Amplitude-phase compensation generalized repetitive control system design method, equipment and medium

Abstract

The invention relates to the field of intelligent control system design, and discloses an amplitude-phase compensation generalized repetitive control system design method, equipment and a medium, and the method comprises the steps: constructing a generalized improved repetitive controller to adjust control and learning behaviors, and compensating the influence of a low-pass filter on the amplitude and phase of a passing signal; proving the system stability by using a small gain theorem; evaluation indexes irrelevant to errors are obtained through recursive iteration and matrix differential equation solving derivation, and the flexibility and optimization capacity of system design are improved. The method has the beneficial effect that the periodic signal tracking precision of the repetitive control system is remarkably improved. According to the method, an error-independent evaluation function is innovatively introduced, and the limitation that a traditional repetitive controller depends on tracking error evaluation is broken through, so that the flexibility and optimization capability of system design are improved, technical guidance is provided for solving the tracking problem of periodic signals in an actual system, and the method has important theoretical and application values.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control system design, and in particular to a design method, equipment and medium for an amplitude-phase compensated generalized repetitive control system. Background Art

[0002] In actual control engineering, periodic control tasks are widely used in many industrial and automation systems. These systems need to accurately control periodic signals to ensure their stability and efficient operation.

[0003] Traditional controllers rely on fixed models and parameters to complete tasks, but these methods often fail to meet high-precision requirements when faced with periodic control problems. For this reason, repetitive controllers have emerged, specifically for optimizing the control of periodic tasks. Unlike ordinary controllers, repetitive controllers not only have basic control functions, but also have learning capabilities. By continuously adjusting the control process within each cycle, the control effect is gradually optimized, thereby achieving accurate tracking of periodic signals.

[0004] Basic repetitive control is only applicable to controlled objects with direct input-output terms. In order to expand its application scope, a low-pass filter is usually introduced before the time-delay link to ensure the stability of the system and form an improved repetitive controller. However, the traditional improved repetitive controller only uses one gain, which makes it impossible to adjust the control and learning behaviors independently, thus limiting its flexibility. To solve this problem, the generalized repetitive controller (GRC) introduces two independent gains, control gain and learning gain, to adjust the control and learning behaviors respectively through structural adjustments, which significantly enhances the controller's adjustment ability.

[0005] Although generalized repetitive control has significant advantages in solving this problem, it still faces two major challenges: first, the low-pass filter causes the amplitude and phase of the signal to change, which in turn affects the gain of the baseband controller, which has a serious impact on the steady-state tracking performance of the system; second, when designing the gain of the repetitive controller, it usually relies on an error-related evaluation function, which makes the parameter selection complicated and unintuitive. Therefore, according to the system characteristics, compensating for the amplitude and phase deviation caused by the low-pass filter and proposing an error-independent evaluation index have important theoretical and application value for promoting the development of repetitive control theory and guiding production operations in actual industrial processes. Summary of the invention

[0006] The purpose of the present invention is to propose a design method, device and medium for an amplitude-phase compensated generalized repetitive control system, so as to solve the technical problems in the existing generalized repetitive control system that the amplitude and phase difference of the fundamental wave caused by the low-pass filter leads to low tracking accuracy and control limitations of the repetitive control system.

[0007] Specifically, the present invention provides a method for designing an amplitude-phase compensated generalized repetitive control system, comprising the following steps:

[0008] S1. Constructing a generalized repetitive control system; the generalized repetitive control system comprises: a controlled object, a generalized improved repetitive controller with amplitude and phase compensation, and a state feedback controller; the generalized improved repetitive controller introduces a constant in a time-delay loop of the repetitive controller and adjusts the time-delay parameter;

[0009] S2. The original structure diagram of the generalized repetitive control system is transformed into an equivalent structure diagram through structural transformation, and on this basis, the asymptotic stability of the system is proved by using the small gain theorem;

[0010] S3. Through recursive iteration and solving matrix differential equations, an evaluation index independent of the error is obtained, and the repetitive controller and state feedback controller gains are designed based on the index.

[0011] A storage medium stores instructions and data for implementing a design method for an amplitude-phase compensated generalized repetitive control system.

