WO2021143319A1 - 一种定制式谐波重复控制器及控制方法 - Google Patents

一种定制式谐波重复控制器及控制方法 Download PDF

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WO2021143319A1
WO2021143319A1 PCT/CN2020/127928 CN2020127928W WO2021143319A1 WO 2021143319 A1 WO2021143319 A1 WO 2021143319A1 CN 2020127928 W CN2020127928 W CN 2020127928W WO 2021143319 A1 WO2021143319 A1 WO 2021143319A1
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controller
repetitive
output
module
loop
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PCT/CN2020/127928
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French (fr)
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卢闻州
陈海英
王尉
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江南大学
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Priority to US17/308,110 priority Critical patent/US11199820B2/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • 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
    • H02M1/00—Details of apparatus for conversion

Definitions

  • the invention relates to a customized harmonic repetitive controller and a control method, belonging to the field of industrial control repetitive controllers.
  • Repetitive control is proposed to achieve high-precision tracking of periodic signals.
  • the AC power provided by the grid is no longer directly used as power supply in these occasions Source, but through various forms of electric energy conversion to obtain the electric energy required by their respective production occasions.
  • inverter equipment is needed. Inverter equipment will receive disturbances from external signals, so it is necessary to adopt advanced The control method to achieve high-precision control, and repetitive control can achieve this goal.
  • Repetitive control is simply added to the input signal of the controlled object.
  • a "past control deviation” is also superimposed, which is the control deviation at this moment in the previous cycle. Reflect the deviation from the previous operation to the present, and add it to the controlled object together with the "current deviation” for control.
  • This control method where the deviation is repeatedly used, is called repeated control. After several cycles of repeated control, the tracking accuracy of the system can be greatly improved, and the quality of the system can be improved.
  • This control method is not only suitable for tracking periodic input signals, but also for suppressing periodic interference.
  • the repetitive controller generally consists of three parts: the internal model of the repetitive signal generator, the period delay link and the compensator.
  • the internal model of, the number of memory cells it occupies is at least N 0 , so the dynamic response of the traditional repetitive controller is slow.
  • the high-order repetitive controller has the ability to deal with frequency changes, that is, the ability to deal with the mismatch between the controller's internal model and the periodic signal. Therefore, expanding the order of the controller is a way to solve the internal model An effective approach to the mismatch problem.
  • the structure of the (nk ⁇ m) sub-harmonic repetitive controller proposed by Wenzhou Lu et al. has a forward path leading out in front of the addition loop, which does not meet the standards of high-order repetitive controllers.
  • the structure is structured, so it is impossible to expand the order to improve the performance of the controller, which limits the use of high-order (nk ⁇ m) harmonic repetitive controllers.
  • the present invention provides a customized harmonic Wave repeat controller and control method.
  • the first object of the present invention is to provide a repetitive controller, the repetitive controller comprising: a repetitive control gain module, a positive feedforward gain module, a subtraction loop, two addition loops and three identical time delay modules;
  • the input terminal of the repeated control gain module is used as the input terminal of the repeated controller
  • the output terminal of the repeated control gain module is used as the first input terminal of the first addition loop
  • the output terminal of the first addition loop is used as the second addition loop.
  • the first input and the output of the second addition loop are respectively connected in series with the positive feedforward gain module and the first time delay module, followed by the positive input and negative input of the subtraction loop, and the output of the subtraction loop is connected in series with the second time delay
  • the module is followed by the second input terminal of the first addition loop, which is also the output terminal of the repeat controller.
  • the output terminal of the positive feedforward gain module is connected in series with the third time delay module and then is connected with the second input terminal of the second addition loop.
  • the repeat controller further includes: a low-pass filter and a phase lead compensation module;
  • a low-pass filter is connected in series, and the output end of the subtraction loop is connected in series with the second time delay module and then the phase lead compensation module.
  • the transfer function of the repetitive controller including the low-pass filter and the phase lead compensation module is:
  • Q(z) is the low-pass filter
  • A(z) is the phase lead compensation module
  • c() is the output of the repetitive controller
  • e() is the input of the repetitive controller, that is, the control error of the control system
  • K rc is the repetitive control gain parameter
  • s is the Laplace variable of the continuous-time system
  • z is the variable of the z-transformation of the discrete-time system
  • T 0 is the fundamental wave period
  • f 0 is the fundamental frequency
  • ⁇ 0 is the fundamental angular frequency
  • T s is the sampling period
  • n, k and m are integers not less than zero and n ⁇ 0, n >m.
  • the expressions corresponding to c() are c(s) and c(z), and the expressions corresponding to e() are e(s) and e( z);
  • the expressions corresponding to Q() are Q(s) and Q(z), and the expressions corresponding to A() are A(s) and A(z).
  • the low-pass filter is a zero-phase low-pass filter.
  • the repetitive control gain module is a proportional constant used to adjust the speed of the repetitive controller to track or eliminate specific subharmonics, that is, the error between the output signal of the repetitive controller and the reference signal The convergence rate.
  • the second object of the present invention is to provide an h-order repetitive controller, h ⁇ 2, the h-order repetitive controller is obtained by expanding the above repetitive controller, and the expansion method is: taking ⁇ w h M h () from The cumulative sum of 1 to h is used as the forward path of the controller, and the internal model of the periodic signal is constructed in the form of output positive feedback, where w h is a constant coefficient, and M() is composed of three time delay modules and a positive feedforward gain module Periodic signal generator.
  • the transfer function of the periodic signal generator M() of the h-order repetitive controller is:
  • M(s) is the transfer function of the periodic signal generator M() of the h-order repetitive controller when the repetitive controller adopts an analog time delay module
  • M(z) is the repetitive controller adopts a digital time delay module
  • the third object of the present invention is to provide a control method of a repetitive controller, which is used to eliminate (nk ⁇ m) times by using the repetitive controller or the multimode repetitive controller or the h-order repetitive controller.
  • n, k, and m are integers not less than zero and n ⁇ 0, n>m, the method includes:
  • Repetitive control gain module The output of the repetitive control gain module is obtained after the input of the repetitive controller is subjected to the repetitive control gain;
  • Positive feedforward gain module Pass the output of the second addition loop through the positive feedforward gain module to obtain the output of the positive feedforward gain module;
  • the first addition loop add the output of the repeated control gain module and the output of the subtraction loop delayed by the second time delay module to obtain the output of the first addition loop;
  • the second addition loop add the output of the first addition loop and the output of the positive feedforward gain module delayed by the third time delay module to obtain the output of the second addition loop;
  • Subtraction loop subtract the output of the positive feedforward gain module from the output of the second addition loop delayed by the first time delay module to obtain the output of the subtraction loop;
  • the first time delay module delays the output of the second addition loop
  • the second time delay module delay the output of the subtraction loop
  • the third time delay module delays the output of the positive feedforward gain module.
  • the method further includes:
  • the speed at which the repetitive controller tracks or eliminates specific harmonics is adjusted, that is, the convergence speed of the error between the output signal of the repetitive controller and the reference signal.
  • the method further includes:
  • the time delay module is an analog or digital time delay module
  • the transfer function of the repeat controller is as follows:
  • c() is the output of the repetitive controller
  • e() is the input of the repetitive controller, that is, the control error of the control system
  • k rc is the repetitive control gain parameter
  • s is the Laplace variable of the continuous time system
  • Z is the variable of the z-transformation of the discrete-time system
  • N T 0 /T s is an integer
  • T 0 is the period of the fundamental wave
  • f 0 is the frequency of the fundamental wave
  • ⁇ 0 is the fundamental angular frequency
  • T s is the sampling period
  • n, k, and m are integers not less than zero and n ⁇ 0, n>m.
  • the expressions corresponding to c() are c(s) and c(z), and the expressions corresponding to e() are e(s) and e( z).
