priority constraints without increasing the violation of lower priority constraints. Therefore, applying slack variables and model redefinition to address unrealizable LP solutions is a very flexible and effective approach.

  Further, the above-described principle of handling constraints can be used to create a plurality of changes in the constraint model to satisfy more specific requirements. Similarly, this approach can be used for other real-time optimization applications that do not use MPC control, for example, gasoline blend optimization. Further, the optimizer 54 can use the techniques described above to achieve range control, ideal pause values in situations where there is one or more feasible solutions. Thus, the optimizer 54 may use these techniques when using the objective function in situations where a feasible solution cannot be obtained, or when it is possible to obtain one or more feasible solutions but within the setpoint range. For example, when the objective function is used in a situation where it is desired to further optimize to the ideal pause value, it can be used for optimization.

Referring again to FIG. 2, after determining the set of solutions of the manipulated variable target, the optimizer 54 provides a set of optimal or target manipulated variables MV _T to the target conversion block 55, the block uses a steady-state gain matrix determining a manipulated variable obtained from the target steady state control and the target manipulated variables MV _T Te. This conversion is computer-directed. Because the steady state gain matrix defines the interaction between the manipulated variables and the control and auxiliary variables, thereby defined goals (steady state) from the operating variables MV _T, the target manipulated variables CV _T and the target auxiliary variables This is because it can be used to determine _AVT independently.

Once this is determined, at least a subset of the target control variables CV _T and target auxiliary variables AV _T , N are provided as inputs to the MPC controller 52, which, as described above, uses these target control variables CV _T and target an auxiliary variable AV _T, determines a new set of steady state manipulated variables (over control horizon) MV _SS. The MV _SS is to advance the current control variable CV and manipulated variables AV at the end point of the control horizon to a target value CV _T and AV _T. Naturally target, as is well known, MPC controller is for changing stepwise the manipulated variable to reach a steady state value of these variables MV _SS, this variable MV _SS is theoretically, as determined by the optimizer 54 the manipulated variables MV _T. Optimizer 54 and MPC controller 52 during each process scan, for operation as described above, the target value MV _T manipulated variable sometimes changed during the scan. As a result, MPC controller, particularly noise, unexpected Impossible disturbance, if there is change of process 50, may not actually reach even once to any particular set of these target manipulated variables MV _T is there. However, the optimizer 54 always drives the controller 52 to move the manipulated variable MV to the optimal solution.

  As is well known, the MPC controller 52 includes a control prediction process model 70, which comprises an N × (M + D) step response matrix (N is the number of control variables CV plus the number of auxiliary variables AV, M May be the number of manipulated variables, and D may be the number of disturbance variables DV. The control prediction process model 70 creates, on the output 72, a pre-calculated prediction for each of the control variable CV and the auxiliary variable AV, and the vector adder 74 compares these predictions for the current time to the actual measured control value. An error vector or correction vector is created on input 76 by subtracting from the values of variable CV and auxiliary variable AV.

Next, the control prediction process model 70 uses the N × (M + D) step response matrix to form the control horizontal line based on the disturbance variables and the manipulated variables provided to the other inputs of the control prediction process model 70. A future control parameter is predicted for each of the control variables CV and the auxiliary variables AV that exceed. The control prediction process model 70 also provides the predicted steady state values of the control and auxiliary variables, CV _SS and AV _SS, to the input processing / filter block 58.

Control target block 80, the control target vector for each of the N target control variables CV _T and the auxiliary variables AV _T provided by the target conversion block 55 by using the trajectory filter 82 which is set in advance for the block 38 To determine. In particular, the trajectory filter provides a unit vector that defines how the control and auxiliary variables are gradually driven to their respective target values. Control target block 80, using the unit vector and the target variables CV _T and AV _T, for each of the control and auxiliary variables determining the change in the target variables CV _T and AV _T in the course of the period defined by the control horizon period , Create a dynamic control target vector. Subsequently, the vector adder 84 subtracts the future control parameter vector of each of the control variable CV and the auxiliary variable AV from the dynamic control vector to determine an error vector of each of the control variable CV and the auxiliary variable AV. The future error vector of each of the control variable CV and the auxiliary variable AV is provided to an MPC algorithm that operates to select an manipulated variable MV step that minimizes, for example, a minimum square error beyond the control horizon. Naturally, the MPC algorithm or controller is an M × M process model or a M × M process model created from the relationship between the N control variables and auxiliary variables input to the MPC controller and the M manipulated variables output from the MPC controller 52. Use the control matrix.

  More specifically, the MPC algorithm that works with the optimizer has two main purposes. One is to try to minimize the CV control error with the minimum MV movement within the motion constraint, and the other is to find the optimal steady state MV value set by the optimizer and the optimal steady state MV value. The goal is to achieve the target CV value calculated directly from the value.

  Initially unconstrained MPC algorithms to achieve these goals can be extended to include the MV target in the lowest squared solution. The objective function of this MPC controller is as follows.

Here, CV (k) is a predicted vector that is p steps ahead of the controlled output, R (k) is a reference trajectory (set point) vector that is p steps ahead, and ΔMV (k) is a control movement that is c steps ahead. ^{vector, Γ y = diag [Γ y} 1, ···, Γ y p] is a penalty matrix of output ^{error, Γ u = diag [Γ u} 1, ···, Γ u c] is controlled movement Penalty matrix, p is the predicted horizon (number of steps), c is the control horizon (number of steps), Γ ^o is the sum of controller output movements beyond the control horizon, related to the target optimal change in MV defined by the optimizer Error penalty. For simplicity of presentation, the objective function is shown as a single input / single output (SISO) control.