[0012] A device for designing an amplitude-phase compensated generalized repetitive control system comprises: a processor and a storage medium; the processor loads and executes instructions and data in the storage medium to implement a method for designing an amplitude-phase compensated generalized repetitive control system.

[0013] The beneficial effect provided by the present invention is: significantly improving the tracking accuracy of periodic signals in repetitive control systems. This method breaks through the limitation of traditional repetitive controllers relying on tracking error evaluation by innovatively introducing an error-independent evaluation function, thereby improving the flexibility and optimization capability of system design, providing technical guidance for solving the tracking problem of periodic signals in actual systems, and having important theoretical and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic flow chart of the method of the present invention;

[0015] Figure 2 is a system structure block diagram in an embodiment of the present invention;

[0016] Figure 3 In the embodiment of the present invention Figure 2 Equivalent structural block diagram of ;

[0017] Figure 4 This is a tracking error effect diagram in an embodiment of the present invention;

[0018] Figure 5 1 is a diagram showing the effect of the embodiment of the present invention with and without amplitude and phase compensation errors;

[0019] Figure 6It is a schematic diagram of the working of the hardware device of an embodiment of the present invention. DETAILED DESCRIPTION

[0020] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0021] Before formally describing the present invention, the scheme of the present invention is first generally described for easy understanding.

[0022] Please refer to Figure 1 The present invention provides a method for designing an amplitude-phase compensated generalized repetitive control system, comprising the following steps:

[0023] S1. Constructing a generalized repetitive control system; the generalized repetitive control system comprises: a controlled object, a generalized improved repetitive controller with amplitude and phase compensation, and a state feedback controller; the generalized improved repetitive controller introduces a constant in a time-delay loop of the repetitive controller and adjusts the time-delay parameter;

[0024] Please refer to Figure 2 , Figure 2 It is a structural block diagram of the generalized repetitive control system of the present invention.

[0025] In step S1, an amplitude-phase compensation generalized repetitive controller structure that compensates for amplitude and phase deviation is used to improve the steady-state tracking performance of the periodic signal, as follows:

[0026] In the generalized improved repetitive controller, by applying a first-order low-pass filter q(s) = ω c / (s+ω c ) can be analyzed and its transfer function is

[0027]

[0028] Among them, ω c represents the cutoff frequency of the low-pass filter; s represents the Laplace operator; ω r =2π / T r , T r represents the period of the reference input signal, and e is a natural constant.

[0029] Analyzing the above formula, we can see that for frequency ω r After the signal passes through a first-order low-pass filter, the amplitude becomes the original The phase lag is (1 / ω r )arctan(ω r / ω c ), which leads to a decrease in the repetitive controller gain at the fundamental frequency, resulting in a larger steady-state tracking error.

[0030] In order to improve the tracking accuracy of the periodic signal, a constant gain is added to the positive feedback loop. And the time lag constant T r Change to T=T r -(1 / ω r )arctan(ω r / ω c ), improve the high-precision control of periodic signals in repetitive control systems, and its state space equation is

[0031]

[0032] Among them, x I (t) is the state variable of the repetitive controller, For x I The derivative of (t), e(t) = r(t)-y(t), r(t) is the reference input, y(t) is the system output. The corresponding transfer function is:

[0033]

[0034] Among them, K C and K L is the repetitive controller gain.

[0035] S2. The original structure diagram of the generalized repetitive control system is transformed into an equivalent structure diagram through structural transformation, and on this basis, the asymptotic stability of the system is proved by using the small gain theorem;

[0036] The controlled object expression is

[0037]

[0038] Among them, x P (t) is the state of the controlled object, For x P (t), A is the system state coefficient matrix; B is the system input coefficient matrix; C is the system output coefficient matrix.

[0039] Let r(t) = 0, in order to analyze the stability of the control system, Figure 2 The control system structure can be converted into Figure 3 For a stable low-pass filter q(s), if the following conditions are met: 1) it is Hurwitz; 2) || k m q(I+GK C -GK L )(I+GK C ) -1 || ∞ <1. Then the system is stable in sliding mode. Here, G=C[sI-(A+BKp )] -1 B.