  • the method further includes: inserting the above-mentioned repeat controller into the feedback control system to eliminate the (nk ⁇ m) harmonic component in the control error, and when inserting into the feedback control system
  • the transfer function of the repeated controller is:
  • Q(z) is a low-pass filter
  • A(z) is a phase lead compensation module
  • the feedback control system is stable when the following two conditions are met:
  • the structure of the repetitive controller provided by the present invention conforms to the standard internal model construction method, that is, a periodic signal generator composed of three time delay modules and a positive feedforward gain module as a whole constitutes a forward path, and outputs a positive feedback form
  • a periodic signal generator composed of three time delay modules and a positive feedforward gain module as a whole constitutes a forward path, and outputs a positive feedback form
  • high-order repetition can be formed
  • the repetitive controller provided by this application takes the entire periodic signal generator as the only forward path and constructs the internal model in the form of output positive feedback. Therefore, it has the ability to expand the order and greatly improves the controller’s performance. flexibility.
  • the h-order (nk ⁇ m) sub-harmonic repetitive controller (h ⁇ 2) which is further expanded by the repetitive controller provided by the present invention, covers a variety of existing high-order repetitive controllers, and provides a Unified form, such as "Second-order RC: analysis, augmentation, and anti-frequency-variation for single-phase grid-tied inverter" by Dapeng Li et al.
  • the h-order (nk ⁇ m) sub-harmonic repetitive controller (h ⁇ 2) which is further expanded by the repetitive controller provided by the present invention, has a faster error convergence speed, and when the internal model and the periodic signal are at the resonance frequency When a mismatch occurs near the point, it will have a certain inhibitory effect on it, and then the performance of the controller will be improved.
  • the repetitive controller provided by the present invention specifically performs error-free tracking or disturbance elimination for (nk ⁇ m) harmonic signals, and can customize different n and m according to the actual needs of eliminating harmonic disturbance signals or tracking reference signals.
  • the three delay links in the repetitive controller provided by the present invention are completely the same, and the delay time ⁇ is equal to 1/n times of the fundamental period T 0.
  • the longest delay time path is composed of two of the above-mentioned delay links, so the total delay time
  • the delay time is (2T 0 /n) ⁇ T 0 , so when the repetitive control gain k rc is the same, the response speed of the repetitive controller provided by the present invention is much faster than that of the general repetitive controller, which eliminates disturbance The speed is greatly improved.
  • the multi-mode repetitive controller provided by the present invention can be used to eliminate all sub-harmonics or any sub-harmonics, and can independently adjust the control gain of each harmonic controller.
  • the repetitive controller provided by the present invention only needs one positive feedforward coefficient module.
  • the controller has a simple structure and is easy to design.
  • the repetition controller provided by the present invention is used to eliminate the disturbance whose ratio of the two frequencies is not an integer multiple of nk+m and nk-m, only one time delay link is needed to construct the internal model of the disturbance signal, thus simplifying the repetition.
  • the design of the time delay link in the controller is not an integer multiple of nk+m and nk-m.
  • the three delay links in the repeat controller provided by the present invention are exactly the same, and the number of memory cells occupied is N/n, so the total number of memory cells is (3N/n), (nk ⁇ m) harmonic numbers
  • the number of storage units occupied by the repeating controller is also much lower than that of the general digital repeating controller.
  • Fig. 1 is a structural block diagram of the (nk ⁇ m) harmonic repetition controller proposed by the present invention.
  • Fig. 2 is the digital realization form of Fig. 1, which is the structural block diagram of the (nk ⁇ m) harmonic digital repetitive controller.
  • Fig. 3 is a structural block diagram of the periodic signal generator located in the forward path in the digital form of the (nk ⁇ m) harmonic repetition controller proposed by the present invention.
  • Fig. 4 is a structural block diagram of an improved (nk ⁇ m) sub-harmonic repetitive controller with the addition of a low-pass filtering link and a phase lead compensation link on the basis of Fig. 1.
  • Fig. 5 is the digital realization form of Fig. 4, which is a structural block diagram of an improved (nk ⁇ m) harmonic digital repetitive controller.
  • Fig. 6 is a structural block diagram of the (nk ⁇ m)-order harmonic digital repetitive controller (h ⁇ 2) expanded to the h-order on the basis of Fig. 2.
  • Fig. 7 is a structural block diagram of an improved h-order (nk ⁇ m) harmonic digital repetitive controller (h ⁇ 2).
  • Fig. 8 is a structural block diagram of an improved h-order (nk ⁇ m) harmonic digital repeat controller when h is taken as an example.
  • Fig. 9 is a structural block diagram of all sub-harmonic repetitive controllers of parallel structure formed by adding the (nk ⁇ m) sub-harmonic repetitive controllers proposed by the present invention in parallel. This structure repetitive controller can control all sub-harmonics To eliminate.
  • Fig. 10 is a structural block diagram of any harmonic repetitive controller of parallel structure formed by adding the (nk ⁇ m) harmonic repetitive controllers proposed by the present invention in parallel.
  • the structure repetitive controller can control any harmonic To eliminate.
  • Fig. 11 is the digital realization form of Fig. 9, which is a structural block diagram of all sub-harmonic digital repeat controllers in parallel structure.
  • Fig. 12 is the digital realization form of Fig. 10, which is a block diagram of a parallel structure of any harmonic digital repeat controller.
  • Fig. 13 is a structural block diagram of all sub-harmonic repetitive controllers in an improved parallel structure with the addition of a low-pass filtering link and a phase lead compensation link on the basis of Fig. 9.
  • Fig. 14 is a structural block diagram of an improved parallel structure arbitrary harmonic repetitive controller with the addition of a low-pass filtering link and a phase lead compensation link on the basis of Fig. 10.
  • Fig. 15 is the digital realization form of Fig. 13, which is a structural block diagram of an improved parallel structure of all sub-harmonic digital repeat controllers.
  • Fig. 16 is the digital realization form of Fig. 14, which is a structural block diagram of an improved parallel structure arbitrary harmonic digital repeat controller.
  • Figure 17 is a block diagram of the control system structure of an improved (nk ⁇ m) harmonic digital repetitive controller superimposed on a general feedback controller.
  • Fig. 18 is a block diagram of the control system structure of an improved h-order (nk ⁇ m) harmonic digital repetitive controller (h ⁇ 2) superimposed on a general feedback controller.
  • Figure 21 is an example of 6k ⁇ 1 RC and second-order 6k ⁇ 1 RC.
  • the reference voltage frequency changes from 50Hz to 49.8Hz, that is, when the internal model of the controller is mismatched with the periodic signal that needs to be tracked or eliminated, the two Comparison chart of the control effect of this controller.
  • Figure 22 is the (nk ⁇ m) harmonic digital repetitive controller or multi-mode digital repetitive controller or h-order (nk ⁇ m) harmonic digital repetitive controller proposed by the present invention added to the control system in a cascaded manner
  • the repetitive controller includes: a repetitive control gain module, a positive feedforward gain module, a subtraction loop, two addition loops, and three identical time delay modules;
  • the input terminal of the repeated control gain module is used as the input terminal of the repeated controller
  • the output terminal of the repeated control gain module is used as the first input terminal of the first addition loop
  • the output terminal of the first addition loop is used as the second addition loop.
  • the first input and the output of the second addition loop are respectively connected in series with the positive feedforward gain module and the first time delay module, followed by the positive input and negative input of the subtraction loop, and the output of the subtraction loop is connected in series with the second time delay
  • the module is followed by the second input terminal of the first addition loop, which is also the output terminal of the repeat controller.
  • the output terminal of the positive feedforward gain module is connected in series with the third time delay module and then is connected with the second input terminal of the second addition loop.
  • c(s) is the output of the repetitive controller
  • e(s) is the input of the repetitive controller, that is, the control system
  • the amount of control error, k rc is the repetitive control gain module.
  • k rc is the repetitive control gain coefficient
  • T 0 is the fundamental wave period
  • f 0 is the fundamental frequency
  • ⁇ 0 is the fundamental angular frequency
  • n , K and m are integers not less than zero and n ⁇ 0, n>m
  • e is a natural constant.
  • the error convergence speed of the system can be changed.
  • the larger the k rc the faster the steady-state error of the system converges.
  • k rc can only be within a certain range. Improve the convergence speed of the system within the range.
  • the three delay links in Figure 1 are exactly the same, and their delay time ⁇ is equal to 1/n times the fundamental period T 0.
