Circuit system iterative learning control method for processing completely unknown state

Abstract

The invention discloses a circuit system iterative learning control method for processing a completely unknown state. The method constructs an adaptive gain state observer to estimate the current of the circuitry. And converting the matrix parameter uncertainty of the circuit system into a scalar form for analysis. An iterative learning controller based on an iterative attenuation factor is constructed to control a circuit system with completely unknown current. Compared with a traditional control method needing an accurate mathematical model, the control algorithm provided by the invention is more novel and simple in application condition. When the method is used for repeated task operation, the control precision is effectively improved, and the method has good engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a circuit system, and more particularly to an iterative learning control method for a circuit system dealing with completely unknown states. Background Art

[0002] As the core carrier of modern industrial automation, intelligent devices and energy management, the design and application of its control circuit directly affect the stability and efficiency of the system. With the development of power electronics technology and embedded control, the circuit system has evolved from traditional discrete components to integrated and digital directions, and needs to meet complex requirements such as high-precision signal processing, real-time feedback regulation and multi-device collaboration at the same time. The circuit system has many different manifestations of complexity, mainly including multi-variables and multi-physical quantities, non-linear characteristics and complex dynamic behaviors caused by various circuit devices, time-varying nature, high control difficulty caused by large-scale, randomness caused by noise interference, and so on. Considering the complexity in the above aspects, the control of the circuit system is very challenging and requires research and adoption of advanced technologies and methods to handle. Summary of the Invention

[0003] The object of the present invention is to propose an iterative learning control method for a circuit system dealing with completely unknown states, which can effectively solve problems existing in the circuit system such as multi-variables and multi-physical quantities, non-linearity, time-varying nature, high control difficulty, randomness, etc., and achieve good control effects.

[0004] The specific technical solution of the present invention is as follows: An iterative learning control method for a circuit system dealing with completely unknown states, comprising the following steps:

[0005] Consider the following circuit system: In the formula, x k (t)=[x 1,k (t)x 2,k (t)] T represents the loop current, x 1,k (t), x 2,k (t) are sub-states of x k (t), k represents the iteration number, t∈[0, T] represents the system operation time, R 1 , R 2 represents the resistance, L 1 , L 2 , M represent the inductance, u k (t) represents the controller, θ(t) represents the matrix parameter uncertainty, ξ(x k (t)) represents the non-linear function related to x k (t), A, B are consistent with the coefficients in the circuit model, and the system output is yk y(t) = Cx k (t), where C is the system output matrix;

[0006] The reference signal of the system is generated by the following reference model: where x r (t) represents the reference state, u r (t) represents the reference input, y r (t) represents the reference output;

[0007] Construct an adaptive - gain state observer to estimate the unknown current of the circuit system: where x r,k (t) represents the current estimate, represents the adaptive gain of the observer, y r,k (t) represents the observer output;

[0008] Define the error variables as: where e x,k (t) represents the estimation error, e y,k (t) represents the tracking error. Since x k (0) is unknown, it is assumed that ||e x,k (0)|| ≤ β e , where ||·|| represents the Euclidean norm of the vector, β e is an unknown constant greater than zero;

[0009] Construct the Lyapunov function W 1,k (t) as: where P is a positive - definite matrix and satisfies A T P + PA=-Q, PB = C T , where Q is a positive - definite matrix;

[0010] ξ(x k (t)) - ξ(x r,k (t)) satisfies the global Lipschitz condition: ||ξ(x k (t)) - ξ(x r,k (t))|| ≤ β z ||e x,k (t)|| where ξ(x r,k (t)) represents the non - linear function related to x r,k (t), βz is a constant greater than zero;

[0011] W 1,k The derivative of (t) is: where λ min (Q) is the minimum eigenvalue of matrix Q;

[0012] Convert the matrix parameter uncertainty θ(t) of the circuit system into a scalar form β θ , where β θ is a constant greater than zero and satisfies ||θ(t)|| ≤ β θ , Further derivation becomes: where is a constant greater than zero, where ε is a constant greater than zero;

