CN113285618A - Frequency self-adaptive FIR (finite impulse response) repeated prediction control method - Google Patents
Frequency self-adaptive FIR (finite impulse response) repeated prediction control method Download PDFInfo
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- H—ELECTRICITY
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- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
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Abstract
The invention discloses a frequency self-adaptive FIR (finite impulse response) repeated prediction control method, which is applied to an MMC (modular multilevel converter) rectifier for controlling frequency fluctuation of a ship shaft generator, and comprises the following steps: in a sampling period, comparing a given voltage with an actual direct current side voltage, inputting a difference value after comparison into an electric ring outer ring PI regulator to calculate to obtain a current value of the motor under a d-q coordinate system, obtaining a reference value of a current inner ring through Clark conversion, making a difference between an alternating current side current value sampled in real time and the reference value of the current inner ring, and using a control signal obtained after calculation of the current inner ring as a PWM modulation signal to carry out PWM switching control; for the current inner loop, the output signal of the voltage outer loop is used as the reference signal of the current inner loop, and the repeated control is added into the dead current inner loop to form a repeated prediction control strategy; and a frequency self-adaptive FIR low-pass filtering link is added in the repeated prediction control to control the frequency fluctuation phenomenon of the ship shaft power generation system.
Description
Technical Field
The invention relates to the field of power electronic converter control of MMC, in particular to a frequency self-adaptive FIR repeated prediction control method.
Background
In recent years, with the updating and upgrading of power electronic devices such as IGBTs, many scholars are devoted to the research on the constant-frequency voltage stabilization of ship shaft generators, and remarkable results are obtained. For example, in the aspect of a power electronic converter of a ship shaft power generation system, the decoupling control of active power and reactive power is realized, and the harmonic distortion rate is low. Document [1] discloses that a PWM rectifier is applied to a ship Permanent Magnet Synchronous Shaft Generator (MPMSSG) based on an LCL filter, and proposes a double closed-loop control strategy based on an improved current inner loop, so that a Luenberger observer can be designed autonomously to predict a capacitance current without additionally adding a sensor, and then the current is fed back through a virtual resistor to introduce active damping, thereby suppressing a resonance peak value of the LCL filter and enhancing a filtering effect. Document [2] applies a two-level converter to a novel broadband brushless excitation synchronous generator, and provides an instantaneous power balance strategy of an outer ring PI-inner ring complex vector PI based on PWM, the method does not need an inductive decoupling link, improves the anti-interference performance of the system, obtains good dynamic and static characteristics, and simultaneously eliminates 5-order and 7-order harmonics of a generator end of a ship shaft generator, but the IGBT switching frequency reaches higher 5kHz, the switching loss is larger, and the method is mainly applied to the low-voltage field of small and medium-sized ship transportation.
The topological structure of the voltage type converter is only two levels with lower equivalent switching frequency and poorer harmonic wave property, but with the increase of ship electric equipment and the improvement of the power electronic conversion device technology, a ship power system in the medium-voltage field begins to become mainstream, and at the moment, the topological structure of the voltage type converter adopts a modular multilevel topological structure (MMC) which has higher equivalent switching frequency, stronger voltage grade expansibility and better harmonic wave property and can meet the requirements of the medium-voltage high-power field. In the control strategy applied to the MMC, dead beat can enable the feedback signal to track the reference signal at the end of a control period for a periodic signal, and compared with other control strategies, the control strategy has the advantages of fast dynamic response and simple algorithm. Document [3] proposes a medium-voltage direct-current power distribution network MMC dead-beat current control strategy, which calculates the number of on-off sub-modules according to the difference value of actual current and reference current at an alternating-current side in each control period, so that an MMC system can increase level switching frequency under the condition that the switching times of the sub-modules are low, and finally the quality of output electric energy is improved. Document [4] performs modeling analysis based on a dq two-phase coordinate system of park transformation, and improves the stability of a current loop and the rapidity of a system by adopting a PI voltage outer loop-a dead beat current inner loop.
Therefore, the prior art has the defects that the lower the switching frequency is, the larger the dead-beat prediction error is for the periodic signal, and if the prediction precision can be improved and the prediction error is reduced, the advantage of dead-beat control can be exerted to the maximum extent.