  • the longest delay time path is composed of two of the above-mentioned delay links, so the total delay time is (2T 0 /n) ⁇ T 0 , therefore, under the same repetitive control gain k rc , the response speed of the customized harmonic repetitive controller proposed in this application is much faster than that of the general repetitive controller, which is (nk ⁇ m )
  • this repetitive controller that is, the customized harmonic repetitive controller proposed in the present invention, is called (nk ⁇ m) sub-harmonic repetitive control Device.
  • c(z) is the output of the repetitive controller
  • e(z) is the input of the repetitive controller, that is, the control error of the control system
  • k rc is the repetitive control gain
  • T 0 is the fundamental wave period
  • f 0 is the fundamental wave frequency
  • ⁇ 0 is the fundamental angle frequency
  • T s is the sampling period
  • n, k and m are not less than zero Integer and n ⁇ 0, n>m.
  • the three time delay links in Figure 2 are exactly the same, the number of memory cells occupied is N/n, so the total number of memory cells is (3N/n), so the (nk ⁇ m) harmonic digital repeat controller occupies The storage space is much less than the general digital repeat controller.
  • Figure 3 shows the digital form of the periodic signal generator located in the forward path in the (nk ⁇ m) sub-harmonic repetition controller proposed by the present invention. It consists of three identical time delay modules and a positive feedforward gain module.
  • the transfer function M(z) can be expressed as:
  • Figure 6 shows the general structure diagram of the h-order (nk ⁇ m) harmonic digital repetitive controller (h ⁇ 2).
  • the h-order (nk ⁇ m) harmonic repetitive controller is also based on Realized digitally, its transfer function can be written in the following form:
  • Figure 7 shows the improved h-order (nk ⁇ m) harmonic digital repetitive controller (h ⁇ 2), which is different from the first-order (nk ⁇ m) harmonic digital repetitive controller because of the order If the low-pass filter Q(z) is still connected in series to the output terminals of the three same time delay modules to filter, the complexity of the controller will inevitably increase, and the design difficulty will also increase greatly.
  • the h-order (nk ⁇ m) harmonic digital repeat controller proposed by the present invention will uniformly connect the low-pass filter Q(z) in series when h ⁇ 2 After that, and still connect the phase lead compensation module A(z) in series at the output of the repeat controller, the transfer function of the improved h-order (nk ⁇ m) harmonic digital repeat controller (h ⁇ 2) can be written as follows form:
  • Figure 8 shows an example of the h-order (nk ⁇ m) harmonic digital repetitive controller when h is set to 2.
  • the second order is usually It is enough, that is, the second-order (nk ⁇ m) harmonic digital repetitive controller, and its transfer function is as follows:
  • Figure 9 shows the parallel structure of the (nk ⁇ m) harmonic repetitive controller proposed by the present invention and all the sub-harmonic repetitive controllers in parallel.
  • the repetitive controller can eliminate all sub-harmonics, and can independently adjust the control gain of each sub-harmonic. Its transfer function is as follows:
  • Figure 10 shows the arbitrary harmonic repetition controller of parallel structure formed by the parallel addition of the (nk ⁇ m) sub-harmonic repetitive controllers proposed by the present invention.
  • the repetitive controller can eliminate any order of harmonics, and can independently adjust the control gain of each order of harmonics. Its transfer function is as follows:
  • n i and mi are arbitrary positive integers.
  • Fig. 11 shows the digital form of all sub-harmonic repetitive controllers in parallel structure, which is formed by the parallel addition of the (nk ⁇ m) sub-harmonic repetitive controllers proposed by the present invention, and its transfer function is:
  • Figure 12 shows the digital form of the arbitrary harmonic repetitive controller of parallel structure formed by the parallel addition of the (nk ⁇ m) sub-harmonic repetitive controllers proposed by the present invention, and its transfer function is:
  • n i and mi are arbitrary positive integers.
  • Figure 13 shows the structure diagram of all sub-harmonic repetitive controllers of the improved parallel structure with the addition of low-pass filtering link Q(s) and phase lead compensation link A(s). Its transfer function is:
  • Figure 14 shows the structural block diagram of the improved parallel structure arbitrary harmonic repetitive controller with the addition of low-pass filter link Q(s) and phase lead compensation link A(s). Its transfer function is:
  • n i and mi are arbitrary positive integers.
  • Figure 15 shows the structural block diagram of the improved parallel structure all sub-harmonic digital repeat controller, and its transfer function is:
  • Figure 16 shows the structural block diagram of the improved parallel structure arbitrary harmonic digital repeat controller, and its transfer function is:
  • n i and mi are arbitrary positive integers.
  • the (nk ⁇ m) harmonic repetitive controller and the h-order (nk ⁇ m) harmonic digital repetitive controller provided in the first embodiment above can be added to the general In the feedback control system, it is used to eliminate the (nk ⁇ m) harmonic component in the control error.
  • the following is an introduction to the (nk ⁇ m) harmonic repetitive controller and the further expanded h-order (nk ⁇ m) harmonic digital repetitive controller by inserting it into the general feedback system:
  • This embodiment takes the (nk ⁇ m) harmonic digital repetitive controller inserted into the general feedback system as an example to introduce the specific implementation of the (nk ⁇ m) harmonic repetitive controller proposed by the present invention. :
  • Figure 17 shows a block diagram of the improved (nk ⁇ m) harmonic digital repeat controller added to the general feedback control system, where G rc (z) is the improved (nk ⁇ m) harmonic digital Repeat controller, G c (z) is the conventional feedback controller, G p (z) is the control object, y d (z) is the reference input of the system and generally the fundamental reference signal y(z) is the actual output of the system, e(z) is the error between the reference and actual signal and is also the input signal of the repetitive controller G rc (z), c(z) is the output signal of the repetitive controller G rc (z) and it is also the error signal e(z) After being added together, it is used as the input of the conventional feedback controller G c (z), u(z) is the output signal of the conventional feedback controller G c (z) and is also the input signal of the control object G p (z), d(z ) Is the disturbance input signal of the system, which is added to the output signal of the controlled object
  • Figure 18 shows the structural block diagram of adding the improved h-order (nk ⁇ m) harmonic digital repeat controller (h ⁇ 2) to the general feedback control system, and the high-order (nk ⁇ m) harmonic digital repeat controller The controller is also added to the general feedback control system in a plug-in manner.
  • the harmonics are mainly concentrated in (4k ⁇ l) times (that is, 3, 5, 7, 9 and other odd-order frequency components), and it is often necessary to correct the fundamental wave
  • the control objective is to make the output voltage accurately track the reference voltage.
  • Figure 19(a) corresponds to the CRC controller
  • Figure 19(b) corresponds to the 4k ⁇ 1RC controller proposed by this application.
  • the total harmonic distortion (THD) is 0.57% and 1.1%, which can reach very small values.
  • CRC needs about 0.7s to reach the steady state; while the 4k ⁇ 1RC corresponding to this application only needs about 0.35s to reach the steady state, so the error convergence speed of 4k ⁇ 1RC It is about twice that of CRC, that is, the error convergence speed of 4k ⁇ 1RC corresponding to this application is significantly faster.
  • the control target is to make the output
  • the (nk ⁇ m) harmonic repetitive controller proposed in the present invention can be further extended to the h-order (nk ⁇ m) harmonic digital repetitive controller (h ⁇ 2), where 6k ⁇ 1 RC and second-order 6k ⁇ 1 RC as an example, through specific simulation examples, it is verified that the high-order (nk ⁇ m) harmonic digital repetitive controller has improved performance compared with the first-order (nk ⁇ m) harmonic digital repetitive controller. It suppresses the mismatch between the internal model of the controller and the periodic signal that needs to be tracked or eliminated near the resonance frequency point, and has a faster error convergence speed.
  • the error convergence time and total harmonic distortion (THD) of the 6k ⁇ 1 RC controller are 0.3s and 1.59%, respectively, while the second-order 6k ⁇ 1 1
  • the error convergence time and total harmonic distortion (THD) of the RC controller are 0.2s and 1.42%, respectively. Therefore, the second-order 6k ⁇ 1 RC controller needs to track or eliminate the internal model of the controller.
  • the periodic signal is mismatched near the resonance frequency point, it has a faster error convergence speed and a lower total harmonic distortion rate.
