JPS63251804A - Setting method for feedback gain of tension controller - Google Patents

Abstract

PURPOSE:To easily and quickly set the feedback gain of a tension controller by changing the ratio between a parameter showing the weight to the manipulated variable and a parameter showing the weight to the tension among those matrices forming a weight matrix. CONSTITUTION:A standard for evaluation is set only at the tension among state variables and a weight matrix Q is defined by an equation II for calculation of gains F1-F4 in response to a matrix element r11 of a weight matrix R when a secondary linear evaluation function is decided for a designing standard of a system consisting of an optimum regulator together with a weight matrix Q used for weighting to a state variable matrix (x) of an equation I. Then r11/q44 is changed so that the gains F1 and F4 are changed. Thus an optimum coefficient matrix (F1-F4) is set. In such a way, the feedback gain of a tension controller is set in a simple and quick way.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a winding machine that continuously winds up an object to be wound, such as a sheet-like material, at a desired target winding tension. The present invention relates to a feedback gain setting method for a tension control device.

(Prior art) In a conventional tension control device for a winder that multiplies several types of state quantities by a constant gain and feeds back the results, the optimum regulator theory in modern control theory is used to determine the gain. A method is known to set the optimal feedback gain by applying .

The figure is a block diagram showing the entire tension control system to which this method is applied.

In the same figure, 1 is a subtraction point, and this subtraction point 1 compares the target tension value T'' and the detected value T and outputs the deviation to the integral element 2.The integral element 2 whose transfer function is 1/s integrates the deviation between the target value T'' and the detected value T and outputs BT.

Here, S represents a Laplace operator. A gain element 3 is connected to the integral element 2, and the gain element 3 multiplies the output er by a gain F4 and outputs F1a.

A conversion element 12 configuring a current (torque) control system for the controlled object 11 is connected to the gain element 3 via an addition point 4 . Note that the controlled object 11 is an isometric representation of the entire winding machine using a block diagram.

The addition point 4 is the output signal F4e□ from the gain element 3,
Tension detection value T2 Feedback signal F1T, which is obtained by multiplying each detection value of the winding speed signal V and torque signal by feedback gain F and F2°F3, respectively.

Add F2v, F, and τ to obtain the added value (F1T+Fz
v + F3 t + F1a) is output to the conversion element 12 as a manipulated variable. The transfer function GC(S) of the conversion element 12 converts the operation iu from the electrical system to the torque system. Specifically, Converts motor current to torque and outputs it. Transfer function GV(S) is applied to conversion element 12 via branch point 13 and subtraction point 14.
The branch point 13 is connected to feed back the feedback signal F3τ to the summing point 4 via the gain element 7 and the summing point 5.

Further, the subtraction point 14 is the subtracted value (τ−
τL) is output to the conversion element 15, which is the transfer function GV(8). This transfer function GV(S) converts the input signal (L at τ-) from a mechanical system to a speed system and outputs a winding speed signal V. Furthermore, the conversion element 15 has a branch point 1
6 and a subtraction point 17, a conversion element 18 is connected, and the branch point 16 is connected to a gain element 8, which in turn sends feedback signals F, V to the summing point 4 via summing points 6, 5. connected to give feedback. On the other hand, at the subtraction point 17, after subtracting the transfer speed signal V of the winding object detected by a speed detector (not shown) from the winding speed signal V, the subtraction value (v − v
o) is output to the transformation element 18 which is the transfer function GT(S).

This transfer function G-r<s) is the input signal (v-v,
) is converted from the velocity system to the tension system, and the velocity (v −
v6) is converted into tension T and output.

The conversion element 18 is also connected to feed back the tension T to the subtraction point 1 via a branch point 19.10. Further, a gain element 9 is connected to the conversion element 18 via a branch point 19°10, and its output side is connected to the addition points 6 and 5.
is connected to the summing point 4 via a conversion element 18
The tension signal T from is converted into F and T by the gain element 9, and then fed back to the controlled object 11 via the summing point 6°5.4.