Disclosure of Invention
According to the problems in the prior art, the invention discloses a frequency self-adaptive FIR repeated prediction control method, which is applied to an MMC rectifier for controlling a ship shaft generator to generate frequency fluctuation and comprises the following steps:
in a sampling period, comparing a given voltage with an actual direct current side voltage, inputting a difference value after comparison into an electric ring outer ring PI regulator to calculate to obtain a current value of the motor under a d-q coordinate system, obtaining a reference value of a current inner ring through Clark conversion, making a difference between an alternating current side current value sampled in real time and the reference value of the current inner ring, and using a control signal obtained after calculation of the current inner ring as a PWM modulation signal to carry out PWM switching control;
for the current inner loop, the output signal of the voltage outer loop is used as the reference signal of the current inner loop, and the repeated control is added into the dead current inner loop to form a repeated prediction control strategy;
and a frequency self-adaptive FIR low-pass filtering link is added in the repeated prediction control to control the frequency fluctuation phenomenon of the ship shaft power generation system.
Further, the voltage prediction quantity in the deadbeat current inner loop is obtained by adopting a linear interpolation method:
known linear interpolation polynomials:
bringing formula 3.17 into formula 3.18:
thus for
The prediction of (a) is as follows:
due to the fact that
As a reference value of the deadbeat current inner loop, which is a control signal of the output of the voltage outer loop controller and which is a direct current quantity at the system steady state, thus predicting
Only when the inverse operation of the park transformation is carried out, two sampling periods are predicted forwards, and the prediction expression is as follows:
further, when a frequency self-adaptive FIR low-pass filtering link is added, a rectangular window with the minimum transition band is adopted for interception:
an ideal low pass filter frequency response is provided:
wherein wc is a cut-off angular frequency, β is an ideal low-pass filter group delay, an impulse response of the ideal low-pass filter is a non-causal infinite length, a window function method is to approximate the ideal low-pass filter by using a causal finite-length impulse response to truncate from a time domain, and according to inverse Fourier transform, a time domain expression of a filter coefficient is as follows:
let the transition band of the rectangular window function be:
m is a set value, the system sampling frequency is set to be f0, the passband of the FIR filter is set to be fm, and then the normalized passband angular frequency expression is as follows:
ωm＝2πfm/fo (1.16)
the cut-off angular frequency expression is:
and then calculating the sampling times N in one fundamental frequency period:
N＝fo/f (1.18)
wherein f is the frequency that the boats and ships axle belt generator that the system sampled in real time sent, and get whole to N again and get decimal Dl:
Dl＝N-N* (1.19)
expression of center of symmetry β:
β＝3+1.5Dl (1.20)
obtaining frequency self-adaptive FIR filter coefficients h (0) -h (4) according to formulas 1.14, 1.15 and 1.17;
when D is not an integer, combining the condition of strict linear phase to obtain the value range of D:
(M-3)/2<D<(M-1)/2 (1.21)
D＝3+Dl (1.22)
and designing a relation according to the filter coefficient:
the coefficients h (5) -h (8) are obtained from equation 1.23, from which the coefficients of the frequency adaptive FIR filtering element are obtained.
By adopting the technical scheme, the frequency self-adaptive FIR repeated prediction control method provided by the invention aims at the problem of frequency micro-change of the ship shaft generator which possibly occurs, compared with the traditional FIR filter, the method has the advantages that the current prediction error can be stabilized at a smaller value, the method adapts to the frequency micro-change condition of the ship shaft generator in real time, the dynamic response speed of the system is ensured to be high, the current prediction error is reduced, and the harmonic distortion rate is lower.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic diagram of a modular multilevel converter topology structure according to the present invention
FIG. 2 is a schematic diagram of a half-bridge sub-module topology according to the present invention
FIG. 3 is a schematic diagram of an inner loop of a dead beat current with weighting factors according to the present invention
FIG. 4 is a schematic diagram of the inner loop of the current with weighting factor repeat prediction in the present invention
FIG. 5 is a double closed-loop control block diagram of the MMC rectifier in the present invention
FIG. 6(a) is a transient performance diagram of the dead-beat method of the present invention
FIG. 6(b) is a graph of transient performance of the repetitive prediction control method of the present invention
FIG. 6(c) is a steady state performance diagram of the method of the present invention using dead-beat