  • the (nk ⁇ m) harmonic digital repetitive controller given in the first embodiment above and the h-order (nk ⁇ m) harmonic digital repetitive controller obtained by further expansion, and all the harmonics/any harmonic digital of the parallel structure The repetitive controller can be inserted or cascaded into the general feedback control system to eliminate the (nk ⁇ m) harmonic component in the control error.
  • the second embodiment gives the (nk ⁇ m) harmonic repetition
  • the controller and the h-order (nk ⁇ m) harmonic digital repeat controller are inserted into the specific implementation mode and simulation experiment of the general feedback control system. This embodiment introduces the addition of the cascade method to the general feedback control system The specific implementation.
  • Figure 22 shows the improved (nk ⁇ m) harmonic digital repetitive controller or parallel structure repetitive controller or h-order (nk ⁇ m) harmonic digital repetitive controller added to the general feedback control in cascade mode.
  • G rc (z) is an improved (nk ⁇ m) sub-harmonic digital repetitive controller
  • G c (z) is a conventional feedback controller
  • G p (z) is the control object
  • y d (z) is the reference input of the system and generally the fundamental wave reference signal y(z) is the actual output of the system
  • e(z) is the error between the reference and the actual signal, and is also the input signal of the repetitive controller G rc (z).
  • c(z) is the output signal of the repetitive controller G rc (z) and is also added to the error signal e(z) as the input of the conventional feedback controller G c (z), u(z) is the conventional feedback control
  • the output signal of the controller G c (z) is also the input signal of the control object G p (z)
  • d(z) is the disturbance input signal of the system, which is added to the output signal of the control object G p (z) to form the actual output Signal y(z).
  • Part of the steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.

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Abstract

一种定制式谐波重复控制器及控制方法，属于工业控制的重复控制器领域。重复控制器将三个时间延迟模块和正前馈增益模块构成的周期信号发生器做为一个整体构成前向通路，并以输出正反馈形式来构造周期信号的内模，使得其结构符合标准的内模构造方法，具备扩阶的能力，大大提升了控制器的灵活性，使控制器消除扰动的速度得到了提高，同时结构简单便于设计。进一步拓展而成的h阶(nk±m)次谐波重复控制器(h≥2)涵盖了现有的多种高阶重复控制器，给出了一种统一形式，使其具有通用性。

Description

一种定制式谐波重复控制器及控制方法 技术领域
本发明涉及一种定制式谐波重复控制器及控制方法，属于工业控制的重复控制器领域。
背景技术
重复控制是为了实现对周期信号的高精度跟踪而提出的，在很多工业应用场景中都需要实现对周期信号的高精度跟踪，比如一些生产场合，这些场合不再直接使用电网提供的交流电作为供电来源，而是通过各种形式的电能变换得到满足各自生产场合所需的电能，在电能变换过程中需要用到逆变器设备，逆变器设备会收到外界信号的扰动，所以需要采用先进的控制方法来实现高精度的控制，而重复控制即可实现这一目的。
重复控制，简单说就是加到被控对象的输入信号中，除偏差信号外，还叠加了一个“过去的控制偏差”，该偏差是上一个周期该时刻的控制偏差。把上一次运行时的偏差反映到现在，和“现在的偏差”一起加到被控对象进行控制，这种控制方式，偏差重复被使用，称为重复控制。经过几个周期的重复控制之后，可以大大提高系统的跟踪精度，改善系统品质。这种控制方法不仅适用于跟踪周期性输入信号，也可以用于抑制周期性干扰。而重复控制器一般由三部分组成：重复信号发生器内模、周期延迟环节和补偿器。
传统的重复控制器采用延迟时间τ为T 0的延迟环节(即周期信号发生器)的正反馈形式来构造基波周期为T 0的周期信号的内模，并将该内模嵌入控制回路中，从而实现对该种周期性信号(包括正弦基波及其各次谐波)的静态无差跟踪控制或扰动消除，但是由于该类重复控制器由输入到输出的延迟时间为基波周期T 0，其响应速度相对较慢，并且实际当中重复控制器多以数字方式z -N/(l-z -N)(其中N＝T 0/T s为整数，T s为采样时间)实现该周期性信号的内模，其所占用的内存单元数目至少为N 0，因此传统重复控制器的动态响应较慢。
为了提升重复控制器的动态性能，目前存在一种将重复控制器与其他控制方法相结合的复合控制策略，此种方法虽然有效，但是却大大增加了控制器设计难度与复杂度，并且在一些实际应用中，需要跟踪或消除的谐波只局限于特定的某些频率，例如三相整流负载给电源系统所造成的谐波污染绝大部分集中于6k±l(k＝1,2,...)次谐波频率处，而单相整流负载给电源系统所造成的谐波污染绝大部分集中于4k±1(k＝1,2,...)次谐波频率(即奇次谐波频率)处；在工业场合中，上述两类谐波占据主导地位。若采用一般的重复控制器来消除这类(nk±m)次谐波，会出现周期性扰动消除非常缓慢的现象，因而无法满足实际系统对控制性能的要求。
针对需要消除特定(nk±m)次谐波的问题，有学者提出了(nk±m)次谐波重复控制器，即Wenzhou Lu等在“A Generic Digital nk±m-Order Harmonic Repetitive Control Scheme for PWM Converters”，IEEE Transactions on Industrial Electronics,2013一文中提出的(nk±m)次谐波重复控制器使上述问题得到了解决，但是在实际应用中，如果参考电压频率/电网电压频率/数字控制系统采样频率等发生变化，则会导致控制器内模与周期信号发生失配，此时若采用Wenzhou Lu等提出的(nk±m)次谐波重复控制器，由于其无法实现扩阶，所以无法应对控制器内模与周期信号发生失配的问题，从而导致谐波抑制性能降低，稳态误差增大，畸变率升高，其控制性能大打折扣。
