An Iterative Learning Control Method for Circuit Systems Based on Observers

Abstract

The present invention discloses an observer-based iterative learning control method for a circuit system. The method first uses a parameter modeling method to establish a circuit system model, and uses a reference track modification method to close the reference track space, that is, when the iteration time is not fixed, the initial value of the reference track of this iteration is equal to the final value of the reference track of the previous iteration. At the same time, an adaptive learning observer is constructed, and a controller based on observer iterative learning control is used to control the circuit system. Compared with traditional control methods that require precise mathematical models, the control algorithm proposed by the present invention is more novel and has simple application conditions. When this method is used for repetitive task operations, it effectively improves the control accuracy and has good engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a circuit system, and in particular to an observer-based iterative learning control method for a circuit system. Background Art

[0002] Circuit system is the core of modern electronic technology and the foundation of electronic equipment and systems. Its development began in the late 19th century and early 20th century, when scientists studied the basic principles of electromagnetic fields and current flow and discovered many basic circuit laws and circuit elements. These discoveries laid the foundation for the development of circuit system. In the early 20th century, circuit system received widespread attention as an important direction of technological development. With the rapid development of semiconductor technology and computer technology, circuit system has been further developed and applied. Circuit system has become an important part of modern industry, military, communication, information processing, home and entertainment and other fields.

[0003] Circuit systems have many different manifestations of complexity, including multiple variables and multiple physical quantities, nonlinear characteristics and complex dynamic behaviors caused by various circuit devices, time-varying, high control difficulty caused by large-scale, randomness caused by noise interference, etc. Considering the complexity of the above aspects, the control of circuit systems is very challenging and requires the research and adoption of advanced technologies and methods to deal with it. Summary of the invention

[0004] The purpose of the present invention is to propose an observer-based iterative learning control method for a circuit system, which can effectively solve the problems of multiple variables and multiple physical quantities, nonlinearity, time-varying, high control difficulty, randomness, etc. existing in the circuit system, and achieve good control effects.

[0005] The specific technical solution of the present invention is as follows: an observer-based circuit system iterative learning control method, comprising the following steps:

[0006] The circuit system model established using the parameter modeling method is as follows:

[0007]

[0008] In the formula, x1, x2 represent the return circuit, R1, R2 represent the resistor, L1, L2 represent the inductor, M represents the mutual inductor, u represents the input voltage, θ T ξ represents input disturbance, П represents input uncertainty, and the system output is y = C T x=x1,T k Indicates the actual iteration duration and satisfies 0<T min ≤T k ≤T.

[0009] Furthermore, by modifying the reference orbit, the reference orbit space is closed, that is, the initial value of the reference orbit of this iteration is equal to the final value of the reference orbit of the previous iteration when the iteration duration is not fixed. The specific steps are as follows:

[0010]

[0011] In the formula, y d (t) represents the original reference orbit of the system, y d，k (t) represents the modified reference orbit, is a differentiable function and satisfies the following requirements:

[0012] ●

[0013] ●

[0014] ● is bounded on [0, T]

[0015] Where T a Indicates the modified length and satisfies 0<T a ≤T k .

[0016] Furthermore, an adaptive learning observer is constructed to estimate the current. The mathematical expression of the observer is as follows:

[0017]

[0018] In the formula, represents the current estimation, A and B are consistent with the coefficients in the circuit model, For The estimated value of is the observer gain, which is an estimate of μ, is the observation output;

[0019] Furthermore, based on the composite energy function, an iterative learning control scheme for the observer-based circuit system involved in the present invention is established as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] Where Γ1, Γ2, Γ3, P are positive definite matrices, and sat represents the saturation limit of the upper and lower bounds of the parameters. The algorithm can ensure the convergence of the virtual estimation error and the virtual tracking error. The proof process is as follows:

[0028] C001: Select a composite energy function of the following form:

[0029] E k (t) = W 1，k (t)+W 2，k (t)+W 3，k (t)+W 4，k (t)

[0030]

[0031] W 2，k (t)=||ε y，k (t)|| 2

[0032]

[0033]

[0034] C002: In the formula,

[0035] C003: Consider the E between the kth and k-1th times k (t) difference ΔE k (t), where:

[0036]

[0037] Where λ1 is the minimum eigenvalue of matrix Q, θ max for The norm upper bound of , L is the unknown Lipschitz constant of the nonlinear function ξ, П max is the upper bound of the norm of П;

[0038]

[0039] Where λ2 is the minimum eigenvalue of the matrix Γ1;

[0040]

[0041]

[0042] C004: Therefore, according to C003, the following formula can be obtained:

[0043]

[0044] C005. Further, considering the boundedness of E1(t), The form is as follows:

[0045]

[0046] C006: The derivation is as follows:

[0047]

[0048]

[0049]

[0050] C007: According to C006, the following formula can be obtained:

[0051]

[0052] C008: In the formula, The derivation results show that E1(t) is bounded;

[0053] C009: Furthermore, the convergence proof of virtual estimation error and virtual tracking error is given:

[0054]

[0055] C010: By E k The positive definiteness of (T) and the boundedness of E1(t) lead to the convergence form of virtual estimation error and virtual tracking error as follows:

[0056]

[0057] BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0059] Figure 2 is a schematic diagram of a circuit system according to an embodiment of the present invention;

[0060] Figure 3 This is the output tracking graph of the fifth iteration of the method proposed in the embodiment;

[0061] Figure 4 This is the output tracking graph of the 10th iteration of the method proposed in the embodiment;

[0062] Figure 5This is the output tracking graph of the 20th iteration of the method proposed in the embodiment; DETAILED DESCRIPTION