  As will be appreciated, the first two terms are the objective functions of the unconstrained MPC controller, and the third term sets additional conditions to make the total output movement of the controller equal to the optimal goal. In other words, the first two terms set the objectives for the dynamic operation of the controller, and the third term sets the steady state optimization goals.

  Like the basic solution for an unconstrained MPC controller, the basic solution for this controller can be expressed as:

Here, .DELTA.MV (k) is the change in MPC controller output at time k, K _AmpC is optimized MPC controller gain is S ^u process dynamic matrix. S ^u can be constructed from the step response of dimension p × c for the SISO model and p * n × c * m for the multi-input / multi-output MIMO model, where m is the operation input, n is a control output.

For the optimized MPC, the dynamic matrix expands to a size: (p + 1) × m for SISO models and (p + m) * n × c * m for MIMO models, resulting in MV errors. Corresponding. E _{p + 1} (k) is the CV error vector above the predicted horizon, and the error in the controller output sum moves over the control horizon in relation to the target optimal change in MV. The matrix Γ is a combination of the matrices Γ ^y and Γ ^o , and is a square matrix of size (p + 1) for a SISO controller and [n (p + m)] for a multivariable controller. The superscript T indicates a transposition matrix.

The optimizer 54 is optimized based on all of the control and auxiliary variables CV and AV, the manipulated variables MV _T to define their own optimal operating point for determining a set of target values, MPC controller 52 in the control matrix It is determined that the operation is performed using only a subset of the control variable CV and the auxiliary variable AV, and that there is no problem even if the output of the manipulated variable MV is actually generated therefrom. The reason is that if the controller 52 advances a subset of the selected control variables CV and auxiliary variables AV to their associated target values, the other parts of the complete set of control and auxiliary variables will also have their target values Because it is located in. As a result, a square (M × M) MPC controller with an M × M control matrix is used with an optimizer using a rectangular (N × M) process model to perform process optimization. This allows standard MPC control techniques to be used with standard optimization techniques without inverting the non-square matrix to an approximation or without taking the risks associated with such transformation techniques in the controller. It becomes.

  In one embodiment, if the MPC controller is squared, i.e., the number of manipulated variables AV is equal to the number of control variables CV, then the target value of manipulated variable MV is effective by changing the CV value as follows: Can be realized.

  Here, ΔMVT is a change in the optimum target value of the MV, and ΔCV is a change in the CV to reach the optimum MV. Of course, the change in CV is performed by managing the CV set point.

In operation, the optimizer 54 sets and updates the steady state target value of the MPC unconstrained controller for each scan. Therefore, MPC controller 52 executes an unconstrained algorithm. The target values CV _T and AV _T are set to account for the constraints, so that the controller works within the constraint limits as long as a feasible solution exists. Therefore, the optimization is integrated with the MPC controller.

  FIGS. 3 and 4 are flowcharts 90 illustrating the steps used to perform integrated model predictive control and optimization. Flowchart 90 is generally divided into two sections, 90a (FIG. 3) and 90b (FIG. 4), with functions occurring before the process operation (90a) and during the process operation, eg, for each scan of the process operation. (90b). Prior to process operation, an operator or engineer performs multiple steps to create an advanced control block 38 that includes an integrated control MPC controller and optimizer. In particular, at block 92, an advanced control template may be selected for use as advanced control block 38. The template may be stored in a library in a configuration application on the user interface 13 and replicated therefrom, and without having a particular MPC, process model and steady state gain / control matrix and a particular objective function. It may include the overall arithmetic and logic functions of MPC controller routine 52 and optimizer 54. The advanced control template may be provided in a module having other blocks, such as, for example, input and output blocks configured to communicate with other devices in the process 50, and PID, There are other types of blocks, such as neural networks and control blocks, including fuzzy logic control blocks. It will be appreciated that, in one embodiment, each block in the module is a purpose in a purpose-based programming paradigm having inputs and outputs interconnected to communicate between the blocks. In operation, the processor running the module executes each block sequentially at different times using the input to the block to produce the output of the block. These are then provided to the inputs of other blocks, as defined by the particular communication link between the blocks.

  The operator defines the specific manipulated, control, constraint, and disturbance variables used in block 38 at block 94. If desired, in a configuration program such as program 40 of FIG. 1, the user views the control template, selects the named inputs and outputs, and browses using any standard browser in the configuration environment. The actual inputs and outputs in the control system may be searched and these actual control variables may be selected as input and output control variables for the control template.

Once the user has selected the inputs and outputs to the advanced control function block, the set points associated with the control variables, the ranges or limits associated with the control variables, auxiliary variables and manipulated variables, and each of the control variables, auxiliary variables and manipulated variables May be defined. Of course, some of this information, such as constraint limits or ranges, may already be associated with these variables. Because these variables are selected or searched for in the process control system configuration environment. The operator configures one or more objective functions to be used within the optimizer by specifying unit costs and / or benefits for each of the manipulated, control, and auxiliary variables, if desired, at block 96 of FIG. May be. Of course, at this point the operator may choose to use the default objective function as described above. Further, the user control variable for each of the auxiliary variables and manipulated variables, each slack variable or penalty ^{variable, S +, S -, S} above, may identify the cost or penalty associated with S _Below the like. The user may, if desired, cause the optimizer to handle or address unrealizable solutions defined by the original constraint limits, such as using slack variables, redefining the constraint limits, or some combination of the two. A specific method may be specified.