20 is a gain setting means, and this gain setting means 12
are used to set the feedback gains F'1 to F4 in each of the gain elements 3, 7, and 8.9, respectively.

A method for setting the feedback gains F to F4 in such a tension control system will be described below.

First, regarding this tension control system, a regulator is constructed using the following state feedback. It is generally known that such a regulator uses the following evaluation function as the overall design standard.

J ” f : (x'Q x + u'Ru) dt here.

R=(rxz) where X is a state variable matrix, Q is a weight matrix for the state variable matrix X, U is a manipulated variable, and R is a weight matrix for the manipulated variable U.

Here, q1□+ qz□e qzay q4*e r
□1 is a parameter having a positive value representing the weight for each of the winding tension T1, the winding speed V, the winding torque τ, the integral value 6T of the winding tension, and the manipulated variable U. Gain F work~
F4 can be determined by solving the Rikachi equation in modern control theory as a value such that the evaluation function J becomes the minimum value.

What value to adopt as gain F~F4 is determined by the above parameters q1□p qzzp qaat q44v
It is determined by changing r□□ appropriately and repeating simulations.

(Problem to be solved by the invention) However, in the above adjustment method, the coefficient matrix [F
It takes a lot of time and effort to adjust the control device because simulations have to be repeated by changing the evaluation criteria by trial and error for each of the four matrix elements of F3 F, ]. Ta.

The present invention was proposed to solve the above-mentioned problems, and its purpose is to use a weight matrix Q in an evaluation function J through trial and error in order to optimally adjust a tension control device.
, H matrix elements (parameters) q□8. q2□, q33
．． q44. It is an object of the present invention to provide a feedback gain setting method for a tension control device that allows the optimum feedback gain to be easily and quickly set without repeating simulation by changing rll.

(Means and operations for solving the problem) In order to achieve the above object, the present invention provides the following features: (1) In order to improve the control response of the tension control device, the control amount is set in the weight matrix Q in the evaluation function J. It is sufficient to set evaluation criteria on the matrix elements to match the tension to its target value ■ Multiply all the matrix elements of the weight matrices Q and H by the same positive constant (for example, k) to obtain the new weight. matrix Q
, R, it will only be multiplied by the minimum value of the evaluation function J, which will change the solution of the Riccati equation in the optimal regulator, that is, the coefficient matrix [F, F, F4) representing the feedback gain. It focuses on the fact that the optimal regulator is not a system design standard, and the weight matrix is used to weight the state variable matrix When determining Q, the evaluation criterion is set only on the tension among the state variables, and the weight matrix Q is set as follows: 1 gain F according to the matrix element rzt of the weight matrix R,
,F,,F,,F4 is calculated and then 'r''11/q4
Gain F>vF2tF2eF by changing 4
, thereby creating the optimal coefficient matrix (FtF, F
, F4). Here, r1□/q
In order to change 44, you can either keep q44 constant and change r □, or you can keep r constant and change q44, but in either case, the evaluation standard will be based only on tension, and the evaluation will be It is possible to set a coefficient matrix that minimizes the value of function J.

(Example) An embodiment of the present invention will be described below with reference to the drawings.

The figure is an isometric block diagram showing the overall configuration of the tension control system to which the present invention is applied, but the details are the same as those described in the (prior art) section, so the explanation will be omitted. .

In the figure, the operation amount U of the controlled object 32 indicating the winding machine is It is expressed as state feedback.

Here, T is the winding tension, ■ is the winding speed, τ is the winding torque, and for the 13th knife, the integral value of the winding tension is the state variable, and F
F2 represents a feedback gain for the winding tension, F2 represents a feedback gain for the winding speed, F3 represents a feedback gain for the winding torque, and F4 represents a feedback gain for the integral value of the winding tension.

The above state feedback U is the evaluation function J=f:(x'
It is expressed as Qx+u'Ru)dt.

or the state variable matrix, Q is the weight matrix for the state variable matrix X, and R is the weight matrix for the operation itu.

First, set q44 to an arbitrary constant, for example 1″′, and set r
An arbitrary value is given to xx, and gains F, , F, , F, , F4 that minimize the evaluation function J are calculated.