[0040] S3. Through recursive iteration and solving matrix differential equations, an evaluation index independent of the error is obtained, and the repetitive controller and state feedback controller gains are designed based on the index.

[0041] Step S3 is specifically as follows:

[0042] S31. Establish error-independent performance indicators by iterative recursion and solving matrix differential equations Among them, A e =A+BK p -B e1 C, B e1 =BK C , B e2 =BK L , used to select adjustment parameters;

[0043] S32. Solve the Riccati equation to obtain the optimal state feedback controller gain

[0044] S33, combining the stability condition in step S2, using the intelligent optimization algorithm to find the best parameter combination, so that Select K C and K L .

[0045] It should be noted that the intelligent optimization algorithm here includes: any one of a genetic algorithm, a particle swarm optimization algorithm and an adaptive multi-swarm particle swarm optimization algorithm.

[0046] Specifically:

[0047] In order to make the subsequent derivation more intuitive, the symbol (k, τ) is used to represent the time t, where t = kT r +τ. The state space equation of the system can be expressed as:

[0048]

[0049] Ignoring the effect of the low-pass filter on the used signal, the repetitive controller can be rewritten as

[0050] u r (k,τ)=K c e(k,τ)+K L x I (k-1,τ),

[0051] Among them, x I (k,τ)=e(k,τ)+x I (k-1,τ). Through iterative optimization, we can get

[0052]

[0053] Then there is

[0054]

[0055] Substituting it into the state space equation of the system, we have

[0056]

[0057] Among them, A e =A+BK p -B e1 C, B e1 =BK C , B e2 =BK L .

[0058] For a given k and τ, r(k,τ) and e(i,τ) (i=0,1,2,L,k-1) are known, and then the solution to the above matrix differential equation is:

[0059] Then there is

[0060] k=0:

[0061]

[0062] k=1:

[0063]

[0064] In repetitive control, the first cycle focuses on learning and control starts from the second cycle. Control performance depends on the indicator Learning performance depends on the indicator These metrics are directly determined by the controller gains and can evaluate control and learning performance without calculating tracking errors. They provide clear guidance for system design and help optimize J C and J L To meet different application requirements.

[0065] The parameter design process includes: selecting the appropriate low-pass filter frequency to meet ω c ≥5ω r ; By minimizing the performance evaluation index

[0066]

[0067] To design the state feedback controller gain K P , where Q S and RS is the weight matrix. By solving the algebraic Riccati equation:

[0068]

[0069] Get the optimal state feedback control gain:

[0070]

[0071] Design evaluation indicators according to actual needs, such as Design K to meet the system stability conditions C and K L .

[0072] Embodiment 1:

[0073] In this embodiment, for a given system, a control target is set, that is, to achieve effective tracking of periodic signals. The periodic reference input is set to r(t) = 2sin2πt. The experimental results are shown in Figure 4 The experimental results show that a design method of amplitude-phase compensation generalized repetitive control system based on error-independent evaluation function enables the system to have satisfactory periodic signal tracking performance. In order to highlight the effectiveness of the present invention, Figure 5 The comparison of tracking errors with and without amplitude-phase compensation shows that amplitude-phase compensation can effectively improve the steady-state tracking performance of periodic signals.

[0074] Embodiment 2:

[0075] See also Figure 6 , Figure 6 4 is a schematic diagram of the working of the hardware device of an embodiment of the present invention, wherein the hardware device specifically comprises: an amplitude-phase compensated generalized repetitive control system design device 401, a processor 402 and a storage medium 403.

[0076] An amplitude-phase compensated generalized repetitive control system design device 401: The amplitude-phase compensated generalized repetitive control system design device 401 implements the amplitude-phase compensated generalized repetitive control system design method.

[0077] Processor 402: The processor 402 loads and executes the instructions and data in the storage medium 403 to implement the amplitude-phase compensated generalized repetitive control system design method.

[0078] Storage medium 403: The storage medium 403 stores instructions and data; the storage medium 403 is used to implement the amplitude-phase compensated generalized repetitive control system design method.

