A data driven control method and system for a club system

Abstract

The present invention provides a data-driven control method and system for a ball-bar system, comprising: applying continuous excitation to the system multiple times, collecting corresponding response information, obtaining input and output data, and then obtaining an equivalent representation of the system state feedback; using an equivalent state space expression, based on Lyapunov stability theory, giving the design constraint conditions for the ball-bar system state feedback control to meet the asymptotic stability requirements; solving the design constraint conditions for the state feedback control system to meet the asymptotic stability requirements, and then solving the system's stable state feedback gain using the relevant parameters that meet the constraint conditions. The present invention solves the technical problems of the existing ball-bar system controller design technology, such as complex controller design, complex parameter adjustment, and poor control accuracy.

Description

Technical Field

[0001] The present invention relates to the field of club system control, and in particular to a data-driven control method and system for a club system. Background Art

[0002] The ball-and-bar system is a typical single-input single-output and open-loop unstable system. Due to its simplicity and safety, the system is often used as a classic teaching device in the field of control. In actual industrial environments, most systems are unstable. Directly applying immature control strategies to industrial practice has certain unpredictable dangers. At this time, the ball-and-bar system can solve this problem well: as a representative model of an unstable system, we can first apply various algorithms and control strategies to the ball-and-bar model to verify the feasibility and effectiveness of various algorithms and control strategies. Therefore, the ball-and-bar system has become a hot research issue in the field of control.

[0003] The shortcomings of the existing club system control are mainly reflected in the following four aspects:

[0004] 1. It is impossible to obtain an accurate model and model parameters. In the prior art, most ball-bar systems are designed based on mechanism modeling to design controllers. However, it is too complicated to establish a complete ball-bar model. For the convenience of theoretical analysis and control design, people generally make some assumptions to obtain an ideal mathematical model. However, the ideal mathematical model needs to ignore some actual conditions, which is likely to lead to deficiencies in the design results in practical applications and fail to provide good control effects. For example, the existing invention patent document "A particle swarm optimization method for an adaptive ball-bar system based on prior knowledge" with publication number CN112987572A improves the particle swarm algorithm by improving the nonlinear inertia weight, using an adaptive change strategy containing a variation factor, and combining a priori knowledge with a fitness function of traditional performance integrals. The improved particle swarm optimization algorithm is used for the proportional integral differential controller used in the ball-bar system to find the equilibrium position to stabilize the ball-bar system. It can be seen from the description of the existing patent that the existing technology designs a PID controller for the outer ring bar control loop and a proportional speed compensator based on the ball bar system structure, controls the internal motor control loop that has little impact on the ball bar system control effect according to the time domain requirements, and takes into account factors such as position coordinates and ball bar speed. However, it does not take into account parameters such as the guide rail inclination angle, ball speed and guide rail rotation angular velocity, which can easily lead to reduced control accuracy and restrict the control effect on the ball bar system.

[0005] 2. Parameter adjustment is complex. In the existing ball-bar system control technology, the design of the ball-bar system controller mostly requires parameter design, such as PID control. In practice, most of the ways to select coefficients are only through debugging methods, which is a cumbersome process, and the method of only providing adjustment has a great deal of randomness, and it is impossible to guarantee that the obtained parameters provide an ideal control effect. For example, the existing invention patent application document "A control method, system and medium for finite-time stability of a nonlinear ball-bar system" with announcement number CN113655716A includes the following control method: determining the state variable model and state variable error model of the nonlinear ball-bar system; the state variable model includes a first state variable and a second state variable; the state variable error model includes a first state variable error and a second state variable error; selecting a first Lyapunov function, and determining a virtual control quantity based on the first Lyapunov function, the state variable model and the state variable error model; selecting a second Lyapunov function, and determining a control law based on the second Lyapunov function. It uses the first Lyapunov function and the second Lyapunov function to determine the control law of the state feedback control system of the ball-bar system and the virtual control quantity, and introduces a state variable model and a state variable error model. The amount of adjustment parameters is huge, and the types and logic of parameter adjustment are complex, which reduces the robustness of the existing algorithm.

