Expansion structure-based model-free control method for disturbed circuit system

Abstract

The invention discloses a model-free control method for a disturbed circuit system based on an expansion structure. According to the method, an expansion structure containing matrix variables is established, then the model-free control method for the disturbed circuit system based on the expansion structure is designed, effectiveness is demonstrated, and the model-free control problem of the disturbed resistor-inductor-capacitor parallel circuit system is effectively relieved.

Description

Technical Field

[0001] The present invention relates to a control method for a circuit system, and in particular to a model-free control method for a disturbed circuit system based on an extended structure. Background Art

[0002] Circuit systems are widely used in important industries such as automobiles, robots, and intelligent manufacturing. However, due to the inherent unmodeled dynamic characteristics, it is difficult or even impossible to obtain an accurate model of the system. How to design a controller using only measured input and output data is a very meaningful task. Based on this idea, researchers have conducted a lot of research on data-driven controller design and achieved a series of results.

[0003] However, the above research work mainly focuses on the control method of ideal circuit system, without considering the influence of data disturbance, which has certain limitations. In order to reduce the limitations, it is necessary to study the model-free control method of disturbed circuit system. Summary of the invention

[0004] The purpose of the present invention is to propose a model-free control method for a disturbed circuit system based on an extended structure, which can effectively solve the model-free control problem of a disturbed circuit system that cannot be modeled.

[0005] The specific technical solution of the present invention is as follows: A model-free control method for a disturbed circuit system based on an extended structure comprises the following steps:

[0006] An extended structure containing matrix variables is established, including:

[0007] Suppose there are two quadratic inequalities f(z) and g(z), where z∈R is the independent variable and R represents the set of real numbers. According to the existing results, if there exists a scalar λ≥0 such that f(z)-λg(z)≥0 for any z, then f(z)>0 holds for all z that satisfies g(z)>0. Based on this, we can obtain an extended structure containing matrix variables, namely: select symmetric matrices M and N, where M 11 , M 12 , M 22 , N 11 , N 12 and N 22 is the block matrix, M 22 ≤0,N 22 ≤0, if and only if there exists λ≥0 and β>0 such that When established, there were in, is the core of the matrix N. So far, the extended structure containing matrix variables has been established;

[0008] A model-free control method for disturbed circuit systems based on extended structures is designed and its effectiveness is demonstrated. The specific steps are as follows:

[0009] For a resistor, inductor, and capacitor parallel circuit system, its characteristics are:

[0010] Where U C is the capacitor voltage, I L is the inductor current, R1 and R2 are resistors, C is the capacitor, L is the inductor, and U is the power supply voltage;

[0011] Let the capacitor voltage U C =x1(t), inductor current I L =x2(t), power supply voltage U=u(t), using the above characteristics, the state space model of the resistor, inductor and capacitor parallel circuit system is established as:

[0012] In the formula,

[0013] The state space model of the resistor-inductor-capacitor parallel circuit system is discretized as x(t+1)=A s x(t)+B s u(t)+B s d(t)

[0014] In the formula, A s and B s All are unknown, d(t) is the system disturbance;

[0015] Run the RC parallel circuit system offline and collect a set of data x = [x(0) x(1) … x(T)] and U - =[u(0) u(1) … x(T-1)], where T is the sampling time; define X + =[x(1) x(2) … x(T)], X - =[x(0) x(1) … x(T-1)], D - =[B s d(0) B s d(1) … B s d(T-1)],D - Unknown, obviously, X + =A s X - +B s U - +D - ;

[0016] Since the perturbation d(t) has an upper bound, the data set D - Satisfy the following formula:

[0017] In the formula, Φ 11 , Φ 12 , Φ 22 is a known matrix, and

[0018] For dataset X + , X - , U - and D - , there are multiple solutions (A, B) such that the following holds: X + =AX - +BU - +D -

[0019] The multiple solutions (A, B) of the above equation are written in a set form, that is: ∑ = {(A, B) | The above equation is true}. Obviously, the resistor, inductor, and capacitor parallel circuit system matrix (A s , B s )∈∑, therefore, the controller is designed to make the system corresponding to each (A, B) in the set ∑ stable, then the resistor, inductor and capacitor parallel circuit system can also be stable. To this end, the above equation is transformed to obtain: D - =X + -AX - -BU -

[0020] Substituting the above formula into Among them, there are:

[0021] The stability criterion corresponding to the known discrete system is: P-(A+BK)P(A+BK) T >0

[0022] Where P = P T >0 is the Lyapunov matrix, K is the controller gain,

[0023] Using Schur's complement theorem on the above formula, we can get:

[0024] Combining the above two inequalities and using the established extended structure with matrix variables, we can get the controller gain K = LP -1 , where matrices L and P are required to satisfy the following matrix inequality conditions:

[0025] In the formula, α≥0, β>0,

[0026] Under the constraints of the above inequality conditions, the resistor, inductor and capacitor parallel circuit system can be stable under the action of the controller u(t) = Kx(t). The proof process is as follows:

[0027] A001: Define matrices J and Q as follows:

[0028] In the formula, J 11 =P,J 12 =[0 0],

[0029] A002: Select appropriate L, P, α, β to make the following equation true:

[0030] A003: Define K = LP -1 And using the Schur complement operation on A002, we can get:

[0031] A004: The extended structure containing matrix variables established by A003 is:

[0032] A005: Therefore, the parallel circuit system can be stabilized under the action of the controller u(t)=Kx(t).