[0079] The beneficial effects of the present invention are as follows: the present invention provides a design method for a generalized repetitive control system with amplitude and phase compensation based on an error-independent evaluation function, constructs a generalized improved repetitive controller to adjust the control and learning behavior, and compensates for the influence of the low-pass filter on the amplitude and phase of the passing signal; uses the small gain theorem to prove the stability of the system; and derives error-independent evaluation indicators by recursive iteration and solving matrix differential equations, thereby improving the flexibility and optimization capability of the system design. The beneficial effects of the present invention are that the tracking accuracy of periodic signals in repetitive control systems is significantly improved. This method breaks through the limitations of traditional repetitive controllers that rely on tracking error evaluation by innovatively introducing an error-independent evaluation function, thereby improving the flexibility and optimization capability of the system design, and provides technical guidance for solving the tracking problem of periodic signals in actual systems, and has important theoretical and application value.

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A design method for an amplitude-phase compensated generalized repetitive control system, characterized by: The following steps are involved: S1. Constructing a generalized repetitive control system; the generalized repetitive control system comprises: a controlled object, a generalized improved repetitive controller with amplitude and phase compensation, and a state feedback controller; the generalized improved repetitive controller introduces a constant in a time-delay loop of the repetitive controller and adjusts the time-delay parameter; S2. The original structure diagram of the generalized repetitive control system is transformed into an equivalent structure diagram through structural transformation, and on this basis, the asymptotic stability of the system is proved by using the small gain theorem; S3. Through recursive iteration and solving matrix differential equations, an evaluation index independent of the error is obtained, and the repetitive controller and state feedback controller gains are designed based on the index.

2. The method for designing an amplitude-phase compensated generalized repetitive control system according to claim 1, characterized in that: The transfer function of the generalized improved repetitive controller is: Among them, K C and K L is the gain of the generalized improved repetitive controller; constant gain Parameters introduced for amplitude and phase compensation, q(s) = ω c / (s+ω c ) is a first-order low-pass filter, ω c represents the cutoff frequency of the low-pass filter; s represents the Laplace operator; ω r =2π / T r , T r represents the period of the reference input signal, e is a natural constant; T = T r -(1 / ω r )arctan(ω r / ω c ).

3. A method for designing an amplitude-phase compensated generalized repetitive control system as claimed in claim 2, characterized in that: The expression of the controlled object is as follows: Among them, x P (t) is the state of the controlled object, For x P (t), A is the system state coefficient matrix; B is the system input coefficient matrix; C is the system output coefficient matrix; y(t) is the system output signal.

4. The method for designing an amplitude-phase compensated generalized repetitive control system according to claim 3, characterized in that: In step S2, the small gain theorem is specifically as follows: Let the disturbance signal r(t) = 0. For a stable low-pass filter q(s), the following conditions are met: 1) it is Hurwitz; 2) || k m q(I+GK C -GK L )(I+GK C ) -1 || ∞ <1, then the system is stable in sliding mode, where G = C[sI-(A+BK p )] -1 B.

5. The design method of an amplitude-phase compensated generalized repetitive control system according to claim 4, characterized in that: Step S3 is specifically as follows: S31. Establish error-independent performance indicators J by iterative recursion and solving matrix differential equations C =1+CA e -1 B e1 , J L =1+CA e -1 B e2 ; Among them, A e =A+BK p -B e1 C, B e1 =BK C , B e2 =BK L , used to select adjustment parameters; S32. Solve the Riccati equation to obtain the optimal state feedback controller gain S33, combining the stability condition in step S2, using the intelligent optimization algorithm to find the best parameter combination, so that Select K C and K L .

6. A method for designing an amplitude-phase compensated generalized repetitive control system as claimed in claim 5, characterized in that: The intelligent optimization algorithm in step S33 includes: any one of a genetic algorithm, a particle swarm optimization algorithm and an adaptive multi-swarm particle swarm optimization algorithm.

7. A storage medium, characterized in that: The storage medium stores instructions and data for implementing a method for designing an amplitude-phase compensated generalized repetitive control system as described in any one of claims 1 to 6.

8. A design device for an amplitude-phase compensation generalized repetitive control system, characterized in that: include: A processor and a storage medium; the processor loads and executes instructions and data in the storage medium to implement a method for designing an amplitude-phase compensated generalized repetitive control system as described in any one of claims 1 to 6.

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