[0006] 3. Low efficiency of controller design. Most controller designs do not take into account the aging and wear of equipment associated with the long-term use of the ball-bar system, such as the wear of gears and the aging of motors in the ball-bar system. These problems will cause the design object to deviate from the standard model and lead to deficiencies in the actual application of the control method based on the mathematical model. Therefore, in response to changes in the above models, the controller needs to be redesigned to ensure the stability of the system. In addition, most ball-bar system controllers are based on mechanism modeling, and the required complete ball-bar model structure is very complex, which also leads to low efficiency of controller design. For example, the existing invention patent document "A semi-physical simulation experimental platform for a magnetic levitation ball-bar system based on a fast model" with a publication number of CN107942726A includes a mechanical part and an electrical part. The mechanical part adopts an electromagnetic drive method, and uses a high-precision and high-linearity ultrasonic sensor and an angle potentiometer to respectively measure the position of the ball and the angle of rotation of the balance bar; the electrical part includes a TMS320F28027s DSP control board, a PWM switching power amplifier, and a signal acquisition circuit for an ultrasonic sensor and an angle sensor. The platform is connected to a PC via a USB interface. The model designed by the user in the Simulink environment is compiled into an executable file and downloaded to the controller through the XDS100 simulator for execution. From the technical details of the implementation of the prior art, it can be seen that although the prior solution takes into account the position of the ball and the rotation angle of the balance bar, it only adopts the excitation electromagnet to adsorb the armature to make the balance beam rotate around the ball bearing, the angle sensor measures the rotation angle of the shaft to calculate the angular velocity at the corresponding moment, the ultrasonic sensor measures the position of the ball, and the DSP control controller calculates the corresponding control amount according to the sensor feedback signal, and outputs it to the PWM power amplifier in the form of PWM wave, which is input into the excitation electromagnet after amplification, in order to achieve stable control of the ball. In the process of processing the controller data, the progressive stability of the controller is not considered, and the prior art cannot completely solve the stability problem of the controller.

[0007] Fourth, the controller has low precision. Existing technologies such as: He Zhen, Wang Yi, Zhou Changhao, Liu Yanwen. Nonlinear Problems of Ball-Rod System [J]. Acta Automatica Sinica, 2007(05):550-553.DOI:10.16383 / j.aas.2007.05.018., this method proposes a pole configuration method to avoid self-oscillation, but the controller design methods in this article are relatively random. For example, PID control mainly relies on adjusting the three parameters of proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd to determine the performance of the controller, and the coefficients selected in practice are only selected by debugging, which is a cumbersome process; and the controller designed by the pole configuration method only needs to configure the poles in the negative half plane of the complex domain to make the closed-loop system stable; and the actual pole selection is also relatively random. If inappropriate poles are selected, the characteristics of the closed-loop system will be affected. Existing technologies such as: Pang Yongxin, Jin Di, Meng Xiandong. Modeling, simulation and controller design of ball-bar system [J]. Journal of Wuhan University (Engineering Edition), 2005(06):142-146, proposed a control method based on an optimal robust controller. This document simplifies the constructed ball-bar model for the convenience of theoretical analysis and control design. However, since the model has been overly simplified, this is likely to lead to deficiencies in the design in practical applications and fail to provide good control effects.

[0008] In summary, the ball-bar system controller based on complete mechanism modeling in the prior art has the problem of overly complex design, which leads to technical problems such as low controller design efficiency, complex parameter adjustment and poor control accuracy. Summary of the invention

[0009] The technical problem to be solved by the present invention is how to solve the technical problems of complex controller design, complex parameter adjustment and poor control accuracy in the existing ball bar system technology.