根据现有的高阶重复控制理论，高阶重复控制器具备应对频率变化的能力，即具备应对控制器内模与周期信号失配的能力，因此扩展控制器的阶数是一种解决内模失配问题的有效途径，然而上述Wenzhou Lu等提出的(nk±m)次谐波重复控制器的结构上具有一条在加法环前方引出的前向通路，并不符合高阶重复控制器的标准构造结构，因此无法进行扩阶以提升控制器性能，限制了高阶(nk±m)次谐波重复控制器的使用。
针对于此，有必要发明一种新的(nk±m)次谐波重复控制器，使其在具备传统(nk±m)次谐波重复控制器的功能的同时，在结构上更加规范，并且可以进行扩阶，以应对在实际应用中出现的内模失配问题，进而提高控制器的鲁棒性与灵活性。
发明内容
为了解决现有的(nk±m)次谐波重复控制器在面对内模失配问题时，无法构造高阶重复控制器进而提升控制器性能的问题，本发明提供了一种定制式谐波重复控制器及控制方法。
本发明的第一个目的在于提供一种重复控制器，所述重复控制器包括：重复控制增益模块、正前馈 增益模块、一个减法环、二个加法环和三个相同的时间延迟模块；
其中，重复控制增益模块的输入端作为所述重复控制器的输入端，重复控制增益模块的输出端作为第一加法环的第一输入端，第一加法环的输出端作为第二加法环的第一输入端，第二加法环的输出端分别串接正前馈增益模块和第一时间延迟模块后接减法环的正输入端和负输入端，减法环的输出端串接第二时间延迟模块后接第一加法环的第二输入端，同时也是重复控制器的输出端，正前馈增益模块的输出端串接第三时间延迟模块后接第二加法环的第二输入端。
可选的，所述重复控制器还包括：低通滤波器和相位超前补偿模块；
所述三个相同的时间延迟模块后分别串联一个低通滤波器，所述减法环的输出端串接第二时间延迟模块后接相位超前补偿模块。
可选的，包含有低通滤波器和相位超前补偿模块的重复控制器的传递函数为：
Figure PCTCN2020127928-appb-000001
或
Figure PCTCN2020127928-appb-000002
其中，Q(z)为低通滤波器，A(z)为相位超前补偿模块；c()为重复控制器的输出量，e()为重复控制器的输入量即控制系统的控制误差量，k rc为重复控制增益参数，s为连续时间系统的拉普拉斯变量，z为离散时间系统的z变换的变量；N＝T 0/T s为整数，T 0为基波周期，T 0＝2π/ω 0＝l/f 0，f 0为基波频率，ω 0为基波角频率，T s为采样周期，n、k和m为不小于零的整数且n≠0，n>m。
所述重复控制器分别采用模拟或数字时间延迟模块时，c()对应的表达式分别为c(s)和c(z)，e()对应的表达式分别为e(s)和e(z)；Q()对应的表达式分别为Q(s)和Q(z)，A()对应的表达式分别为A(s)和A(z)。
可选的，所述低通滤波器为零相位低通滤波器。
可选的，所述重复控制增益模块为一比例常数，用于实现对重复控制器跟踪或消除特定次谐波的速度的调节，也即所述重复控制器的输出信号与参考信号之间误差的收敛速度。
本发明的第二个目的在于提供一种h阶重复控制器，h≥2，所述h阶重复控制器由上述重复控制器扩展得到，扩展方法为：将∑w hM h()进行从1到h的累和作为控制器前向通路，并以输出正反馈形式来构造周期信号的内模，其中w h为常系数，M()为三个时间延迟模块和正前馈增益模块构成的周期信号发生器。
可选的，所述h阶重复控制器的周期信号发生器M()的传递函数为：
Figure PCTCN2020127928-appb-000003
或
Figure PCTCN2020127928-appb-000004
其中，M(s)为所述重复控制器采用模拟时间延迟模块时h阶重复控制器的周期信号发生器M()的传递函数；M(z)为所述重复控制器采用数字时间延迟模块时h阶重复控制器的周期信号发生器M()的传递函数。
本发明的第三个目的在于提供一种重复控制器的控制方法，所述方法用于利用上述重复控制器或上述多模重复控制器或上述h阶重复控制器进行消除(nk±m)次谐波，n、k和m为不小于零的整数且n≠0，n>m，所述方法包括：
重复控制增益模块：将重复控制器的输入量经过重复控制增益后得到重复控制增益模块的输出量；
正前馈增益模块：将第二加法环的输出量经过正前馈增益模块后得到正前馈增益模块输出量；
第一加法环：将重复控制增益模块输出量与第二时间延迟模块延迟输出的减法环输出量相加得到第一加法环输出量；
第二加法环：将第一加法环的输出量与第三时间延迟模块延迟输出的正前馈增益模块输出量相加得到第二加法环输出量；
减法环：将正前馈增益模块的输出量与第一时间延迟模块延迟输出的第二加法环输出量相减得到减法环的输出量；
第一时间延迟模块：将第二加法环输出量延迟输出；
第二时间延迟模块：将减法环输出量延迟输出；
第三时间延迟模块：将正前馈增益模块输出量延迟输出。
可选的，所述方法还包括：
通过调节重复控制增益实现调节所述重复控制器跟踪或消除特定次谐波的速度，也即所述重复控制器的输出信号与参考信号之间误差的收敛速度。
可选的，所述方法还包括：
根据所需要跟踪或消除的谐波次数确定正前馈增益模块的参数。
可选的，所述时间延迟模块为模拟或数字时间延迟模块，所述重复控制器的传递函数如下：
Figure PCTCN2020127928-appb-000005
或
Figure PCTCN2020127928-appb-000006
其中，c()为重复控制器的输出量，e()为重复控制器的输入量即控制系统的控制误差量，k rc为重复控制增益参数，s为连续时间系统的拉普拉斯变量，z为离散时间系统的z变换的变量；N＝T 0/T s为整数，T 0为基波周期，T 0＝2π/ω 0＝l/f 0，f 0为基波频率，ω 0为基波角频率，T s为采样周期，n、k和m为不小于零的整数且n≠0，n>m。
所述重复控制器分别采用模拟或数字时间延迟模块时，c()对应的表达式分别为c(s)和c(z)，e()对应的表达式分别为e(s)和e(z)。
可选的，所述方法还包括：将上述重复控制器以插入方式加入到反馈控制系统中用于消除控制误差当中的(nk±m)次谐波分量，当以插入方式加入到反馈控制系统时，重复控制器的传递函数为：
Figure PCTCN2020127928-appb-000007
其中，Q(z)为低通滤波器，A(z)为相位超前补偿模块；
所述反馈控制系统在满足下述两个条件时是稳定的：
①未插入重复控制器前的闭环系统传递函数的极点位于单位圆内；
②所述插入的控制器中重复控制增益参数k rc满足0<k rc<2。
本发明有益效果是：
1、本发明提供的重复控制器的结构符合标准的内模构造方法，即将三个时间延迟模块和正前馈增益模块构成的周期信号发生器作为一个整体构成前向通路，并以输出正反馈形式来构造周期信号的内模，根据现有的高阶重复控制理论，即只有当周期信号发生器整体作为唯一的前向通路，并且以输出正反馈的形式构造内模时，可以构成高阶重复控制器，而本申请提供的重复控制器则是将周期信号发生器整体作为唯一的前向通路，并以输出正反馈的形式构造内模，因此具备扩阶的能力，大大提升了控制器的灵活性。
2、本发明提供的重复控制器进一步拓展而成的h阶(nk±m)次谐波重复控制器(h≥2)涵盖了现有的多种高阶重复控制器，给出了一种统一形式，如Dapeng Li等所著的“Second-order RC:analysis,augmentation,and anti-frequency-variation for single-phase grid-tied inverter”，IET Power Electronics,2018 一文中所应用的高阶基本重复控制器即为本发明h阶(nk±m)次谐波重复控制器当h＝2、n＝1、m＝0时的特例；又如Ramos G A等人所著的“Power factor correction and harmonic compensation using second-order odd-harmonic repetitive control”，IET control theory&applications一文中所应用到的高阶奇次谐波重复控制器即为本发明h阶(nk±m)次谐波重复控制器当h＝2、n＝4、m＝1时的特例，因此，本申请所给出的h阶(nk±m)次谐波重复控制器具有通用性。
3、本发明提供的重复控制器进一步拓展而成的h阶(nk±m)次谐波重复控制器(h≥2)具有更快的误差收敛速度，并且当内模与周期信号在谐振频率点附近发生失配时，对其具有一定的抑制作用，进而使控制器的性能得到提升。