  Once the inputs (control variables, auxiliary variables and disturbance variables) and outputs (manipulated variables) are named and linked to the advanced control template and their weights, limits and set points are associated with them, the advanced control in block 98 of FIG. The template is downloaded to the controller selected in the process as a functional block used for control. The basic nature of the control block and the manner in which the control block is constructed is described in US Pat. No. 6,445,963 entitled "Integrated Advanced Control Blocks in Process Control System". ing. The patent is assigned to the assignee of the present invention and is hereby expressly incorporated by reference. The patent describes the nature of creating an MPC controller in a process control system and does not describe how the optimizer is connected to that controller, but does not describe the basic steps for connecting and configuring the controller. It is understood that can be used in the control block 38 described herein, together with a template that includes any of the logic elements described herein with respect to the control block 38 herein, as well as those described in the cited patents. Will.

  In any case, after the advanced control template has been downloaded to the controller, the operator may execute a test phase of the control template at block 100 to select a step response matrix and a process model to be used in the MPC controller algorithm. Good. As described in the aforementioned patent, during the test phase, the control logic in the advanced control block 38 provides the process with a series of pseudo-random waveforms as manipulated variables, and the control and auxiliary variables (essentially by the MPC controller). Are treated as control variables). If desired, the manipulated and disturbance variables and the control and auxiliary variables may be collected by the historian 12 of FIG. 1, and the operator may obtain this data from the historian 12 and in any manner operate on this data. A configuration program 40 (FIG. 1) for performing trending and acquiring or determining a matrix of step responses may be set. Each step response specifies the response in time of one of the control or auxiliary variables to a unit change in one (and only) of the manipulated and control variables. The unit change is typically a step change, but may be another type of change, such as an impulse change or a ramped change. On the other hand, if desired, the control block 38 generates step response matrices in response to the data collected in applying the pseudo-random waveforms to the process 50, and creates and installs these waveforms in the advanced control block 38. May be provided to the operator interface 13 used by the operator or user to perform the operation.

  Once the step response matrix has been created, if the number of control and auxiliary variables exceeds the number of manipulated variables, use the step response matrix to convert a subset of the control and auxiliary variables used in the MPC Select as an M × M process model or control matrix to be inverted and used in 52. This selection process may be performed manually by an operator or automatically by a routine within a user interface 13 that has access to a step response matrix, for example. In general, a single control variable and auxiliary variable will be identified as being most closely related to the single auxiliary variable. Thus, a single and singular (ie different) control or auxiliary variable (input to the process controller) is associated with each different manipulated variable (output of the process controller), which causes the MPC algorithm to have an M × M step response. Can be based on a process model created from the set of

  In one embodiment, which takes a heuristic approach to pairing, an automated routine or operator selects M sets of control and auxiliary variables, where M equals the number of manipulated variables. This is to select a single control or auxiliary variable with a combination of maximum gain and fastest response time for a unit change in one particular manipulated variable and to pair these two variables. Of course, in some cases, a particular control or auxiliary variable may have a large gain and a fast response time for multiple manipulated variables. Here, the control variable or the auxiliary variable may be paired with any related operation variable, and may be actually paired with an operation variable that does not generate the maximum gain and the fastest response time. In aggregate, manipulated variables that result in lower gain or slower response times may not have an acceptable effect on other control or auxiliary variables. Therefore, a pair of control variables and auxiliary variables, one of which is the manipulated variable and the other, is a pair of the control and auxiliary variables representing the control variable that is most responsive to the manipulated variable and the manipulated variable. To be selected. Further, it is ok that not all control variables are selected as one of a subset of the M control and auxiliary variables, so the MPC controller does not receive all control variables as inputs. The set of target values for the control and auxiliary variables is used to represent the operating point of the process where the unselected control variables (and the unselected auxiliary variables) are at their set points or within a defined operating range. Because it is chosen by the optimizer.

  Of course, one has dozens and even hundreds of control and auxiliary variables, and the other has dozens or hundreds of manipulated variables, so at least from a visual point of view, It may be difficult to select a set of control and auxiliary variables that respond optimally. To solve this problem, the advanced control block generation routine 40 in the operator interface 13 includes or presents a set of screen displays to the user or operator, which the operator can use during operation by the MPC controller 52. The control and auxiliary variables to be used as a subset of the control and auxiliary variables used may be assisted or enabled to make a suitable choice.

  Accordingly, the operator may be presented with a screen at block 120 of FIG. 3 to allow the operator to view the response of each control and auxiliary variable to a particular or selected one operating variable. The operator may scroll one at a time through the manipulated variables, view the step response of each control variable and auxiliary variable for each of the various manipulated variables, and optimize the One control or auxiliary variable to respond to may be selected. Operators typically seek to select a control or manipulated variable that has the best combination of highest steady state gain and fastest response time for the manipulated variable.

  As will be appreciated, such a display screen allows the operator to visually select a subset of the M control and auxiliary variables used as inputs to the MPC control algorithm, and these variables are This is especially helpful if you have large quantities. Of course, the set of control and constraint variables determined in block 74 may be automatically or electronically selected based on some preset criteria or selection routine. The selection routine may select an input variable to use based on a combination of gain response and time delay determined from a step response for the control and auxiliary variables.

  In another embodiment, the automatic selection process may determine the control matrix by first selecting an input / output matrix based on the condition number of the matrix. For example, the condition number may be minimized to some desired degree and a control configuration may be created from the control matrix.