[0013] The constructed controller is as follows:

[0014] The parameter update law is in the following form: where γ 1 , γ 2 represents a gain greater than zero, Λ k is an iterative decay factor that satisfies where τ 1 is a sufficiently large positive constant;

[0015] Construct a composite energy function to analyze the convergence of the tracking error. The proof process is as follows:

[0016] C001: Select a composite energy function of the following form: where

[0017] C002: Consider the difference ΔE k (t) between E k-1 (t) and E k (t), where:

[0018] C003: Because ΔW 2,k (t) continues to be derived as:

[0019] C004: Similar to ΔW 2,k (t), ΔW 3,k (t) is:

[0020] C005: According to C002, C003, and C004, the following formula can be obtained: In the formula,

[0021] C006: According to C005, the following formula can be obtained:

[0022] C007: According to C006, the convergence forms of the estimation error and the tracking error are as follows: In the formula, λ max (P -1 ) is the maximum eigenvalue of matrix P -1 , λ max (C T C) is the maximum eigenvalue of matrix C T C;

[0023] C008: Considering the boundedness of E k (t), according to C006, it can be obtained:

[0024] C009: According to C008, if E 1 (t) is bounded, then E k (t) is bounded. Next, prove the boundedness of E 1 (t):

[0025] C010: According to C009 and it can be obtained that E 1 (t) is bounded. Furthermore, according to C008, it can be obtained that E k (t) is bounded. Description of the Drawings

[0026] Figure 1 is the flowchart of the method according to the embodiment of the present invention;

[0027] Figure 2 is the system output tracking diagram using the method proposed by the present invention;

[0028] Figure 3 is the observer output tracking diagram using the method proposed by the present invention;

[0029] Figure 4 The tracking error convergence graph of the method proposed by the present invention; Detailed implementation mode

[0030] The present invention will be further clarified below in conjunction with embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0031] As Figure 1 shown, a circuit system iterative learning control method for dealing with completely unknown states includes the following steps:

[0032] Step 1: Set the initial values of the parameters;

[0033] Step 2: Update the algorithm parameters;

[0034] Step 3: According to the updated algorithm parameters, generate the control input u k (t) in real time;

[0035] Step 4: According to the tracking error generated by the control input u k (t), synchronously update the algorithm parameters;

[0036] Step 5: Repeat Steps 3 and 4 until the end of this iteration and enter the next iteration;

[0037] Step 6: The following introduces an embodiment of the present invention: Consider a circuit system iterative learning control method for dealing with completely unknown states, and its corresponding mathematical model is:

[0038] Among them, the system parameters are: R 1 = 1Ω, R 2 = 1Ω is the circuit resistance, L 1 = 0.36H, L 2 = 0.5H are inductors, M = 0.15H is a mutual inductor, θ(t)ξ(x k (t)) = x 2,k (t)sin 3 (t) + 0.8sin 2 (t)sin(x 1,k (t));

[0039] The desired reference input is: The ideal operating length T of the system is 3s;

[0040] Figure 1 is the method flow chart of the embodiment of the present invention; Applying the proposed method, Figure 2 、 3respectively represent the system output and the observer output tracking diagrams, Figure 4 represents the tracking error convergence diagram. It can be seen from these three diagrams that the proposed method has a good application effect in the circuit system, and a satisfactory tracking performance can be obtained after the 10th iteration.

[0041] References

[0042] [1] X. Li, D. Shen, B. Ding. Iterative learning control for output tracking of nonlinear systems with unavailable state information. IEEE Transactions on Neural Networks and Learning Systems, vol. 33, pp. 5085 - 5092, 2022.

[0043] [2] Z. Wang, M. Shen, L. Li. Observer - based iterative learning control with varying iteration lengths and alignment condition. Journal of the Franklin Institute, vol. 361, 107325, 2024.