4、本发明提供的重复控制器专门针对(nk±m)次谐波信号进行无误差跟踪或扰动消除，可以根据消除谐波扰动信号或跟踪参考信号的实际需求，定制不同的n和m的数值。如针对三相逆变中消除(6k±l)次谐波及跟踪基波参考信号的需要，只需令n＝6和m＝1即可；对单相逆变中消除奇次谐波及跟踪基波参考信号的需要，只需令n＝4和m＝1即可。并且，本发明提供的重复控制器中三个延迟环节完全相同，其延迟时间τ都等于基波周期T 0的1/n倍，最长延迟时间路径由两个上述延迟环节组成，因此其总延迟时间为(2T 0/n)＜T 0，因此在重复控制增益k rc相同的情况下，本发明提供的重复控制器的响应速度要比一般的重复控制器快得多，其消除扰动的速度大大提高。
5、本发明提供的多模重复控制器可以用来消除所有次谐波或任意次谐波，并可独立调节各次谐波控制器的控制增益。
6、本发明提供的重复控制器除三个时间延迟模块及重复控制增益模块外，仅需要一个正前馈系数模块，控制器结构简单，便于设计。
7、本发明提供的重复控制器用来消除nk+m和nk-m这两种频率之比不为整数倍关系的扰动时只需要一种时间延迟环节来构造扰动信号内模，因此简化了重复控制器中时间延迟环节的设计。
8、本发明提供的重复控制器中三个延迟环节完全相同，占用的内存单元数目都为N/n，因此其总内存单元数目为(3N/n)，(nk±m)次谐波数字重复控制器占用的存储单元的数目也大大低于一般的数字重复控制器。
附图说明
为了更清楚地说明本发明实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1是本发明提出的(nk±m)次谐波重复控制器的结构框图。
图2是图1的数字实现形式，为(nk±m)次谐波数字重复控制器的结构框图。
图3是本发明提出的(nk±m)次谐波重复控制器的数字形式中位于前向通路的周期信号发生器的结构框图。
图4是在图1基础上加入低通滤波环节和相位超前补偿环节的改进的(nk±m)次谐波重复控制器的结构框图。
图5是图4的数字实现形式，为改进的(nk±m)次谐波数字重复控制器的结构框图。
图6是在图2的基础上扩展为h阶的(nk±m)次谐波数字重复控制器(h≥2)的结构框图。
图7为改进的h阶的(nk±m)次谐波数字重复控制器(h≥2)的结构框图。
图8是以h取2时为例的改进的h阶(nk±m)次谐波数字重复控制器的结构框图。
图9是将本发明所提出的(nk±m)次谐波重复控制器并联相加而成的并联结构所有次谐波重复控制器的结构框图，该结构重复控制器可对所有次谐波进行消除。
图10是将本发明所提出的(nk±m)次谐波重复控制器并联相加而成的并联结构任意次谐波重复控制器的结构框图，该结构重复控制器可对任意次谐波进行消除。
图11是图9的数字实现形式，为并联结构所有次谐波数字重复控制器的结构框图。
图12是图10的数字实现形式，为并联结构任意次谐波数字重复控制器的结构框图。
图13是在图9的基础上加入低通滤波环节和相位超前补偿环节的改进的并联结构所有次谐波重复控制器的结构框图。
图14是在图10的基础上加入低通滤波环节和相位超前补偿环节的改进的并联结构任意次谐波重复控制器的结构框图。
图15是图13的数字实现形式，为改进的并联结构所有次谐波数字重复控制器的结构框图。
图16是图14的数字实现形式，为改进的并联结构任意次谐波数字重复控制器的结构框图。
图17是改进的(nk±m)次谐波数字重复控制器叠加一般反馈控制器的控制系统结构框图。
图18是改进的h阶(nk±m)次谐波数字重复控制器(h≥2)叠加一般反馈控制器的控制系统结构框图。
图19是将本发明所提出的(nk±m)次谐波重复控制器令n＝1和m＝0和令n＝4和m＝1时的控制器结合一般反馈控制器应用时的两种复合控制下的稳态输出波形和误差收敛变化图。
图20是将本发明所提出的(nk±m)次谐波重复控制器令n＝1和m＝0和令n＝6和m＝1时的控制器结合一般反馈控制器应用时的两种复合控制下的稳态输出波形和误差收敛变化图。
图21是以6k±1 RC与二阶6k±1 RC为例，当参考电压频率从50Hz变为49.8Hz时，即控制器内模与所需要跟踪或消除的周期信号发生失配时，两种控制器的控制效果对比图。
图22是本发明所提出的(nk±m)次谐波数字重复控制器或多模数字重复控制器或h阶(nk±m)次谐波数字重复控制器以级联方式加入到控制系统中的控制框图。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚，下面将结合附图对本发明实施方式作进一步地详细描述。
实施例一：
本实施例提供一种重复控制器，所述重复控制器包括：重复控制增益模块、正前馈增益模块、一个减法环、二个加法环和三个相同的时间延迟模块；
其中，重复控制增益模块的输入端作为所述重复控制器的输入端，重复控制增益模块的输出端作为第一加法环的第一输入端，第一加法环的输出端作为第二加法环的第一输入端，第二加法环的输出端分别串接正前馈增益模块和第一时间延迟模块后接减法环的正输入端和负输入端，减法环的输出端串接第二时间延迟模块后接第一加法环的第二输入端，同时也是重复控制器的输出端，正前馈增益模块的输出端串接第三时间延迟模块后接第二加法环的第二输入端。
如图1所示，为本申请提供的定制式谐波重复控制器的结构框图，c(s)为重复控制器的输出量，e(s)为重复控制器的输入量亦即控制系统的控制误差量，k rc为重复控制增益模块。
该定制式谐波重复控制器传递函数为：
Figure PCTCN2020127928-appb-000008
式(1)中，k rc为重复控制增益系数，T 0为基波周期，T 0＝2π/ω 0＝l/f 0，f 0为基波频率，ω 0为基波角频率，n、k和m为不小于零的整数且n≠0，n>m；e为自然常数。
通过调节增益系数k rc的数值，可以改变系统的误差收敛速度，k rc越大，系统稳态误差收敛的速度越快，但k rc过大会导致系统超出稳定范围，所以k rc只能在一定范围内提高系统的收敛速度。
图1中的三个延迟环节完全相同，其延迟时间τ都等于基波周期T 0的1/n倍，最长延迟时间路径由两个上述延迟环节组成，因此其总延迟时间为(2T 0/n)＜T 0，因此在重复控制增益k rc相同的情况下，本申请提出的定制式谐波重复控制器的响应速度要比一般的重复控制器快得多，这是(nk±m)次谐波重复控制器的一大优点，并且控制器除三个相同的时间延迟环节及重复控制增益模块外，仅存在一个正前馈增益模块，使得控制器的结构简单，设计更加便捷。
式(1)变形如下：
Figure PCTCN2020127928-appb-000009
上式要求m≠0；
当m＝0时，消除(nk±m)次谐波的重复控制器传递函数可以化成如下形式：
Figure PCTCN2020127928-appb-000010
综合上述两式，因此可得图1所示的重复控制器的极点在频率为(nk±m)ω 0处，即极点频率为mω 0，(n±m)ω 0，(2n±m)ω 0，(in±m)ω 0，...，(其中i＝1,2,3...)。
由于该重复控制器在频率为(nk±m)ω 0处的增益为无穷大，因此能够彻底消除控制误差e(s)中的频率为(nk±m)ω 0的谐波分量，从而实现对(nk±m)次谐波扰动的完全消除或无误差跟踪，故将该重复控制器，即本发明所提出的定制式谐波重复控制器，称为(nk±m)次谐波重复控制器。
实际应用当中，可针对不同场合的需求，赋予m和n以不同的数值，即可实现对特定(nk±m)次谐波的无误差跟踪或扰动抑制。例如对于三相逆变器带三相整流负载的情况，由于其谐波主要集中在(6k±l)次(即5、7、11、13等次)谐波频率分量处，且常需要对基波参考信号进行跟踪，所以只需令n＝6和m＝1,就可实现对基波参考信号的无误差跟踪和对(6k±l)次谐波的完全消除；对于单相逆变器带单相整流负载的情况，由于其谐波主要集中在(4k±l)次(即3、5、7、9等奇次)频率分量处，且常需要对基波参考信号进行跟踪，所以只需令n＝4和m＝1，就可实现对基波参考信号的无误差跟踪和对奇次谐波的完全消除。
实际当中重复控制器多以数字方式加以实现并得以应用。图1所示的重复控制器所对应的数字实现 如图2所示，其传递函数为：
Figure PCTCN2020127928-appb-000011
其中c(z)为重复控制器的输出量，e(z)为重复控制器的输入量亦即控制系统的控制误差量，k rc为重复控制增益，N＝T 0/T s为整数，T 0为基波周期，T 0＝2π/ω 0＝l/f 0，f 0为基波频率，ω 0为基波角频率，T s为采样周期，n、k和m为不小于零的整数且n≠0，n>m。