In this example, for the process gain matrix A, the condition number of the matrix A ^T A may be determined by performing a matrix controllability test. In general, a small condition number means a high controllability, and a large condition number means a low controllability and a large number of control steps or movements during the dynamic control operation. Since there is no exact criterion for the degree of controllability tolerance, the condition number can also be used as a relative comparison of various potential condition matrices and as a test for ill-conditioned matrices. As is well known, the condition number of an ill-conditioned matrix approaches infinity. Mathematically, bad conditions arise in the case of collinear process variables, i.e., by collinear rows or columns in the control matrix. Thus, the main factor affecting condition number and controllability is the interrelationship between rows and columns of the matrix. Careful selection of input and output variables in the control matrix can reduce conditional issues. Practically, if the condition number of the control matrix is 500 or more, you should be concerned. In the case of such a matrix, the movement of the manipulated variable of the controller is significantly excessive.

  As mentioned above, while the control matrix solves the problem of dynamic control, the LP optimizer solves the steady-state optimization problem, and even if the MPC controller blocks have unequal numbers of MVs (including AV) and CVs, the control matrix is Must have a square input / output matrix. To start selecting the inputs and outputs of the control matrix used to generate the controller, all available MVs are usually included or selected as control outputs. Once the output (MV) has been selected, the process output variables (ie, CV and AV) that form part of the dynamic control matrix must be selected in such a way as to create a square control matrix that is not ill-conditioned.

  Here, one method for automatically or manually selecting CV and AV as inputs in the control matrix is described, but it is understood that other methods may be used.

  Step 1—If possible, select CVs until the number of CVs equals the number of MVs (ie, the number of controller outputs). If there are more CVs than MVs, the CVs may be selected in any order based on desired criteria, such as priority, gain or phase response, user input, etc. If the total number of possible CVs is equal to the number of MVs, proceed to step 4 and test whether the resulting square control matrix condition number is acceptable. If the number of CVs is less than the number of MVs, the AV is selected as described in step 2. If there is no CV to be defined, select the AV with the largest gain for the MV and go to step 2.

  Step 2—Calculate one by one the condition numbers of all possible AVs added to the already selected control matrix defined by the previously selected CV and AV. As will be appreciated, the matrix defined by the selected CV includes a row for each of the selected CV and AV, defining the steady state gain of that CV or AV for each previously selected MV. Is done.

  An AV determined in Step 3-Step 2 and having the minimum condition number of the resulting matrix is selected, and the matrix is defined as the selected matrix added with the selected AV. At this point, if the number of MVs is equal to the number of selected CVs plus the selected AVs (ie, if the matrix is now squared), go to step 4. Otherwise, return to step 2.

Step calculated 4- condition number of created square control matrix A _c. If desired, it may be used condition number calculation of the matrix A _c, instead of the matrix A _c ^T A _c. Because the condition numbers of these different matrices are related as other square roots.

  If the condition number calculated in step 5 to step 4 is accepted, associate the MV with all CVs and the selected AV. This is done by selecting the CV or AV that has the largest gain for a particular MV until the paired process is completed. At this point, the selection process is complete. However, when the condition number exceeds the minimum allowable condition number, the last AV / CV added to the control matrix is removed, and the wraparound procedure of step 6 is performed.

Step 6-Perform a wrap-around procedure, one at a time, on each selected MV and calculate the condition number of the resulting matrix for each wrap-around procedure. In essence, the wrap-around procedure is performed by interleaving one-unit responses for each different MV in place of the removed AV (or CV). The one-unit response is one unit at some positions in the rows of the matrix and zero at other positions. In short, in this case, the particular MVs are used as inputs and outputs, respectively, instead of the AVs forming a well-conditioned square control matrix. As an example, for a 4 × 4 matrix, 1000,0100,0010, and combinations 0001 are arranged in rows of the removed AV line gain matrix A _c.

  Step 7-After performing the wrap-around procedure for each MV, select the combination that minimizes the condition number. If there is no improvement, keep the original matrix. At this point, select the CV or AV that has the largest gain in relation to the particular MV except the MV used to control the MV itself (ie, the wrap-around MV), and select all the selected CVs and AVs. Associate with MV.

  Of course, the control matrix defined by this procedure and the resulting condition number may be provided to the user, who may accept or reject the use of the defined control matrix in the creation of the controller. .

  In the automatic procedure described above, only one MV was selected to control (ie, wrap around) the MV itself for the purpose of improving controllability. In a manual procedure, the number of wraparound MVs may be arbitrary. The MV selected to control the MV itself is clear from the absence of a corresponding output variable selection in the controller configuration. If the number of MVs is larger than the total number of CVs plus AVs, more MVs can be used as wraparound for control. Thus, a square control matrix is ultimately provided to the controller having each MV as an output. The process of doing wrap around and using this means that the number of CVs and AVs selected for the control matrix may be less than the number of MVs controlled by the controller, the difference being It will be appreciated that this is the number of MV wraparounds input to This wraparound procedure can be used in a process in which the number of CVs and AVs is smaller than the number of MVs.

  Of course, the condition number is calculated as described above using the steady state gain, whereby the control matrix essentially defines the controllability in the steady state. Process dynamics (dead time, lag, etc.) and model uncertainties also affect dynamic controllability. This effect can be taken into account by changing the priority of the process variables (eg, control and auxiliary variables) and may be ordered to be included in the control matrix based on the effect on dynamic control.