FIG. 6(d) is a steady state performance diagram of the method of the present invention employing repetitive predictive control
FIG. 7(a) is a current diagram of AC side of the invention using the dead-beat method
FIG. 7(b) is a current diagram of the AC side of the repetitive predictive control method of the present invention
FIG. 7(c) is a graph of phase current distortion rate of a phase using the dead-beat method in the present invention
FIG. 7(d) is a graph of phase current distortion rate of the a-phase current using the repetitive predictive control method of the present invention
FIG. 8(a) is an error diagram of the dead beat method of the present invention
FIG. 8(b) is an error diagram of the repetitive prediction control method according to the present invention
FIG. 9(a) is a diagram showing the voltage tracking at the DC output side after the sudden increase of fundamental frequency by 2Hz in the present invention
FIG. 9(b) is a diagram showing the voltage tracking at the DC output side after the sudden increase of fundamental frequency by 2Hz in the present invention
FIG. 10(a) is a diagram showing the error of the current prediction in the alpha axis after 2Hz abrupt increase of fundamental frequency in the present invention
FIG. 10(b) is a diagram showing the error of the current prediction in the alpha axis after 2Hz abrupt increase of fundamental frequency in the present invention
FIG. 11(a) is a graph showing the comparison of the characteristics of the AC side current after the fundamental frequency is suddenly increased by 2Hz
FIG. 11(b) is a graph showing the comparison of the characteristics of the AC side current after the sudden increase of the fundamental frequency by 2Hz
FIG. 11(c) is a graph showing the comparison of the characteristics of the AC side current after the fundamental frequency is suddenly increased by 2Hz
FIG. 11(d) is a graph showing the comparison of the characteristics of the AC side current after the fundamental frequency is suddenly increased by 2Hz
FIG. 12(a) is a graph showing the comparison of the filtering effect of the present invention after 2Hz fundamental frequency surge
FIG. 12(b) is a graph showing the comparison of the filtering effect of the present invention after 2Hz fundamental frequency surge
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
in fig. 1, the ac side is a ship shaft generator and three-phase resistive inductors are connected in series, the upper and lower bridge arms of each phase in the main circuit respectively include N identical submodules and a current-limiting inductor, and the dc side is a load resistor. U shapesa、Usb、 Usc、Isa、Isb、IscThree-phase AC voltage and current output by the generator G for the ship shaft, R, L equivalent resistance and inductance on AC side, Ua、Ub、UcFor MMC input terminal voltage, LsIs a bridge arm inductance, Upa、Ipa、Upb、Ipb、Upc、IpcFor bridge arm voltage, current, U, of bridge arm on each phasena、Ina、Unb、Inb、Unc、IncBridge arm voltage and current U of each phase lower bridge armdc、IdcThe voltage and current are output by the common direct current bus, the SM is a half-bridge submodule, and the submodule structure is shown in figure 2. The middle points of the upper and lower bridge arms are AC input/output side ports, and the output/input ends of each phase are connected together to form a common DC bus. During the operation of the rectification, the rectification is carried out,the MMC input end is in a sine waveform, voltage balance at two sides of MMC topology is guaranteed by controlling switching of the submodules, an ideal direct-current voltage waveform is further obtained, and meanwhile, in order to stabilize voltage and current at a direct-current side, an upper bridge arm and a lower bridge arm have a complementary relation, namely the sum of the input quantity of each phase of the submodules is always kept to be N; in a similar way, when the inverter works, the input end of the MMC is in a direct-current waveform, the alternating-current output side obtains a sinusoidal step wave by controlling the switching of the sub-modules, and the more the number of the sub-modules is, the closer the sub-modules are to the sinusoidal waveform, the more the step number is (N + 1).
In fig. 2, each half-bridge sub-module topology structure diagram is shown, and the switch can be enabled to output 0 or U through the action of pulse signals of a modulation strategyoTwo levels, wherein S1、S2Is an IGBT switching tube, D1、D2Is an IGBT anti-parallel diode, UoIs the voltage of the energy storage capacitor, UsmIs the output voltage, IsmThe output current is the higher the number of the submodules connected in series is, the higher the voltage is easily expanded. The MMC system outputs different levels by modulating the on or off of each phase module, and can be divided into 3 types of working states, namely 6 working modes according to the on and off conditions:
submodule throw-in state
When the upper bridge arm and the lower bridge arm of the submodule are switched on and off, the submodule is in an input state, and the submodule outputs a voltage, a capacitance and a voltage U at the momento. If Ism>0, then the current passes through S1Is connected in parallel with the diode D1Charging the sub-module capacitor; if Ism<0, the sub-module capacitance passes S1And (4) discharging.