[0010] The present invention adopts the following technical solutions to solve the above technical problems: A data-driven control method for a club system includes:

[0011] S1. Applying continuous excitation of no less than n+1 order to the ball-bar system, where n is the system state order, and collecting the excitation response information of the ball-bar system to obtain input and output data, thereby obtaining an equivalent state space expression of the ball-bar system state feedback, said step S1 comprising:

[0012] S11, generating input data of random initial conditions;

[0013] S12, applying a random input sequence of a fixed length to each input channel of the system, thereby sequentially obtaining output data and input data of a preset length;

[0014] S13. When the input data meets the continuous excitation condition and satisfies T≥(m+1)n+m, obtain the continuous excitation condition data to ensure that the data encodes all information to achieve direct design of the control law;

[0015] S14, when the input data of the system meets the continuous excitation condition, an equivalent representation form of the closed-loop state feedback u=Kx is obtained;

[0016] S2. On the basis of the equivalent state space expression, based on the Lyapunov stability theory, the Lyapunov function is listed on the basis of the equivalent representation of the state feedback of the closed loop of the system, and the design constraint conditions of the state feedback control system of the ball-bar system and the stable state feedback gain expression of the system are obtained, wherein the design constraint conditions satisfy the asymptotic stability of the system. Step S2 includes:

[0017] S21, under the condition of continuous excitation, write the Lyapunov function based on the equivalent representation of the state feedback of the system closed loop in step S14;

[0018] S22, based on the Lyapunov function obtained in step S21, combined with the preset equation relationship, obtain the first constraint condition to ensure the stability equivalence of the system;

[0019] S23, using a preset equivalent conversion condition to equivalently convert the first constraint condition to obtain a design constraint condition, and obtaining an applicable constraint condition by equivalent processing;

[0020] S24. Under the condition that applicable constraints are met, a steady-state feedback gain expression of the system is obtained;

[0021] S3. Use the linear matrix inequality toolbox in Matlab to solve the design constraints, and use the constraints that satisfy the system stability to solve the system's steady-state feedback gain.

[0022] The present invention provides a design method for a ball-bar system controller (system's stable state feedback gain) based on data-driven, which effectively guarantees the control performance of the ball-bar system. At the same time, in the design process of the controller, the system does not need to include mathematical model information of the controlled process, which solves the modeling problem that the system's physical model and structural parameters are difficult to obtain, thereby greatly improving the efficiency of controller design. For the ball-bar system in the present invention, the ball in the system can start from any initial state, and ultimately stabilize at the equilibrium point as the design goal. The technical problems of complex controller design, complex parameter adjustment, and poor control accuracy in the existing ball-bar system controller design technology are solved.

[0023] In a more specific technical solution, in step S13, the system inputs the sequence U 0,1,T= [u(0), u(1), ..., u(T-1)] satisfies the continuous excitation condition of order n+1, where the positive integer n represents the state order of the system, and u(i) is the system input of the i-th cycle (i is a non-negative integer), U 0,1,T It means starting from the first system input u(0), and then taking the system input in sequence with one cycle added to the sampling time, taking T system inputs in total until u(T-1), and forming a new matrix from these state sequences. The positive integer T is the number of input sequences, T satisfies the relationship T≥(m+1)n+m, and the positive integer m represents the input order of the system. The continuous excitation condition data is obtained by this logic to ensure that the data encodes all information to realize the direct design of the control law:

[0024]

[0025] In formula (1), U 0,1,T =[u(0),u(1),...,u(T-1)], μ∈R m is the system input, X 0,1,T =[x(0),x(1),...,x(T-1)] means starting from the system state x(0), the system state is taken one cycle at each subsequent input moment, and the T-th system state x(T-1) is taken, and these state sequences form a large matrix, where x∈R n Represents the state of the system, rank represents the order of the matrix to be obtained, n represents the order of the system state x, and m represents the order of the system input μ.