  Other heuristic procedures can be used to improve both steady state and dynamic controllability. Such a procedure typically has multiple (and possibly conflicting) heuristics that are applied in several phases of creating the control matrix, thereby providing some improvement in the control matrix. Select an appropriate set of control inputs. In one such heuristic procedure, CVs and MVs are grouped by AV based on the highest gain relationship. Then, for each MV grouping, select one process output with the fastest dynamic and significant gain. This selection process may prioritize CV over AV (if everything else is equal) given the reliability interval. The process model generation routine then uses the parameters selected from each group during generation of the MPC control. Since only a single parameter is selected for each MV, the response matrix is square and can be inverted.

  In any case, once a subset of the M (or less) control and auxiliary variables to input to the MPC controller has been selected, block 124 of FIG. 3 uses the MPC control algorithm of FIG. Generate a process model or controller to use. As is well known, this controller generation step is a computer intensive procedure. Block 126 then downloads the MPC process model (which inherently includes the control matrix) or controller and, if necessary, the step response and steady state response gain matrices to control block 38, which data is used for operation. Is incorporated in the control block 38. At this point, the control block 38 is ready for online operation within the process 50.

  If desired, the process step responses may be reconstructed or provided in other ways than those that generated these step responses. For example, the step response may be duplicated from a different module stored in the system to specify the step response of a particular control or auxiliary variable to a manipulated or disturbance variable. In addition, the user may define or specify parameters for the step response, such as steady state gain, response time, first order time constraints and squared error. Also, if desired, the user may view and change the properties of the step response by specifying different parameters, such as different gains or time constraints. If the user specifies a different gain or other parameter, the step response model can be mathematically recreated to include the new parameter or set of parameters. This action is useful if the user knows the parameters of the step response and the generated step response needs to be modified to meet or fit these parameters.

Referring now to FIG. 4, during each operating cycle or scan of advanced control block 38, the basic steps created using flowchart 90a of FIG. 3 are performed, while process 50 is operating online. It has been shown. At block 150, the MPC controller 52 (FIG. 2) receives and processes the measured control variable CV and auxiliary variable AV values. In particular, the control prediction process model processes CV, AV and DV measurements or inputs to create future control parameter vectors, while creating the predicted steady state control variable CV _SS and auxiliary variable AV _SS .

Then, at block 152, the input processing / filter block 58 (FIG. 2) processes or filters the predicted control variable CV _SS , auxiliary variable AV _SS and manipulated variable MV _SS created by the MPC controller 52; This filtered value is provided to optimizer 54. The optimizer 54 executes standard LP techniques at block 154 to identify or control variables that maximize or minimize the selected or default objective function but do not violate any limits of auxiliary and manipulated variables. maintained within or within a certain range for these variables set points, determining a set of M manipulated variable target MV _T. Typically, the optimizer 54 calculates the target manipulated variable resolution MV _T by advancing each of the control and auxiliary variables to their limits. As described above, a solution exists when each of the control variables is located at its own set point (sometimes initially treated as the upper limit of the control variable) and each of the auxiliary variables is within its own constraint. Often. In such a case, the optimizer 54 may be output only manipulated variable target MV _T determined to produce the best results of the objective function.

  However, in some cases, some or all of the auxiliary or manipulated variables are severely constrained, and an operating point is searched where all control variables are at their set points and all auxiliary variables fall within their respective constraint limits. Sometimes things are impossible. Because there is no such solution. In such a case, the optimizer 54 generates a new objective function and / or selects a new set of limits using slack variables and / or the limit redefinition techniques described above, as indicated by block 155. . Block 154 then returns the newly created objective function and / or the optimizer with bounds that may or may not include penalty variables and determine the optimal solution. If there is no feasible solution, or again an unacceptable solution, block 155 operates again to define a new set of limits or a new objective function to use in further passes of the optimizer. For example, in a first pass having an unrealizable solution, block 155 may choose to use slack variables and provide a new objective function for use in a second pass of the optimizer. After the second pass, if an unrealizable or unacceptable solution is obtained, block 155 redefines the constraint limits with or without penalty variables, and these new constraint limits and, if possible, A new objective function may be provided to block 154 for use in the third pass. Of course, block 155 may use the combination of slack variables and limit redefinition to provide the optimizer to use the new objective function and limits in any pass. Block 155 also naturally employs any other desired strategy for selecting a new objective function or redefining constraint limits in situations where a feasible solution cannot be obtained using the original objective function. You can also. If desired, the initial objective function run at block 154 includes a slack variable penalty that causes the process variable to advance to a limit, set point, or ideal rest value during the optimizer's first pass (and subsequent passes). May be. Further, the original objective function used in block 154 may include slack variable constraints that are initially handled, which may be used in the first pass of the optimizer. Then, in subsequent runs, if necessary, the redefinition of the limits may be used alone or in conjunction with a penalized slack variable. Similarly, in subsequent passes of the optimizer, using the techniques described above, the process variables may be reduced to limits, set points, ideal rest values, etc. using one or both of slack variables and limit redefinition. You may proceed.

In any case, after obtaining a solution that block 154 can be realized, or accepted, block 156, using the target conversion block 55 (FIG. 2), the target value of the manipulated variables MV _T using steady state step response gain matrix It determines a target value of the control variables CV _T and the auxiliary variables AV _T from providing a subset of N of these selected values (N is M and equal or less), the MPC controller 52 as the target input. The MPC controller 52 operates at block 158 as described above as an unconstrained MPC controller using a control matrix or logic derived therefrom to determine the future CV and AV vectors of these target values, and Is performed to create a future error vector. The MPC algorithm operates in a known manner and determines steady state manipulated variables MV _SS based on a process model generated from the M × M step response, and inputs these MV _SS values to an input processing / filter block 58 (FIG. 2). To provide. The MPC algorithm also determines the MV steps that are output to the process 50 at block 160 and outputs the first order of these steps to the process 50 in any suitable manner.