Submodule cut-out state
When the lower bridge arm of the submodule is switched on and the upper bridge arm of the submodule is switched off, the submodule is in a cutting-off state, the submodule is bypassed at the moment, and the output voltage is 0. If Ism>0, then the current passes through S1(ii) a If Ism<0, then the current passes through S2Is connected in parallel with the diode D2。
Submodule lockout condition
When the upper and lower bridge arms of the sub-module are both turned off, the sub-module is in a locked state,the working state belongs to an abnormal mode, and at the moment, the current of the system can only form a path through a diode, and generally occurs in the stages of starting, switching dead zone, failure and the like of the system. If Ism>0, then the current passes through S1Is connected in parallel with the diode D1Charging the sub-module capacitor, wherein the sub-module output voltage is Uo(ii) a If Ism<0, then the current passes through S2Is connected in parallel with the diode D2The sub-module output voltage is 0.
Therefore, a mathematical model of the MMC in a three-phase stationary coordinate system can be written:
and then converting into a mathematical model under a two-phase static coordinate system:
and finally converting into a dead-beat mathematical model:
wherein U isavIs an average value of TsThe system sample time.
Further, the deadbeat current inner loop control link is as follows:
the deadbeat current inner loop control block diagram is shown in fig. 3, and the corresponding closed loop transfer function can be written:
in formula 1.4, kLFor the inductance prediction coefficient, r is a weighting factor, and it can be seen from fig. 3 that the weighting corresponding to the actual feedback current is 1-r, so r should not be selected too large. The characteristics can be known according to the Zhuoli stability criterion in a discrete systemThe essential condition for the roots of the equations to lie all within the unit circle of the Z plane is:
further, a specific mode of adding repetitive control in the deadbeat current inner loop to form a repetitive prediction control strategy is as follows:
adding repetitive control on the basis of dead beat to form a repetitive prediction current inner loop control block diagram as shown in fig. 4, a corresponding closed loop transfer function can be written:
in equation 1.5, Q is a frequency adaptive FIR low pass filter.
Further, the specific design mode of the frequency self-adaptive FIR low-pass filtering link is as follows:
let the unit impulse response of the FIR filter be h (n),0< n < M-1, and the relationship of the FIR filter output with length M to the input time sequence x (n) be given by a finite convolution sum form, with the difference equation as follows:
the transfer function Z domain expression is:
the frequency domain response expression is:
when strict linear phase is required, the time for which each frequency component signal is delayed is the same, and no signal distortion is caused, then the corresponding phase-frequency characteristic θ (w) can be written as:
θ(ω)＝-DTsω (1.9)
wherein D is a group delay constant, TsFor the system sampling time, the requirement that equation 1.9 holds is the strict linear phase requirement [5 ]]Comprises the following steps:
1.10 the system of equations can be derived as:
the strict linear phase filter coefficient design relation can be obtained from equation 1.11:
as can be seen from equation 1.12, when the first half coefficients of the filter are designed by the design method, the second half coefficients can be obtained.
In order to design an FIR filter with adjustable amplitude-frequency characteristics to play a role of filtering, firstly, an ideal low-pass filter frequency response is set:
wherein wcThe method is characterized in that the cut-off angular frequency is adopted, beta is the time delay of an ideal low-pass filter group, the impulse response of the ideal low-pass filter is non-causal infinite length, a window function method is started from a time domain, the causal finite length impulse response is used for truncation to approximate the ideal low-pass filter, and according to inverse Fourier transform, the time domain expression of the filter coefficient is as follows:
from the equation 1.14, the filter coefficient h (m) is a function symmetric with respect to β, and changing the value of β can change the filter coefficient h (m) to further change the amplitude-frequency characteristic diagram of the FIR filter. Therefore, the FIR filter is specifically designed by the following steps:
because the rectangular window has the minimum transition zone, the rectangular window is selected for interception, and the transition zone of the rectangular window function is as follows:
m was 9. Let the system sampling frequency be f0The FIR filter having a passband of fmThen the normalized passband angular frequency expression is:
ωm＝2πfm/fo (1.16)
the cut-off angular frequency expression is:
and then calculating the sampling times N in one fundamental frequency period:
N＝fo/f (1.18)
wherein f is the frequency (normally 50Hz) generated by the ship shaft generator sampled in real time by the system, the frequency adaptability is ensured, and N is rounded to N to obtain decimal Dl：
Dl＝N-N* (1.19)
Taking a symmetry center beta expression:
β＝3+1.5Dl (1.20)
the frequency adaptive FIR filter coefficients h (0) -h (4) can be obtained according to equations 1.14, 1.15, and 1.17. When D is not an integer, combining the condition of strict linear phase, the value range of D can be obtained:
(M-3)/2<D<(M-1)/2 (1.21)
and M has been calculated to be 9, so we here take:
D＝3+Dl (1.22)
the coefficients h (5) -h (8) are obtained from equation 1.12. Therefore, the frequency self-adaptive FIR filter coefficient design is completed.