[0026] In a more specific technical solution, in step S14, the state feedback equivalent representation of the system closed loop is:

[0027] x(k+1)=Ax(k)+Bu(k)=(A+BK)x(k)=X 1,1,T G K x(k) (2)

[0028] In formula (2), A∈R n×n and B∈R n×m is the system coefficient matrix, x(k) is the system state in the kth period, u(k) is the system input in the kth period, K is the state feedback gain of the system, X 1,1,T =[x(1),x(2),...,x(T)] represents starting from the system state x(1), and taking the system state at the subsequent input time by one cycle, and taking the T-th system state x(T) in total, and forming a large matrix from these state sequences. The matrix G with T rows and n columns in formula (2) is K satisfy:

[0029]

[0030] In the above formula, I n represents the n-order identity matrix, U 0,1,T It means starting from the first system input u(0), the sampling time is then increased by one cycle to take the system input, a total of T system inputs are taken until u(T-1), and the matrix U is obtained 0,1,T =[u(0),u(1),...,u(T-1)],X 0,1,T It means starting from the first system state x(0), and then sampling time is added to the system state in turn, taking T system inputs until x(T-1), and getting the matrix X 0,1,T =[x(0),x(1),...,x(T-1)].

[0031] Among them, under the condition that formula (3) is valid, formula (2) can be deduced by the following logic:

[0032]

[0033] In a more specific technical solution, step S21 is for the state feedback equivalent representation of the closed loop of the system in equation (2), and only when there exists a matrix P>0, the Lyapunov function is listed, and the condition for the closed loop system satisfying u=Kx to be asymptotically stable is:

[0034] X 1,1,T G K PG K T X 1,1,T T -P<0 (5)

[0035] The following logic proves that equation (5) is true and satisfies the asymptotic stability of the ball-bar system:

[0036] The Lyapunov function is designed as follows:

[0037] V(x(k))=x T (k)Px(k) (6)

[0038] Where P matrix is ​​a positive definite matrix, let ΔV(x(k)) be:

[0039] ΔV(x(k))=V(x(k+1))-V(x(k))

[0040] =x T (k+1)Px(k+1)-x T (k)Px(k) (7)

[0041] Since x(k+1)=X 1,1,T G k Substituting x(k) into equation (7) yields:

[0042] ΔV(x(k))=x T (k+1)Px(k+1)-x T (k)Px(k)

[0043] =x T (k)G k T X 1,1,T T PX 1,1,T G k x(k)-x T (k)Px(k) (8)

[0044] =x T (k)[G k T X 1,1,T T PX 1,1,T G k -P]x(k)

[0045] If ΔV(x(k))<0, the system is considered stable and the system stability condition is transformed into:

[0046] X 1,1,T G K PG K T X 1,1,T T -P<0 (9).

[0047] In a more specific technical solution, in step S22, based on the Lyapunov function obtained in step S21, on the basis of equation (5), let Q = G K P, the system stability condition is equivalent to: there are two matrices Q and P>0, satisfying the following logic equations (10), (11) and (12),

[0048] X 1,1,T QP -1 Q T X T 1,1,T -P<0 (10)

[0049] X 0,1,T Q=P (11)

[0050] U 0,1,T Q=KP (12)

[0051] In which, the equation condition Q=G K Substituting P into equation (5) yields equation (10), and deducing equation (11), equation (12) and the following equation (13) based on equation (3):

[0052]

[0053] Formula (10), formula (11), formula (12) and formula (13) are used as the first constraint conditions to ensure the stability of the system.

[0054] The present invention utilizes an equivalent state space expression and, based on Lyapunov stability theory, provides design constraints for ball-bar system state feedback control to meet asymptotic stability requirements, and solves the system's stable state feedback gain based on the design constraints, thereby reducing the complexity of ball-bar system controller design.