  In operation, for example, one or more monitoring applications running on one of the interfaces 13 may take information directly or through the historian 12 from an advanced control block or other functional blocks communicatively connected thereto. One or more viewing or diagnostic screens may be provided to the user or operator to view the operating status of the advanced control block. The functional block technology features a cascade input (CAS_IN) and a remote cascade input (RCAS_IN) and corresponding buck calculation outputs (BKCAL_OUT and RCAS_OUT) for both control and output function blocks. Using these connectors, it is also possible to place a supervisory optimized MPC control strategy on top of an existing control strategy and view it using one or more viewing screens or displays. . Similarly, the goals of the optimized MPC controller can be modified from the strategy if desired.

Although the advanced function blocks described here have the optimizer located in the same function block and therefore run on the same device as the MPC controller, it is also possible to run the optimizer on another device. In particular, the optimizer may be located on a different device, such as in one of the user's workstations 13, and communicates with the MPC controller as described in conjunction with FIG. 2 during each execution or controller scan. , The target manipulated variable (MV _T ) or a subset of the control variable (CV) and auxiliary variable (AV) determined therefrom may be calculated and provided to the MPC controller. Of course, a special interface, such as a known OPC interface, may be used to provide a communication interface between the controller or a functional block having an MPC controller therein and a workstation or other computer implementing or executing the optimizer. . As with the embodiment described with respect to FIG. 2, the optimizer and MPC controller must communicate with each other during each scan cycle to provide integrated optimal MPC control.

  Of course, any other type of optimizer desired, such as a known or standard real-time optimizer already present in the process control environment, can also use the unachievable techniques described herein. This feature can be used to advantage even when the optimization problem is nonlinear and its solution requires nonlinear programming techniques. Further, while the optimizer 54 has been described as being used to create target variables for MPC routines, the optimizer 54 may use the infeasibility techniques described herein, such as PID controllers, fuzzy logic controllers, etc. Target values or other variables used by other types of controllers can also be created.

  Although the advanced control blocks and other blocks and routines described herein have been described herein when used in conjunction with a fieldbus and a standard 4-20 milliamp device, it will be appreciated that these are other processes. It may be implemented using a control communication protocol or programming environment, and may be used with other types of devices, functional blocks or controllers. Although the advanced control blocks and associated generation and test routines described herein are preferably implemented in software, they may be implemented in hardware, firmware, etc., and may be implemented in other processing units associated with the process control system. May be done. Thus, the routines 40 described herein may be implemented in a standard general purpose CPU or special purpose hardware or firmware, such as an ASIC, if desired. When implemented in software, the software may be stored in RAM or ROM, such as a computer or processor, or in a computer-readable memory, such as a magnetic disk, laser disk, optical disk, or other storage medium. Similarly, the software may be, for example, a computer readable disk or other portable computer storage mechanism or modulation through a communication channel, such as a telephone line, the Internet, which provides such software via a portable storage medium. (Considered to be the same as or interchangeable with) the user or the process control system via a known or desired provision method.

  Thus, while the present invention has been described with reference to particular examples, this is for illustrative purposes only and is not limiting. It will be apparent to those skilled in the art that modifications, additions, or omissions can be made to the embodiments disclosed herein without departing from the spirit and scope of the invention.

FIG. 1 is a block diagram of a process control system including a control module having an advanced controller function block integrating an optimizer and an MPC controller. FIG. 2 is a block diagram of the advanced controller functional block of FIG. 1 with an integrated optimizer and MPC controller. 3 is a flowchart illustrating a method of creating and mounting the integrated optimizer and MPC controller functional blocks of FIG. 2. 3 is a flowchart illustrating the operation of the integrated optimizer and MPC controller of FIG. 2 during an online process operation. FIG. 3 is a graph illustrating a method of using a slack variable in an objective function of the optimizer of FIG. 2 to relax constraints or limits on manipulated variables. FIG. 3 is a bluff diagram illustrating a method of relaxing a range associated with a set point using a slack variable in an objective function of the optimizer of FIG. 2. FIG. 3 is a bluff diagram illustrating a method of relaxing two sets of ranges associated with set points using low and high slack variables in the objective function of the optimizer of FIG. 2. FIG. 3 is a graph illustrating a method of redefining a constraint model or a constraint limit of a manipulated variable and using a penalty variable associated with a new constraint model in an objective function of the optimizer of FIG. 2. FIG. 5 is a graph illustrating the use of both slack variables and constraint model redefinition for optimization when one or more manipulated variables are out of bounds. FIG. 7 is a graph illustrating the use of slack variables for optimization when there is an ideal rest value of the manipulated variable.