As shown in fig. 5, a diagram of a double closed loop control for repeated prediction of an MMC rectifier is shown, in which a ship shaft generator is enabled to generate a stable three-phase alternating current through an excitation voltage regulation controller and a speed regulation controller, and a stable direct current voltage is output through the MMC rectifier after the stable three-phase alternating current flows through an alternating current side resistance inductor. The voltage outer ring adopts conventional PI control, the collected output direct current side voltage is used as feedback to make difference with a direct current voltage reference value, and then the voltage outer ring passes through an outer ring PI controller, and the output of the outer ring is used as the current reference of the current inner ring; the current inner loop adopts frequency self-adaptive repeated prediction control with time delay, and finally the control voltage output by the voltage and current double closed loops outputs PWM waves through a phase-shift carrier modulation strategy to carry out on-off control on each switch submodule of the MMC so as to finally obtain a target voltage and current waveform.
As can be seen by comparing the 4 experimental results in fig. 6, in both control methods, the voltage tracking at the dc output side can stably track the given voltage after the maximum overshoot of about 20% and the transient response time of about 0.1s, and the maximum deviations are both 5V after the voltage tracking enters the steady state; 1) and 3) in fig. 7, it can be seen that when the outer loop PI-inner loop deadbeat control is adopted, the current on the alternating current side can present a three-phase symmetrical waveform after steady-state operation, and the distortion rate of the a-phase current is 2.91%. And 2) and 4) in fig. 7, when the outer loop PI-inner loop repeated prediction control is adopted, the current on the alternating current side can also present a three-phase symmetrical waveform after steady-state operation, and the distortion rate of the a-phase current is 2.53%. Taking the prediction error of the current under the α axis as an example in fig. 8, it can be seen that the prediction error amplitude of the current inner loop is about 9A when the dead beat method is adopted, and the prediction error amplitude of the current inner loop is about 2A when the repetitive prediction control method is adopted. Therefore, after the current inner loop is changed into the repeated prediction control, the repeated prediction control can keep good dynamic and static characteristics of the deadbeat current inner loop for the direct current side voltage tracking; for the alternating-current side current characteristic, the repeated prediction control can make the current distortion rate lower; in terms of current prediction errors, repeated prediction control can have better prediction accuracy, and the operation of an MMC system is facilitated.
In order to verify the control effect of the repeated prediction control of the frequency-adaptive FIR filter on the prediction precision of the voltage and the current inner loop at the direct current output side of the MMC, a comparison experiment is carried out on the fundamental frequency increased by 2Hz when the simulation is carried out for 0.5s and the repeated prediction control under the conventional FIR filter without the frequency adaptation, and it can be seen that when the fundamental frequency is increased by 2Hz when the simulation is carried out for 0.5s, the fluctuation of the output voltage at the direct current side in the graph of 9-a) is gradually reduced after about 20V is increased, and the steady state is achieved after the recovery time of 0.15 s; in FIG. 9-b), the fluctuation of the output voltage at the DC side is gradually reduced after the fluctuation is increased by about 20V, and the steady state is achieved after the recovery time of 0.08 s; the magnitude of the current prediction error in FIG. 10-a) is gradually increased from 2A to 10A and is maintained; 10-b) the magnitude of the current prediction error gradually increases from 2A to 10A and gradually returns to 2A at time 0.75 s; in fig. 11, the amplitude of the ac side current is reduced by about 5A under the two control methods, and three-phase symmetry is maintained, the ac side current THD under the frequency-free adaptive filter is 3.24%, and the ac side current THD under the frequency-adaptive filter is 2.68%. It can be seen in fig. 12 that the pre-and post-filtering effect is significant under both filters. The comparison experiment shows that after the fundamental frequency is mutated, the repeated prediction control with the frequency self-adaptive FIR filter has better performance in the aspects of MMC direct current output side voltage control, current prediction error and alternating current side current THD than the conventional repeated prediction control, and is more suitable for the condition that the frequency of three-phase alternating current sent by a ship shaft generator is slightly changed.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
[1] Ganshihong, Brouss New, Zhaowei, Chentaishan an LCL filter-based PWM rectifier [ J ] of a ship shaft generator, Shanghai university bulletin, 1672-.