Claims

1. A circuit system iterative learning control method for processing completely unknown states, characterized in that: The following steps are involved: Construct an adaptive gain state observer to estimate the current of the circuit system; Convert the matrix parameter uncertainty of the circuit system into scalar form for analysis; An iterative learning controller based on iterative attenuation factor is constructed to control a circuit system with completely unknown current.

2. The iterative learning control method for a circuit system for processing a completely unknown state according to claim 1, characterized in that: Construct an adaptive gain state observer to estimate the current of the circuit system: Consider the following circuit system: In the formula, x k (t) = [x 1,k (t)x 2,k (t)] T represents the loop current, x 1,k (t),x 2,k (t) is x k (t), k represents the number of iterations, t∈[0,T] represents the system running time, R1, R2 represents resistance, L1, L2, M represents inductance, u k (t) represents the controller, θ(t) represents the matrix parameter uncertainty, ξ(x k (t)) represents the k (t) related nonlinear function, A and B are consistent with the coefficients in the circuit model, and the system output is y k (t) = Cx k (t), where C is the system output matrix; The reference signal of the system is generated by the following reference model: In the formula, x r (t) represents the reference state, u r (t) represents the reference input, y r (t) represents the reference output; Construct an adaptive gain state observer to estimate the unknown current of the circuit system: In the formula, x r,k (t) represents the estimated current value, represents the adaptive gain of the observer, y r,k (t) represents the observer output.

3. The iterative learning control method for a circuit system processing a completely unknown state according to claim 1, characterized in that: Convert the matrix parameter uncertainty of the circuit system into scalar form for analysis: Define the error variable as: In the formula, e x,k (t) represents the estimation error, e y,k (t) represents the tracking error, because x k (0) Unknown, so assume || e x,k (0)||≤β e , where ||·|| represents the Euclidean norm of the vector, β e is an unknown constant greater than zero; Construct Lyapunov function W 1,k (t) is: Where P is a positive definite matrix and satisfies A T P+PA=-Q,PB=C T , where Q is a positive definite matrix; ξ(x k (t))-ξ(x r,k (t)) satisfies the global Lipschitz condition: ||ξ(x k (t))-ξ(x r,k (t))||≤β z ||e x,k (t)|| In the formula, ξ(x r,k (t)) represents the r,k (t) related nonlinear function, β z is a constant greater than zero; W 1,k The derivative of (t) for: In the formula, λ min (Q) is the minimum eigenvalue of the matrix Q; Convert the matrix parameter uncertainty of the circuit system θ(t) into a scalar form β θ , where β θ is a constant greater than zero and satisfies ||θ(t)||≤β θ , Further derivation becomes: In the formula, is a constant greater than zero, where represents the unknown gain, ε is a constant greater than zero; 4. The iterative learning control method for a circuit system processing a completely unknown state according to claim 1, characterized in that: Construct an iterative learning controller based on iterative attenuation factor to control a circuit system with completely unknown current: The constructed controller looks like this: The parameter update law is as follows: Where γ1,γ2 represent gains greater than zero, Λ k The iterative attenuation factor satisfies Where τ1 is a sufficiently large positive constant; Construct a composite energy function to analyze the convergence of the tracking error. The proof process is as follows: B001: Select the following composite energy function: In the formula, B002: Consider E k (t) and E k-1 (t) The difference between k (t), where: B003: Because ΔW 2,k (t) Continue to deduce as follows: B004: Similar to ΔW 2,k (t), ΔW 3,k (t) is: B005: According to B002, B003, and B004, the following formula can be obtained: In the formula, B006: According to B005, the following formula can be obtained: B007: According to B006, the convergence form of the estimation error and tracking error is as follows: In the formula, λ max (P -1 ) is the matrix P -1 The maximum eigenvalue of max (C T C) is the matrix C T The largest eigenvalue of C; B008: Consider E k The boundedness of (t) can be obtained according to B006: B009: According to B008, if E1(t) is bounded, then E k (t) is bounded. The following proves the boundedness of E1(t): B010: Based on B009 and It can be seen that E1(t) is bounded, and then according to B008, E k (t) Bounded.

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