Explanation of reference numerals

10 Process control system
11 Process controller
12 Data historian
13 Workstation, computer, user interface
14 Display screen
26, 28 input / output (I / O) card
29 Communication Network
15-22 field device
32, 34 routines
36 Control loop
38 Advanced control block
40 Advanced control block generation routine
42 Control Block Generation Routine
44 Process Modeling Routine
46 Control Logic Parameter Creation Routine
48 Optimizer Routine
50 processes
52 MPC controller
54 Optimizer
55 Target conversion block
56 step response model or control matrix
58 Input processing / filter block
62 selection block
64 objective function
66, 76 inputs
70 Control prediction process model
72 outputs
74, 84 vector adder
80 Control target block
82 Trajectory Filter
90 Flowchart
101 Trend plot area
102 plots
104 mode
106 Set time
112, 114 lines
116 Model creation button
200 display screen
Area 204, 208
212, 216 columns
220 gain
224 Dead Time
228 column of available variables
232a add button
232b remove button
236 back button

Claims (53)

A process control method,
Running an optimizer that produces a solution that defines a set of target values using an objective function;
Determining whether the solution is feasible for a set of process variable constraints,
If the solution is not feasible,
(1) redefining a process variable constraint of at least one process variable to define upper and lower limits of a new process variable constraint for the one process variable;
(2) A new objective function is created by adding a penalty variable to the objective function of the one process variable, wherein the penalty variable is a new process variable constraint of the one process variable. Based on an amount that differs from one of the limits,
(3) rerunning the optimizer with the new objective function and creating a new solution defining a set of new target values at the new process variable constraint limit of the one process variable; ,
Providing the controller with the target value or the new target value;
Driving the controller using the target value or the new target value to create a set of control signals for controlling the process.   The method of claim 1, wherein a set of slack variables is provided to the objective function, and a penalty for at least one of the process variables is based on an amount by which the at least one process variable violates an associated constraint. Further comprising the step of defining.   3. The method of claim 2, wherein a unit penalty associated with the set of slack variables in the objective function defining one or more economic costs is much greater than a unit cost variable. A method comprising steps.   The method of claim 1, wherein a set of slack variables is provided to the objective function, and a penalty for at least one of the process variables is based on an amount by which the at least one process variable differs from an ideal pause value. Further comprising the step of defining.   5. The method of claim 4, wherein setting a unit penalty associated with the set of slack variables that is much greater than a unit cost variable in the objective function that defines one or more economic costs. A method comprising steps.   The method of claim 1, wherein a set of slack variables is provided to the objective function, and a penalty for at least one of the process variables is based on an amount by which the at least one process variable differs from a set point. The method further comprising the step of defining.   7. The method of claim 6, wherein a unit penalty associated with the set of slack variables is set much greater than a unit cost variable in the objective function that defines one or more economic costs. A method that includes a step.   2. The method of claim 1, providing a unit penalty for the penalty variable that is much greater than one or more unit cost variables in the objective function that define one or more economic costs. A method comprising steps.   The method of claim 1, comprising providing a unit penalty for the penalty variable that is greater than any of the unit cost variables in the objective function that defines an economic cost.   The method of claim 1, wherein running the controller comprises running a multiple input / multiple output controller.   The method of claim 10, wherein running the multi-input / multi-output controller includes running a model predictive control type controller. A system adapted to be executed on a processor used for process control,
A computer readable medium;
An optimizer routine stored on the computer readable medium and adapted to be executed on the processor to generate a solution defining a set of target values using an objective function;
A feasibility enabled routine stored on the computer readable medium and adapted to be executed on the processor to determine whether the solution is feasible for a set of process variable constraints. If the solution is not feasible,
Redefining a process variable constraint for at least one process variable, defining upper and lower limits of a new process variable constraint for the one process variable;
A new objective function is created by adding a penalty variable of the one process variable to the objective function, wherein the penalty variable is such that the one process variable is the new process variable constraint limit of the one process variable. Penalizing the objective function based on the amount different from one;
Re-running the optimizer routine with the new objective function and creating a new solution defining a set of new target values with the new process variable constraint limits of the one process variable; The corresponding routine,
Stored on the computer readable medium and adapted to be executed on the processor to create a set of control signals for controlling the process using the target value or the new target value; A controller routine.   13. The system of claim 12, wherein the objective function defines a penalty for at least one of the process variables based on an amount by which the at least one process variable violates an associated constraint. The system containing the function.   14. The system of claim 13, wherein the objective function is associated with the set of slack variables that is much larger than a unit cost variable in the objective function that defines one or more economic costs. System, including unit penalties.   13. The system of claim 12, wherein the objective function defines a penalty for at least one of the process variables based on an amount by which the at least one process variable differs from an ideal pause value. The system, including.   16. The system of claim 15, wherein the objective function is associated with the set of slack variables that is much larger than a unit cost variable in the objective function that defines one or more economic costs. System, including unit penalties.   13. The system of claim 12, wherein the objective function defines a set of slack variables that define a penalty for at least one of the process variables based on an amount by which the at least one process variable differs from a set point. Including, system.   18. The system of claim 17, wherein the objective function is associated with the set of slack variables that are much larger than a unit cost variable in the objective function that defines one or more economic costs. System, including unit penalties.   13. The system of claim 12, wherein the objective function is a unit of the penalty variable that is much larger than one or more unit cost variables in the objective function that define one or more economic costs. System, including penalties.   13. The system of claim 12, wherein the objective function includes a unit penalty for the penalty variable that is greater than any unit cost variable in the objective function that defines an economic cost.   13. The system of claim 12, wherein the controller routine includes a multiple input / multiple output controller routine.   22. The system of claim 21, wherein the multi-input / multi-output controller routine includes a model predictive control type controller routine. A process control method,
Defining at least one constraint associated with each of the set of process variables;
Defining an objective function including one or more economic unit costs associated with the process variable and a penalty variable associated with the one process variable that violates the constraint of one of the process variables. Wherein the penalty variable has a unit penalty greater than each economic unit cost.