图2中的三个时间延迟环节完全相同，占用的内存单元数目都为N/n，因此其总内存单元数目为(3N/n)，因此(nk±m)次谐波数字重复控制器占用的存储空间比一般的数字重复控制器要少得多。
图3所示为本发明提出的(nk±m)次谐波重复控制器中位于前向通路的周期信号发生器的数字形式，由三个完全相同的时间延迟模块和一个正前馈增益模块构成，其传递函数M(z)可表示为：
Figure PCTCN2020127928-appb-000012
在实际应用中，为提高控制系统的稳定性和抗干扰能力，通常需要对图1或图2中的(nk±m)次谐波重复控制器加以改进，改进的方法是在重复控制器中加入低通滤波器环节Q(s)或Q(z)和相位超前补偿环节A(s)或A(z)，如图4和图5所示，其中图5是图4的数字实现形式。
图4所示的改进的(nk±m)次谐波重复控制器的传递函数可以写成如下形式：
Figure PCTCN2020127928-appb-000013
图5所示的改进的(nk±m)次谐波数字重复控制器的传递函数可以写成如下形式：
Figure PCTCN2020127928-appb-000014
图6所示为h阶(nk±m)次谐波数字重复控制器(h≥2)的通用结构框图，在实际应用中，h阶(nk±m)次谐波重复控制器同样是以数字方式实现的，其传递函数可以写成如下形式：
Figure PCTCN2020127928-appb-000015
其中
Figure PCTCN2020127928-appb-000016
图7所示为改进的h阶(nk±m)次谐波数字重复控制器(h≥2)，与一阶(nk±m)次谐波数字重复控制器所不同的是，由于阶数的增加，如果依然在三个相同的时间延迟模块的输出端分别串接低通滤波器Q(z)进行滤波，那么必然会造成控制器的复杂程度大大增加，设计难度也会大大增加，因此本发明所提出的h阶(nk±m)次谐波数字重复控制器当h≥2时，统一将低通滤波器Q(z)串接在
Figure PCTCN2020127928-appb-000017
后即可，并依然在重复控制器的输出端串接相位超前补偿模块A(z)，改进的h阶(nk±m)次谐波数字重复控制器(h≥2)传递函数可以写成如下形式：
Figure PCTCN2020127928-appb-000018
其中
Figure PCTCN2020127928-appb-000019
图8所示为h取2时的h阶(nk±m)次谐波数字重复控制器的例子，为避免因阶数增加导致控制器的复杂程度与设计难度增加，通常来讲二阶就足够了，即二阶(nk±m)次谐波数字重复控制器，其传递函数如下：
Figure PCTCN2020127928-appb-000020
其中
Figure PCTCN2020127928-appb-000021
图9所示为由本发明所提的(nk±m)次谐波重复控制器并联相加而成的并联结构所有次谐波重复控制器，对于n、m、k的不同取值，该结构重复控制器可以对所有次谐波进行消除，并且可以独立调节各次谐波的控制增益，其传递函数如下：
Figure PCTCN2020127928-appb-000022
其中，n和m都为正整数，且当n为偶数时，m＝0，1…n/2；当n为奇数时，m＝0，1…[n/2]。
图10所示为由本发明所提的(nk±m)次谐波重复控制器并联相加而成的并联结构任意次谐波重复控制器，对于n、m、k的不同取值，该结构重复控制器可以对任意次谐波进行消除，并且可以独立调节各次谐波的控制增益，其传递函数如下：
Figure PCTCN2020127928-appb-000023
其中，n i、m i为任意正整数。
图11所示为由本发明所提的(nk±m)次谐波重复控制器并联相加而成的并联结构所有次谐波重复控制器的数字形式，其传递函数为：
Figure PCTCN2020127928-appb-000024
其中，n和m都为正整数，且n为偶数时，m＝0，1…n/2；当n为奇数时，m＝0，1…[n/2]。
图12所示为由本发明所提的(nk±m)次谐波重复控制器并联相加而成的并联结构任意次谐波重复控制器的数字形式，其传递函数为：
Figure PCTCN2020127928-appb-000025
其中，n i、m i为任意正整数。
图13所示为加入低通滤波环节Q(s)和相位超前补偿环节A(s)的改进的并联结构所有次谐波重复控制器的结构框图，其传递函数为：
Figure PCTCN2020127928-appb-000026
其中，n和m都为正整数，且n为偶数时，m＝0，1…n/2；当n为奇数时，m＝0，1…[n/2]。
图14所示为加入低通滤波环节Q(s)和相位超前补偿环节A(s)的改进的并联结构任意次谐波重复控制器的结构框图，其传递函数为：
Figure PCTCN2020127928-appb-000027
其中，n i、m i为任意正整数。
图15所示为改进的并联结构所有次谐波数字重复控制器的结构框图，其传递函数为：
Figure PCTCN2020127928-appb-000028
其中，n和m都为正整数，且n为偶数时，m＝0，1…n/2；当n为奇数时，m＝0，1…[n/2]。
图16所示为改进的并联结构任意次谐波数字重复控制器的结构框图，其传递函数为：
Figure PCTCN2020127928-appb-000029
其中，n i、m i为任意正整数。
实施例二：
上述实施例一所给出的(nk±m)次谐波重复控制器以及进一步扩展得到的h阶(nk±m)次谐波数字重复控制器，可以以插入或级联方式加入到一般的反馈控制系统中用于消除控制误差当中的(nk±m)次谐波分量。以下分别对(nk±m)次谐波重复控制器以及进一步扩展得到的h阶(nk±m)次谐波数字重复控制器以插入方式加入到一般反馈系统中进行介绍：
(一)对于(nk±m)次谐波重复控制器
本实施例以将(nk±m)次谐波数字重复控制器以插入方式加入到一般反馈系统中为例，介绍本发明所提出的(nk±m)次谐波重复控制器的具体实施方式：
图17所示是将改进的(nk±m)次谐波数字重复控制器加入到一般反馈控制系统中的结构框图，其中，G rc(z)为改进的(nk±m)次谐波数字重复控制器，G c(z)为常规反馈控制器，G p(z)为控制对象，y d(z)为系统的参考输入且一般为基波参考信号y(z)为系统实际输出，e(z)为参考与实际信号的误差同时也是重复控制器G rc(z)的输入信号，c(z)为重复控制器G rc(z)的输出信号同时也与误差信号e(z)相加后一起作为常规反馈控制器G c(z)的输入，u(z)为常规反馈控制器G c(z)的输出信号同时也是控制对象G p(z)的输入信号，d(z)为系统的扰动输入信号，它与控制对象G p(z)的输出信号相加形成实际输出信号y(z)。
图18所示是将改进的h阶(nk±m)次谐波数字重复控制器(h≥2)加入到一般反馈控制系统中的结构框图，高阶(nk±m)次谐波数字重复控制器同样是以插入式的方式加入到一般反馈控制系统中。
为验证本发明所提出的(nk±m)次谐波重复控制器的有效性与实用性，进行了基于Matlab/Simulink的仿真实验如下：
对于单相逆变器带单相整流负载的情况，由于其谐波主要集中在(4k±l)次(即3、5、7、9等奇次)频率 分量处，且常需要对基波参考信号进行跟踪，所以只需令n＝4和m＝1，就可实现对基波参考信号的无误差跟踪和对奇次谐波的完全消除，控制目标为使输出电压精确跟踪参考电压，其中参考电压V ref＝156sin100πt，如图19所示为在FC(状态反馈控制器)的基础上，t＝0.1s时，重复控制增益k rc相同的情况下，分别加入传统重复控制器(Zhou K,Wang D，“Digital repetitive learning controller for three-phase CVCF PWM inverter[J]”，IEEE Transactions on Industrial Electronics,2001)即CRC控制器和本申请所提出的4k±1RC控制器的两种复合控制下的稳态输出波形和误差收敛变化图，其中图19(a)对应于CRC控制器，图19(b)对应于本申请提出的4k±1RC控制器。
根据图19(a)和(b)可知，分别采用CRC和4k±1RC后，其总谐波畸变率(Total Harmonic Distortion，THD)分别为0.57％和1.1％，都可以达到非常小的数值，但是在具有与CRC几乎同样的谐波抑制效果的同时，CRC需要约0.7s达到稳态；而本申请对应的4k±1RC则仅需要约0.35s达到稳态，因此4k±1RC的误差收敛速度约为CRC的2倍，即本申请对应的4k±1RC的误差收敛速度明显较快。