[0055] In a more specific technical solution, step S23 includes:

[0056] S231, in the equation (12): X 0,1,T On the basis that Q=P holds true, the system stability condition is equivalent to: there exists a matrix Q that satisfies the following equations (14), (15) and (16):

[0057] X 1,1,T Q(X 0,1,T Q) -1 Q T X T 1,1,T -X 0,1,T Q<0 (14)

[0058] X 0,1,T Q>0 (15)

[0059] U 0,1,T Q=KX 0,1,T Q (16)

[0060] Where P = X 0,1,T Substituting Q into equation (10) and equation (12) respectively, we get equation (14) and equation (16), and replacing P = X 0,1,T Substitute Q into P>0 to derive equation (15);

[0061] S232. From the design point of view, we may first focus on equation (14) and equation (15), and convert equation (14) and equation (15) to obtain the following equation (17):

[0062]

[0063] In a more specific technical solution, in step S24, on the basis of the establishment of formula (17), the expression of the system's stable state feedback gain K obtained based on formula (16) satisfies the following formula (18):

[0064] K=U 0,1,T Q(X 0,1,T Q)-1 (18).

[0065] In a more specific technical solution, step S3 includes:

[0066] S31. According to formula (10), formula (12) and the condition of P>0, the following equivalent transformation conditions can be obtained:

[0067]

[0068] X 0,1,T Q=P (20)

[0069] S32. Under the conditions of satisfying equations (19) and (20), the steady-state feedback gain of the system can be obtained;

[0070] On the basis of satisfying equations (19) and (20), according to equation (16) U 0,1,T Q=KP, and the system's stable state feedback gain K satisfies:

[0071] K=U 0,1,T QP -1 (twenty one).

[0072] The present invention uses K obtained in formula (21) as the stable state feedback gain of the system, which can ensure the asymptotic stability of the ball-bar system.

[0073] The present invention uses the linear matrix inequality toolbox in Matlab to solve the design constraints of the state feedback control system that meet the asymptotic stability requirements, and then uses the relevant parameters that meet the constraints to solve the state feedback controller gain, thereby converting the controller design problem into a simple linear matrix inequality problem, reducing the algorithm complexity, so that the ball in the ball-bar system will eventually stabilize at the designed equilibrium position starting from any state and position. When in the equilibrium position, the guide rail inclination angle, the guide rail inclination angle change rate, and the ball speed are all close to 0.

[0074] The controller design of the present invention utilizes the online or offline historical I / O data of the controlled system and the knowledge obtained through data processing to design the controller, and realizes stable control in situations where the disturbance is unknown and it is difficult to accurately obtain system parameters and precise models. It reduces the dependence of the controller design on the model while improving the design efficiency of the controller, and has the characteristics of high efficiency and universality.

[0075] In a more specific technical solution, a data-driven control system of a ballbar system includes:

[0076] The equivalent state space processing module is used to apply continuous excitation of not less than n+1 order to the ball-bar system and collect the excitation response information of the ball-bar system to obtain input and output data, thereby obtaining the equivalent state space expression of the ball-bar system state feedback, wherein n is the system order. The equivalent state space processing module includes:

[0077] Initialization module, used to generate random initial condition data;

[0078] An input-output data module, for applying a random input sequence of a fixed length to each input channel, thereby obtaining output data of a preset length and input data in sequence;

[0079] An input coding module is used to obtain continuous excitation condition data when the input data meets the continuous excitation condition and satisfies T≥(m+1)n+m, ensuring that the data encodes all information to realize the direct design of the control law. The input coding module is connected to the input and output data module;

[0080] An equivalent representation module is used to obtain an equivalent representation form of the closed-loop state feedback u=Kx when the input data meets the continuous excitation condition. The equivalent representation module is connected to the input encoding module and the input and output data module;

[0081] The asymptotic stability constraint condition processing module is used to process the equivalent state space expression using Lyapunov stability theory to obtain the design constraint condition of the state feedback control system of the ball-bar system, wherein the design constraint condition satisfies the asymptotic stability. The asymptotic stability constraint condition processing module is connected with the equivalent state space processing module. The asymptotic stability constraint condition processing module includes:

[0082] A Lyapunov function processing module is used to process the design constraints of the closed-loop system under the state feedback u=Kx when the continuous excitation condition is met, and to obtain the Lyapunov function inequality by using the positive definite matrix P when the closed-loop system meets the specific system state condition;

[0083] An asymptotic stability module is used to determine whether the state feedback control system achieves asymptotic stability when the Lyapunov function inequality is satisfied, and the asymptotic stability module is connected to the Lyapunov function processing module;

[0084] The first constraint module is used to make Q = G K P, converting the Lyapunov function inequality according to the system state at time k, thereby obtaining the first constraint condition, and the first constraint module is connected to the Lyapunov function processing module;

[0085] An applicable constraint module, used for equivalently converting the first constraint condition by using a preset equivalent conversion condition to obtain a stable design constraint condition, and obtaining an applicable constraint condition by equivalent processing, and the applicable constraint module is connected to the first constraint module;

[0086] A stable controller module, used for processing to obtain a controller satisfying system stability when applicable constraint conditions are met, and the stable controller module is connected to the first constraint module;

[0087] The conversion module is used to solve the design constraint conditions by using the linear matrix inequality toolbox in Matlab, and solve the steady-state feedback gain of the system by using the constraint conditions under which the system is stable. The conversion module is connected with the applicable constraint module and the stable controller module.

[0088] Compared with the prior art, the present invention has the following advantages: the present invention provides a ball-bar system controller (system stable state feedback gain) design based on data drive, which effectively guarantees the control performance of the ball-bar system. At the same time, in the design process of the controller, the system does not need to include mathematical model information of the controlled process, which solves the modeling problem of the system physical model and structural parameters that are difficult to obtain, thereby greatly improving the efficiency of controller design. For the ball-bar system in the present invention, the ball in the system can start from any initial state, and finally stabilize at the equilibrium point as the design goal. The technical problems of complex controller design, complex parameter adjustment, and poor control accuracy in the design technology of the existing ball-bar system controller are solved.

[0089] The present invention utilizes an equivalent state space expression and, based on Lyapunov stability theory, provides design constraints for ball-bar system state feedback control to meet asymptotic stability requirements, and solves the system's stable state feedback gain based on the design constraints, thereby reducing the complexity of ball-bar system controller design.

[0090] The present invention uses the linear matrix inequality toolbox in Matlab to solve the design constraints of the state feedback control system that meet the asymptotic stability requirements, and then uses the relevant parameters that meet the constraints to solve the state feedback controller gain, thereby converting the controller design problem into a simple linear matrix inequality problem, reducing the algorithm complexity, so that the ball in the ball-bar system will eventually stabilize at the designed equilibrium position starting from any state and position. When in the equilibrium position, the guide rail inclination angle, the guide rail inclination angle change rate, and the ball speed are all close to 0.

[0091] The controller design of the present invention utilizes the online or offline historical I / O data of the controlled system and the knowledge obtained through data processing to design the controller, and realizes stable control in the case of unknown disturbances, and it is difficult to accurately obtain system parameters and precise models, and reduces the dependence of the controller design on the model while improving the design efficiency of the controller, and has the characteristics of high efficiency and universality. The present invention solves the technical problems of complex controller design, complex parameter adjustment, and poor control accuracy in the design technology of the existing ball bar system controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 A schematic diagram of basic steps of a data-driven control method for a club system according to Embodiment 1 of the present invention;

[0093] Figure 2 This is a schematic diagram of a club system model according to Example 1 of the present invention;

[0094] Figure 3 The relevant parameter representation and unit diagram of the system state space expression under the reference mechanism modeling of Example 1 of the present invention;

[0095] Figure 4 The figure is a graph showing the position, speed, angle between the guide rail and the horizontal plane, and angular velocity transformation curve of the angle between the guide rail and the horizontal plane of the ball on the guide rail under data-driven control according to Example 1 of the present invention;

[0096] Figure 5 This is a schematic diagram of data flow processing for obtaining state feedback gain through data driven control in Example 1 of the present invention;