[0033] At this point, the design and effectiveness demonstration of the model-free control method for the disturbed circuit system based on the extended structure have been completed. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0035] Figure 2 The state curve diagram of the method proposed by the present invention is adopted in the embodiment; DETAILED DESCRIPTION

[0036] 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.

[0037] like Figure 1As shown, a model-free control method for a disturbed circuit system based on an extended structure comprises the following steps:

[0038] Step 1: Let u(t) = rand(1) enter the system and collect data offline, i.e., U, X;

[0039] Step 2: Use the collected data to solve the proposed linear matrix inequality and obtain the controller gain K;

[0040] Step 3: Use K to configure the controller;

[0041] Step 4: Update the control input u(t) online;

[0042] Step 5: Use the online updated input u(t) to control the circuit system;

[0043] Step 6: Repeat step 4 to enter the next cycle.

[0044] An embodiment of the present invention is described below:

[0045] Considering the model-free control problem of the disturbed resistor, inductor and capacitor parallel circuit system, its discretized state space model is: x(t+1)=A s x(t)+B s u(t)+B s d(t)

[0046] in, d(t)=0.01rand(1);

[0047] Figure 1 is a flow chart of a method according to an embodiment of the present invention; applying the proposed method, Figure 2 The state curve diagram after the proposed method is applied to the system. From this figure, it can be seen that the proposed method can obtain a satisfactory control performance without the need for system model information.

[0048] References

[0049] [1] De Persis C, Tesi P. Formulas for data-driven control: Stabilization, optimality, and robustness[J]. IEEE Transactions on Automatic Control, 2019, 65(3): 909-924.

[0050] [2] Berberich J, J,Müller M A,et al.Data-driven model predictivecontrol with stability and robustness guarantees[J].IEEE Transactions onAutomatic Control,2020,66(4):1702-1717.

Claims

1. A model-free control method for a disturbed circuit system based on an extended structure, characterized in that: The following steps are involved: An extended structure containing matrix variables is established, including: Suppose there are two quadratic inequalities f(z) and g(z), where z∈R is the independent variable and R represents the set of real numbers. According to the existing results, if there exists a scalar λ≥0 such that f(z)-λg(z)≥0 for any z, then f(z)>0 holds for all z that satisfies g(z)>0. Based on this, we can obtain an extended structure containing matrix variables, namely: select symmetric matrices M and N, where M 11 , M 12 , M 22 , N 11 , N 12 and N 22 is the block matrix, M 22 ≤0,N 22 ≤0, if and only if there exists λ≥0 and γ>0 such that When established, there were in, is the core of the matrix N. So far, the extended structure containing matrix variables has been established; A model-free control method for disturbed circuit systems based on extended structures is designed and its effectiveness is demonstrated. The specific steps are as follows: For a resistor, inductor, and capacitor parallel circuit system, its characteristics are: Where U C is the capacitor voltage, I L is the inductor current, R1 and R2 are resistors, C is the capacitor, L is the inductor, and U is the power supply voltage; Let the capacitor voltage U C =x1(t), inductor current I L =x2(t), power supply voltage U=u(t), using the above characteristics, the state space model of the resistor, inductor and capacitor parallel circuit system is established as: In the formula, The state space model of the resistor-inductor-capacitor parallel circuit system is discretized as x(t+1)=A s x(t)+B s u(t)+B s d(t) In the formula, A s and B s All are unknown, d(t) is the system disturbance; Run the RC parallel circuit system offline and collect a set of data sets X = [x(0) x(1) … x(T)] and U - =[u(0) u(1) … x(T-1)], where T is the sampling time; define X + =[x(1) x(2) … x(T)], X - =[x(0)x(1) … x(T-1)], D - =[B s d(0) B s d(1) … B s d(T-1)],D - Unknown, obviously, X + =A s X - +B s U - +D - ; Since the perturbation d(t) has an upper bound, the data set D - Satisfy the following formula: In the formula, Φ 11 , Φ 12 , Φ 22 is a known matrix, and For dataset X + , X - , U - and D - , there are multiple solutions (A, B) such that the following holds: X + =AX - +BU - +D - The multiple solutions (A, B) of the above equation are written in a set form, that is: ∑ = {(A, B) | The above equation is true}. Obviously, the resistor, inductor, and capacitor parallel circuit system matrix (A s , B s )∈∑, therefore, the controller is designed to make the system corresponding to each (A, B) in the set ∑ stable, then the resistor, inductor and capacitor parallel circuit system can also be stable. To this end, the above equation is transformed to obtain: D - =X + -AX - -BU - Substituting the above formula into Among them, there are: The stability criterion corresponding to the known discrete system is: P-(A+BK)P(A+BK) T >0 Where P = P T >0 is the Lyapunov matrix, K is the controller gain, Using Schur's complement theorem on the above formula, we can get: Combining the above two inequalities and using the established extended structure with matrix variables, we can get the controller gain K = LP -1 , where matrices L and P are required to satisfy the following matrix inequality conditions: In the formula, α≥0, β>0, Under the constraints of the above inequality conditions, the resistor, inductor and capacitor parallel circuit system can be stable under the action of the controller u(t) = Kx(t). The proof process is as follows: A001: Define matrices J and Q as follows: In the formula, J 11 =P,J 12 =[0 0], A002: Select appropriate L, P, α, and γ to make the following equation true: A003: Define K = LP -1 And using the Schur complement operation on A002, we can get: A004: The extended structure containing matrix variables established by A003 is: A005: Therefore, the parallel circuit system can be stabilized under the action of the controller u(t)=Kx(t). At this point, the design and effectiveness demonstration of the model-free control method for the disturbed circuit system based on the extended structure have been completed.

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