而对于三相逆变器带三相整流负载的情况，由于其谐波主要集中在(6k±l)次(即5、7、11、13等次)谐波频率分量处，且常需要对基波参考信号进行跟踪，所以只需令n＝6和m＝1，就可实现对基波参考信号的无误差跟踪和对(6k±l)次谐波的完全消除，控制目标为使输出电压精确跟踪参考电压，其中参考电压V abref＝220sin100πt、V bcref＝220sin(100πt-2/3π)、V caref＝220sin(100πt+2/3π)，如图20所示为在FC(状态反馈控制器)的基础上，t＝0.1s时，重复控制增益k rc相同的情况下，分别加入CRC控制器和本申请所提出的6k±1 RC控制器的两种复合控制下的稳态输出波形和误差收敛变化图，其中图20(a)对应于CRC控制器，图20(b)对应于本申请提出的6k±l RC控制器。
根据图20(a)和(b)可知，分别采用CRC和6k±1 RC后其总谐波畸变率(Total Harmonic Distortion，THD)分别为0.38％和1.05％，都可以达到非常小的数值，但是在具有与CRC几乎同样的谐波抑制效果的同时，CRC需要约0.75s达到稳态；而本申请对应的6k±1 RC则仅需要约0.25s达到稳态，因此6k±1 RC的误差收敛速度约为CRC的3倍，即本申请对应的6k±1 RC的误差收敛速度明显较快。
(二)对于h阶(nk±m)次谐波重复控制器
本发明所提(nk±m)次谐波重复控制器可进一步扩展为h阶(nk±m)次谐波数字重复控制器(h≥2)，此处以6k±1 RC与二阶6k±1 RC为例，通过具体仿真实例验证了高阶(nk±m)次谐波数字重复控制器相较于一阶(nk±m)次谐波数字重复控制器，性能有所提升，可以一定程度抑制控制器内模与所需要跟踪或消除的周期信号在谐振频率点附近发生的失配，并且具有更快的误差收敛速度。
如图21所示为频率从50Hz变为49.8Hz时，在FC(状态反馈控制器)的基础上，t＝0.1s时，重复控制增益k rc相同的情况下，分别加入6k±1 RC控制器和所提出的二阶6k±1 RC控制器的两种复合控制下的误差收敛变化图和谐波频谱图，其中图21(a)对应于6k±1 RC控制器，图21(b)对应于二阶6k±1 RC控制器。
根据图21(a)和(b)可知，采用6k±1 RC控制器的误差收敛时间与总谐波畸变率(Total Harmonic Distortion，THD)分别为0.3s和1.59％，而采用二阶6k±1 RC控制器的误差收敛时间与总谐波畸变率(Total Harmonic Distortion，THD)分别为0.2s和1.42％，因此，二阶6k±1 RC控制器在控制器内模与所需要跟踪或消除的周期信号在谐振频率点附近发生失配时，具有更快的误差收敛速度和更低的总谐波畸 变率。
实施例三：
上述实施例一所给出的(nk±m)次谐波数字重复控制器以及进一步扩展得到的h阶(nk±m)次谐波数字重复控制器、并联结构所有次/任意次谐波数字重复控制器可以以插入或级联方式加入到一般的反馈控制系统中用于消除控制误差当中的(nk±m)次谐波分量，实施例二给出了(nk±m)次谐波重复控制器及h阶(nk±m)次谐波数字重复控制器以插入方式加入到一般的反馈控制系统的具体实施方式及仿真实验，本实施例介绍以级联方式加入到一般的反馈控制系统的具体实施方式。
图22所示是将改进的(nk±m)次谐波数字重复控制器或并联结构重复控制器或h阶(nk±m)次谐波数字重复控制器以级联方式加入到一般反馈控制系统中的结构框图，其中，G rc(z)为改进的(nk±m)次谐波数字重复控制器，G c(z)为常规反馈控制器，G p(z)为控制对象，y d(z)为系统的参考输入且一般为基波参考信号y(z)为系统实际输出，e(z)为参考与实际信号的误差同时也是重复控制器G rc(z)的输入信号，c(z)为重复控制器G rc(z)的输出信号同时也与误差信号e(z)相加后一起作为常规反馈控制器G c(z)的输入，u(z)为常规反馈控制器G c(z)的输出信号同时也是控制对象G p(z)的输入信号，d(z)为系统的扰动输入信号，它与控制对象G p(z)的输出信号相加形成实际输出信号y(z)。
本发明实施例中的部分步骤，可以利用软件实现，相应的软件程序可以存储在可读取的存储介质中，如光盘或硬盘等。
以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (8)

  1. 一种重复控制器，其特征在于，所述重复控制器包括：重复控制增益模块、正前馈增益模块、一个减法环、二个加法环和三个相同的时间延迟模块；
    其中，重复控制增益模块的输入端作为所述重复控制器的输入端，重复控制增益模块的输出端作为第一加法环的第一输入端，第一加法环的输出端作为第二加法环的第一输入端，第二加法环的输出端分别串接正前馈增益模块和第一时间延迟模块后接减法环的正输入端和负输入端，减法环的输出端串接第二时间延迟模块后接第一加法环的第二输入端，同时也是重复控制器的输出端，正前馈增益模块的输出端串接第三时间延迟模块后接第二加法环的第二输入端。
  2. 根据权利要求1所述的重复控制器，其特征在于，所述重复控制器还包括：低通滤波器和相位超前补偿模块；
    所述三个相同的时间延迟模块后分别串联一个低通滤波器，所述减法环的输出端串接第二时间延迟模块后接相位超前补偿模块。
  3. 一种h阶重复控制器，h≥2，其特征在于，所述h阶重复控制器由权利要求1所述的重复控制器扩展得到，扩展方法为：将∑w hM h()进行从1到h的累和作为控制器前向通路，并以输出正反馈形式来构造周期信号的内模，其中w h为常系数，M()为三个时间延迟模块和正前馈增益模块构成的周期信号发生器。
  4. 一种重复控制器的控制方法，其特征在于，所述方法用于利用权利要求1或2所述的重复控制器或权利要求3所述的h阶重复控制器进行消除(nk±m)次谐波，n、k和m为不小于零的整数且n≠0，n>m，所述方法包括：
    重复控制增益模块：将重复控制器的输入量经过重复控制增益后得到重复控制增益模块的输出量；
    正前馈增益模块：将第二加法环的输出量经过正前馈增益模块后得到正前馈增益模块输出量；
    第一加法环：将重复控制增益模块输出量与第二时间延迟模块延迟输出的减法环输出量相加得到第一加法环输出量；
    第二加法环：将第一加法环的输出量与第三时间延迟模块延迟输出的正前馈增益模块输出量相加得到第二加法环输出量；
    减法环：将正前馈增益模块的输出量与第一时间延迟模块延迟输出的第二加法环输出量相减得到减法环的输出量；
    第一时间延迟模块：将第二加法环输出量延迟输出；
    第二时间延迟模块：将减法环输出量延迟输出；
    第三时间延迟模块：将正前馈增益模块输出量延迟输出。
  5. 根据权利要求4所述的方法，其特征在于，所述方法还包括：
    通过调节重复控制增益实现调节所述重复控制器跟踪或消除特定次谐波的速度，也即所述重复控制器的输出信号与参考信号之间误差的收敛速度。
  6. 根据权利要求4或5所述的方法，其特征在于，所述方法还包括：
    根据所需要跟踪或消除的谐波次数确定正前馈增益模块的参数。
  7. 根据权利要求4-6任一所述的方法，其特征在于，所述时间延迟模块为模拟或数字时间延迟模块，所述重复控制器的传递函数如下：
    Figure PCTCN2020127928-appb-100001
    或
    Figure PCTCN2020127928-appb-100002
    其中，c()为重复控制器的输出量，e()为重复控制器的输入量即控制系统的控制误差量，k rc为重复控制增益参数，s为连续时间系统的拉普拉斯变量，z为离散时间系统的z变换的变量；N＝T 0/T s为整数，T 0为基波周期，T 0＝2π/ω 0＝l/f 0，f 0为基波频率，ω 0为基波角频率，T s为采样周期，n、k和m为不小于零的整数且n≠0，n>m。
  8. 根据权利要求4-7任一所述的方法，其特征在于，所述方法还包括：将权利要求1或2所述的重复控制器以插入方式加入到反馈控制系统中用于消除控制误差当中的(nk±m)次谐波分量，当以插入方式加入到反馈控制系统时，重复控制器的传递函数为：
    Figure PCTCN2020127928-appb-100003
    其中，Q(z)为低通滤波器，A(z)为相位超前补偿模块；
    所述反馈控制系统在满足下述两个条件时是稳定的：
    ①未插入重复控制器前的闭环系统传递函数的极点位于单位圆内；
    ②所述插入的控制器中的重复控制增益参数k rc满足0<k rc<2。
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