[0097] Figure 6 This is a schematic diagram of a control structure for implementing club system state feedback based on data-driven control according to Example 1 of the present invention. DETAILED DESCRIPTION

[0098] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0099] Example 1

[0100] like Figure 1 , Figure 2 and Figure 3 As shown, a data-driven control method for a club system provided by the present invention comprises the following steps:

[0101] S1. Apply continuous excitation of no less than n+1 order (n is the system state order) to the ball-bar system, and collect the excitation response information of the ball-bar system to obtain input and output data, thereby obtaining an equivalent state space expression of the ball-bar system state feedback;

[0102] S2. On the basis of the equivalent state space expression, based on the Lyapunov stability theory, the Lyapunov function is listed on the basis of the equivalent representation of the closed-loop state feedback of the system, and the design constraints of the state feedback control system of the ball-bar system and the stable state feedback gain of the system are obtained, where the design constraints satisfy the asymptotic stability of the system;

[0103] S3. Using the linear matrix inequality toolbox in Matlab, the design constraints are solved, and the steady-state feedback gain of the system is solved by using the constraints that satisfy the system stability.

[0104] like Figure 2 As shown, the ball-bar system includes: guide rail 1, steel ball 2, transmission wheel 3, belt 4, servo motor 5. The steel ball 2 is gradually stabilized at the target position by changing the inclination angle of the guide rail 1. In the ball-bar system of this embodiment, under the basic condition that the guide rail 1 is horizontal, the steel ball 2 can remain stable at any position on the guide rail. We can freely design the balance point according to the needs. Here we take w=0 (the small ball is located in the middle of the guide rail) as an example. According to the literature: Liu Shiyu. Modeling of ball-bar system and design of its closed-loop controller [J]. Modern Machinery, 2018(06):1-8. DOI:10.13667 / j.cnki.52-1046 / th.2018.06.001., the system state space of the ball-bar system is:

[0105]

[0106] x and y are the first-order derivatives of the system state and the parameters in the system state with respect to time, respectively. The A, B, C, and D matrices are the coefficient matrices of the system. u∈R m is the system input, y∈R p Output for the system.

[0107] The above model can describe the motion law of the system in any state, where the specific representation of the A, B, C, and D matrices is:

[0108]

[0109]

[0110]

[0111]

[0112] in:

[0113]

[0114] J2=(I b +mr 2 ) (7)

[0115]

[0116]

[0117] The above symbolic parameters and their units are: m (unit: kg) represents the mass of the ball, g (unit: N / kg) represents the gravity proportionality coefficient, I r (Unit: kg·m 2 ) represents the guide rail moment of inertia, I p (Unit: kg·m 2 ) represents the moment of inertia of the rotating wheel, r p (Unit: m) represents the radius of the rotating wheel, I m (Unit: kg·m 2 ) represents the motor moment of inertia, r m (unit: m) represents the radius of the motor drive shaft, l (unit: m) represents half the length of the guide rail, l (unit: m) represents half the length of the guide rail, r (unit: m) represents the radius of the ball, k c (Unit: N·m / A) represents the motor torque constant, k e (Unit: V / rpm) represents the motor back electromotive force constant, z m (Unit: Ω) represents the motor armature circuit resistance, r m (Unit: m) represents the radius of the motor drive shaft, I b (Unit: kg·m 2 ) represents the moment of inertia of the ball.

[0118] The state x of the system is selected as follows: is the position of the ball on the rod, α is the inclination angle of the guide rail, and is the speed of the ball and the angular velocity of the guide rail.

[0119] Considering that the above-mentioned complete mechanism-based modeling is too complicated, resulting in difficulty in controller design and low efficiency, a data-driven ball-bar system controller design method is provided here. In the process of designing the ball-bar system controller based on data-driven, there is no need to include the mathematical model information of the controlled process, which solves the modeling problem that the physical model and structural parameters of the system are difficult to obtain. The controller design of the present invention has the characteristics of high efficiency and universality. The invention only uses the online or offline historical I / O data of the controlled system and the knowledge obtained through data processing to design the controller. It realizes stable control in situations where the disturbance is unknown and it is difficult to accurately obtain system parameters and precise models. It reduces the dependence of the controller design on the model while improving the design efficiency of the controller.