[0063] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0064] like Figure 1 As shown, an observer-based circuit system iterative learning control method comprises the following steps:

[0065] Step 1: Set the initial value of the parameter;

[0066] Step 2: Update algorithm parameters;

[0067] Step 3: Generate control input u in real time based on updated algorithm parameters k (t);

[0068] Step 4: According to the control input u k (t) The generated virtual tracking error and the virtual estimation error generated by the observer are used to synchronously update the algorithm parameters;

[0069] Step 5: Repeat steps 3 and 4 until the current iteration ends and the next iteration begins;

[0070] Step 6: An embodiment of the present invention is described below:

[0071] Considering the iterative learning control problem of the circuit system based on the observer, the corresponding mathematical model is:

[0072]

[0073] The system parameters are:

[0074] R1 = 1Ω, R2 = 1Ω is the circuit resistance, L1 = 0.36H, L2 = 0.5H is the inductor, M = 0.15H is the mutual inductor, θ T ξ=x2sin 3 t+0.8sin 2 t sin x1 represents the input disturbance;

[0075] The desired reference orbit is: y d (t) = 12t 2 (1-t); the system's expected running time T is 1s, and the actual running time is T k Evenly distributed over 0.5-1s and

[0076] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 is a schematic diagram of a circuit system of an embodiment of the present invention; applying the proposed method, Figure 3 , 4 , 5 represent the output tracking of the 5th, 10th and 20th iterations of the method proposed in the present invention, respectively. It can be seen from these three figures that the proposed method has a good application effect in the circuit system, and after the 20th iteration, a satisfactory tracking performance can be obtained.

[0077] References

[0078] [1] J.-X.Xu and J.Xu, "Observer based learning control for a class ofnonlinear systems with time-varying parametric uncertainties," IEEETrans.Autom.Control, vol.49, no.2, pp.275-281, Feb.2004.

[0079] [2] Q.Yu and Z.Hou, "Adaptive Fuzzy Iterative Learning Control for High-Speed ​​Trains With Both Randomly Varying Operation Lengths and SystemConstraints," in IEEE Transactions on Fuzzy Systems, vol.29, no.8, pp.2408-2418, Aug.2021.

Claims

1. An observer-based iterative learning control method for a circuit system, characterized in that: The following steps are involved: Use parametric modeling to build circuit system models; By modifying the reference orbit, the reference orbit space is closed, that is, when the iteration time is not fixed, the initial value of the reference orbit of this iteration is equal to the final value of the reference orbit of the previous iteration; Construct an adaptive learning observer and an iterative learning controller based on the observer. The mathematical expression of the observer is as follows: In the formula, represents the current estimation, A and B are consistent with the coefficients in the circuit model, Π represents the input uncertainty, R1, R2 represent the resistance, L1, L2, M represent the inductance, and u k (t) represents the input voltage, θ k represents the unknown matrix time-varying function, For The estimated value of represents a known Lipschitz continuous function associated with the state, is the observer gain, which is μ k The estimated value of θ max for The norm upper bound of , L is the unknown Lipschitz constant of the nonlinear function ξ, Π max is the norm upper bound of Π, is the observation output; Construct virtual estimation error ε x,k (t) and virtual observation error ε y,k (t) are in the following forms: Where, T k Indicates the actual iteration duration and satisfies 0<T min ≤T k ≤T, T represents the expected running time of the system, y d,k (t) represents the modified reference track; Furthermore, an iterative learning control scheme for circuit system trajectory tracking is established as follows: In the formula, Γ1, Γ2, Γ3, P are positive definite matrices, and sat represents the saturation limit of the upper and lower bounds of the parameters; An observer-based iterative learning controller is used to control the circuit system.

2. The observer-based iterative learning control method for circuit systems according to claim 1, characterized in that: The mathematical expression of the circuit system model established using the parameter modeling method is as follows: Where x1, x2 represent the return circuit, u represents the input voltage, ξ represents the known Lipschitz continuous function related to the state, θ represents the unknown matrix time-varying function, θ T ξ together represent the input disturbance.

3. The circuit system iterative learning control method based on observer according to claim 1, characterized in that: By modifying the reference orbit, the reference orbit space is closed, that is, when the iteration time is not fixed, the initial value of the reference orbit of this iteration is equal to the final value of the reference orbit of the previous iteration. The specific steps are as follows: In the formula, y d (t) represents the original reference orbit of the system, is a differentiable function and satisfies the following requirements: · t∈[T a ,T], · t∈[T a ,T], · is bounded on [0,T], Where T a Indicates the modified length and satisfies 0<T a ≤T k .

4. The observer-based iterative learning control method for circuit systems according to claim 1, characterized in that: include: B001: Select the following composite energy function: E k (t)=W 1,k (t)+W 2,k (t)+W 3,k (t)+W 4,k (t) W 2,k (t)=||ε y,k (t)|| 2 B002: wherein B003: Consider the E between the kth and k-1th times k (t) difference ΔE k (t), where: In the formula, λ1 is the minimum eigenvalue of the matrix Q, θ max for The norm upper bound of , L is the unknown Lipschitz constant of the nonlinear function ξ, Π max is the norm upper bound of Π; Where λ2 is the minimum eigenvalue of the matrix Γ1; B004: According to B003, the following formula can be obtained: B005: Further, consider the boundedness of E1(t), The form is as follows: B006: Among them The derivation is as follows: B007: According to B006, the following formula can be obtained: B008: In the formula, The derivation results show that E1(t) is bounded; B009: Further, the convergence proof of virtual current error and virtual tracking error is given: B010: By E k The positive definiteness of (T) and the boundedness of E1(t) lead to the convergence form of virtual current error and virtual tracking error as follows:

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