[2] A novel PWM rectification control strategy [ J ] applied to a ship shaft synchronous generator converter system, China Motor engineering newspaper 0258-.
[3] Guohanshen, Gem, Vanning, Kigyi, Tianyanjun. a deadbeat control strategy that can improve the harmonic characteristics of medium voltage MMC, Chinese Power, ISSN1004-9649, CN11-3265/TM.
[4] Zheng lei.pwm rectifier study based on deadbeat current control [ D ], guangzhou, guangdong university of industry, 2016.
Claims (3)
1. A frequency self-adaptive FIR repeated prediction control method is characterized in that the method is applied to an MMC rectifier for controlling a ship shaft generator to generate frequency fluctuation, and comprises the following steps:
in a sampling period, comparing a given voltage with an actual direct current side voltage, inputting a difference value after comparison into an electric ring outer ring PI regulator to calculate to obtain a current value of the motor under a d-q coordinate system, obtaining a reference value of a current inner ring through Clark conversion, making a difference between an alternating current side current value sampled in real time and the reference value of the current inner ring, and using a control signal obtained after calculation of the current inner ring as a PWM modulation signal to carry out PWM switching control;
for the current inner loop, the output signal of the voltage outer loop is used as the reference signal of the current inner loop, and the repeated control is added into the dead current inner loop to form a repeated prediction control strategy;
and a frequency self-adaptive FIR low-pass filtering link is added in the repeated prediction control to control the frequency fluctuation phenomenon of the ship shaft power generation system.
2. The method of claim 1, wherein the FIR low-pass filtering loop comprises: the voltage pre-measurement in the deadbeat current inner loop is obtained by adopting a linear interpolation method:
known linear interpolation polynomials:
bringing formula 3.17 into formula 3.18:
thus for
The prediction of (a) is as follows:
due to the fact that
As a reference value of the deadbeat current inner loop, which is a control signal of the output of the voltage outer loop controller and which is a direct current quantity at the system steady state, thus predicting
Only when the inverse operation of the park transformation is carried out, two sampling periods are predicted forwards, and the prediction expression is as follows:
3. the method of claim 1, wherein the FIR low-pass filtering loop comprises: when frequency self-adaptive FIR low-pass filtering loop time is added, a rectangular window with the minimum transition band is adopted for interception:
an ideal low pass filter frequency response is provided:
wherein wc is a cut-off angular frequency, β is an ideal low-pass filter group delay, an impulse response of the ideal low-pass filter is a non-causal infinite length, a window function method is to approximate the ideal low-pass filter by using a causal finite-length impulse response to truncate from a time domain, and according to inverse Fourier transform, a time domain expression of a filter coefficient is as follows:
let the transition band of the rectangular window function be:
m is a set value, the system sampling frequency is set to be f0, the passband of the FIR filter is set to be fm, and then the normalized passband angular frequency expression is as follows:
ωm＝2πfm/fo (1.16)
the cut-off angular frequency expression is:
and then calculating the sampling times N in one fundamental frequency period:
N＝fo/f (1.18)
wherein f is the frequency that the boats and ships axle belt generator that the system sampled in real time sent, and get whole to N again and get decimal Dl:
Dl＝N-N* (1.19)
expression of center of symmetry β:
β＝3+1.5Dl (1.20)
obtaining frequency self-adaptive FIR filter coefficients h (0) -h (4) according to formulas 1.14, 1.15 and 1.17;
when D is not an integer, combining the condition of strict linear phase to obtain the value range of D:
(M-3)/2<D<(M-1)/2 (1.21)
D＝3+Dl (1.22)
and designing a relation according to the filter coefficient:
the coefficients h (5) -h (8) are obtained from equation 1.23, from which the coefficients of the frequency adaptive FIR filtering element are obtained.
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| CN102891614A (en) * | 2012-10-26 | 2013-01-23 | 河南师范大学 | Improved dead-beat control method for pulse width modulation (PWM) rectifier at unbalance of voltage of power grid |
| CN105137757A (en) * | 2015-08-31 | 2015-12-09 | 南京航空航天大学 | Repeated controller with frequency adaptive capability, and control method |
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| CN102891614A (en) * | 2012-10-26 | 2013-01-23 | 河南师范大学 | Improved dead-beat control method for pulse width modulation (PWM) rectifier at unbalance of voltage of power grid |
| CN105137757A (en) * | 2015-08-31 | 2015-12-09 | 南京航空航天大学 | Repeated controller with frequency adaptive capability, and control method |
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