Creating a set of process control signals for use in the process control using the objective function.   24. The method of claim 23, wherein defining the at least one constraint comprises defining a set of range limits associated with the one process variable.   24. The method of claim 23, wherein defining the at least one constraint comprises defining a set point associated with the one process variable.   24. The method of claim 23, wherein defining the at least one constraint comprises defining an ideal pause value associated with the one process variable.   24. The method of claim 23, wherein defining the at least one constraint comprises: a first set of range limits associated with the one process variable; and a second set of range limits associated with the one process variable. Defining a set of range limits, wherein defining the objective function comprises: a first penalty variable associated with violation of the first set of range limits; and a violation of the second set of range limits. Defining a second penalty variable associated with the first penalty variable, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable. .   24. The method of claim 23, wherein defining the at least one constraint comprises: a first value associated with the one process variable; and a set of range limits associated with the one process variable. Defining the objective function comprises: a first penalty variable associated with the one process variable different from the first value; and the one penalty variable violating the set of range limits. Defining a process variable and a second penalty variable associated therewith, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable. ,Method.   29. The method according to claim 28, wherein the first value is a set point.   29. The method according to claim 28, wherein the first value is an ideal rest value.   24. The method of claim 23, wherein the objective function is used to optimize a set of control signals over a horizon during which one of the process variables is expected to violate the constraints of the process variable. A method comprising the step of creating a.   24. The method of claim 23, detecting when the one process variable is expected to violate the constraint associated with the one process variable, and redefining the constraint on the one process variable. Redefining the objective function, and using the redefined objective function to generate the set of process control signals if the one process variable is expected to violate the constraints associated with the one process variable. A method comprising the step of determining.   33. The method of claim 32, wherein redefining the objective function comprises adding a further penalty variable to the objective function of the one process variable, wherein the further penalty variable is A method for penalizing the objective function based on an amount by which one process variable differs from the redefined constraint on the one process variable.   34. The method according to claim 33, wherein the step of adding the further penalty variable is greater than the economic unit cost in the objective function defining one or more economic costs. A method comprising setting further unit penalties associated with a penalty variable.   34. The method of claim 33, wherein the step of adding the further penalty variable is further associated with the further penalty variable being greater than the unit penalty associated with the penalty variable in the objective function. A method comprising setting a unit penalty.   34. The method of claim 33, wherein the step of adding the additional penalty variable is associated with the additional penalty variable that is much greater than the unit penalty associated with the penalty variable in the objective function. A method comprising setting an additional unit penalty. A system used for a processor that controls a process,
A computer readable medium;
A first routine stored on the computer readable medium and adapted to be executed on the processor for storing at least one constraint associated with each of a set of process variables;
One or more economical unit costs associated with the process variable and stored on the computer-readable medium, and a penalty variable associated with the at least one process variable that violates a constraint of the one process variable. A second routine, adapted to be executed on the processor, for storing an objective function to be defined;
A third routine stored on the computer readable medium and adapted to be executed on the processor to generate a set of process control signals for using the objective function to control the process; Including the system.   38. The system of claim 37, wherein the at least one constraint on the one process variable includes a set of range limits associated with the one process variable.   38. The system of claim 37, wherein the at least one constraint on the one process variable includes a set point associated with the one process variable.   38. The system of claim 37, wherein the at least one constraint on the one process variable includes an ideal pause value associated with the one process variable.   38. The system of claim 37, wherein the at least one constraint on the one process variable comprises a first set of range limits associated with the one process variable and a second set of range limits associated with the one process variable. And two sets of range limits, the objective function comprising: a first penalty variable associated with the first set of range limits; a second penalty variable associated with the second set of range limits; Wherein the first unit penalty associated with the first penalty variable is less than the second unit penalty associated with the second penalty variable.   38. The system of claim 37, wherein the at least one constraint on the one process variable is a first value associated with the one process variable and a set of ranges associated with the one process variable. And the objective function is associated with a first penalty variable associated with the one process variable different from the first value and with the one process variable violating the set of range limits. A second unit penalty associated with said first penalty variable is less than a second unit penalty associated with said second penalty variable.   43. The system of claim 42, wherein the first value is a set point.   43. The system of claim 42, wherein the first value is an ideal rest value.   38. The system of claim 37, wherein the third routine uses the objective function over a horizon during which the one process variable is predicted to violate the constraint of the one process variable. A system adapted to create an optimal set of process control signals.   38. The system of claim 37, comprising a fourth routine stored on the computer readable medium and adapted to be performed on a processor, wherein one of the process variables is associated with the one of the process variables. Detecting when the constraint is expected to be violated, redefining the constraint of the one process variable, redefining the objective function, and redefining the constraint that the one process variable is associated with the one process variable. And causing the third routine to determine the set of process control signals using the redefined objective function if it is expected to violate the set of process control signals.   47. The system of claim 46, wherein the fourth routine is adapted to redefine the objective function by adding a further penalty variable to the objective function for the one process variable, A system wherein the penalty variable imposes a penalty on the objective function based on an amount by which the one process variable differs from the redefined constraint on the one process variable.   48. The system of claim 47, wherein the fourth routine is adapted to set a further unit penalty associated with the further penalty variable in the objective function that is greater than the economic unit cost. The system.   48. The system of claim 47, wherein the fourth routine sets a further unit penalty associated with the further penalty variable in the objective function that is greater than the unit penalty associated with the penalty variable. A system that is adapted to:   48. The system of claim 47, wherein the fourth routine further comprises: a further unit penalty associated with the further penalty variable in the objective function that is much greater than the unit penalty associated with the penalty variable. A system adapted to set the   38. The system of claim 37, wherein the third routine is an optimizer routine adapted to create a set of target values for a controller.   The system of claim 37, wherein the third routine is a controller routine.   38. The system of claim 37, wherein the third routine is a model predictive control type controller routine.

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