Next, by changing only r1□, the gain FilFl#F according to the matrix element rii of the 1-weight matrix R is obtained.
F4 is changed so that the optimal coefficient matrix [F, F
, F, F4) to adjust the feedback gain in the tension control system.

Originally, each matrix element (Ttts qzzy qzxy (144 and r
A gain setting method has been adopted in which the gain F i l F 29F,, F is obtained by changing li by trial and error using a parameter, but the condition for making the tension T, which is a controlled variable, match its target value T8 is adopted. Although there are multiple variables, the basic state variable is the tension T, so in the present invention, the evaluation criteria in the weight matrix Q is the matrix corresponding to the tension T.
4 It is placed only on q44. In other words, qzx e
It is qzz + qz3″0.

Furthermore, even if the new weight matrices Q and R are obtained by multiplying all the matrix elements of the weight matrices Q and R in the evaluation function J by the same positive constant (for example, k), the minimum This does not change the coefficient matrix (F, 'F2 F, F4) representing the feedback gain, which is the solution to the Riccati equation in the optimal regulator. In other words, if the ratio r1□/q44 of r ll t q44, which is the matrix element of the 1-weight matrices R and Q, is constant, then from the equation of the evaluation function J, the coefficient matrix (F-F
z F3F4) can be uniquely determined. Therefore, in this example, q44 is set as a constant, and the above ratio r□□/q44 is changed by changing only r1□, and the weight rtt for the manipulated variable U is kept constant, and only the tension T, which is a state variable, is evaluated. This weighting is equivalent to that of the standard.

(Effects of the Invention) As described above, according to the present invention, in order to optimally adjust the tension control device, unlike the conventional method, multiple matrix elements of the weight matrices Q and H in the evaluation function J are changed by trial and error. There is no need to repeat simulations, and by changing the ratio of the parameter representing the weight for the manipulated variable and the parameter representing the weight for tension among the matrix elements constituting the weight matrices Q and R, tension can be easily and quickly calculated. This has the effect that the feedback gain of the control device can be set.

[Brief explanation of the drawing]

The figure is a block diagram showing the entire tension control system to which the present invention is applied. 20...gain setting means

Claims (1)

[Claims] In order to continuously wind the object to be wound at a target tension, the state variables of the tension control system, such as the winding tension, winding speed, winding torque, and integral value of the winding tension, are used as state variables. There are status feedback ▲ mathematical formulas, chemical formulas, tables, etc. ▼ [u: manipulated variable, T: winding tension, v: winding speed, τ: winding torque, e_T: integral value of winding tension, F_1: winding Feedback gain for tension, F_2: Feedback gain for winding speed, F_3: Feedback gain for winding torque, F_4: Feedback gain for integral value of winding tension] constitutes a regulator, and the evaluation function ▲ mathematical formula, chemical formula, table, etc. There are ▼ [Here, ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼, ▲ Mathematical formulas, chemical formulas,
There are tables, etc. ▼, R = [r_1_1] x: state variable matrix, Q: weight matrix for state variable matrix x, u: manipulated variable, R: weight matrix for manipulated variable u, q_
1_1, q_2_2, q_3_3, q_4_4: T, V
, a parameter representing the weight for τe_T, r_1_1
: Parameter expressing weight for manipulated variable u] Gains F_1, F_2, F_3, F_ that minimize the value of
In the method of setting the feedback gain of the tension control device by finding the parameter r_1_1, the weight matrix Q is ▲a mathematical formula, a chemical formula, a table, etc.▼ (q_4_4 is an arbitrary constant), and the feedback gain is set according to the parameter r_1_1. F_1, F_2, F_3, F_4 are calculated, and then a simulation is performed by changing the gains F_1, F_2, F_3, F_4 by changing r_1_1/q_4_4, thereby obtaining the optimal gain F_1,
A feedback gain setting method for a tension control device, characterized in that the tension control device of a winding machine is adjusted by determining F_2, F_3, and F_4.