[0120] In step S1, the system inputs the sequence U 0,1,T = [u(0), u(1), ..., u(T-1)] satisfies the continuous excitation condition of order n+1, where the positive integer n represents the state order of the system, and u(i) is the system input of the i-th cycle (i is a non-negative integer), U 0,1,T It means starting from the first system input u(0), and then taking the system input in sequence with a sampling time of one cycle, taking T system inputs in total until u(T-1), and forming a new matrix from these state sequences. The positive integer T is the number of input sequences, T satisfies the relationship T≥(m+1)n+m, and the positive integer m represents the input order of the system; the continuous excitation condition data is obtained by this logic, and the control law is obtained based on it, so as to directly design the data and encode all the input data based on it:

[0121]

[0122] In formula (10), U 0,1,T =[u(0),u(1),...,u(T-1)], μ∈R m is the system input, X 0,1,T =[x(0),x(1),...,x(T-1)] means starting from the system state x(0), the system state is taken one cycle at each subsequent input moment, and the T-th system state x(T-1) is taken, and these state sequences form a large matrix, where x∈R n Represents the state of the system, rank represents the order of the matrix to be obtained, n represents the order of the system state x, and m represents the order of the system input μ.

[0123] The equivalent expression of the closed-loop feedback system is:

[0124] x(k+1)=Ax(k)+Bu(k)=(A+BK)x(k)=X 1,1,T G K x(k) (11)

[0125] In formula (11), A∈R n×n and B∈R n×m is the system coefficient matrix, x(k) is the system state in the kth period, u(k) is the system input in the kth period, K is the state feedback gain of the system, X 1,1,T =[x(1),x(2),...,x(T)] represents starting from the system state x(1), and taking the system state at the subsequent input time by one cycle, and taking the T-th system state x(T) in total, and forming a large matrix from these state sequences. The matrix G with T rows and n columns in formula (11) is K satisfy:

[0126]

[0127] In the above formula, I n represents the n-order identity matrix, U 0,1,T It means starting from the first system input u(0), the sampling time is then increased by one cycle to take the system input, a total of T system inputs are taken until u(T-1), and the matrix U is obtained 0,1,T =[u(0),u(1),...,u(T-1)],X 0,1,T It means starting from the first system state x(0), and then sampling time is added to the system state in turn, taking T system inputs until x(T-1), and getting the matrix X 0,1,T =[x(0),x(1),...,x(T-1)].

[0128] Among them, under the condition that formula (12) is valid, formula (13) is derived by the following logic:

[0129]

[0130] In this embodiment, the step S2 provides the design constraint conditions for the club system state feedback control system to meet the asymptotic stability requirements, including the following steps:

[0131] According to formula (11), the equivalent expression of the closed-loop feedback system is:

[0132] x(k+1)=X 1,1,T G K x(k) (14)

[0133] If and only if there exists a positive definite matrix P, the condition for the Lyapunov function to be asymptotically stable when the closed-loop system satisfies u = Kx is:

[0134] X 1,1,T G K PG K T X 1,1,TT -P<0 (15)

[0135] The following is a proof that equation (15) is valid and satisfies the asymptotic stability of the ball-bar system:

[0136] The Lyapunov function is designed as follows:

[0137] V(x(k))=x T (k)Px(k) (16)

[0138] Where P matrix is ​​a positive definite matrix, let ΔV(x(k)) be:

[0139] ΔV(x(k))=V(x(k+1))-V(x(k))

[0140] =x T (k+1)Px(k+1)-x T (k)Px(k) (17)

[0141] Since x(k+1)=X 1,1,T G k x(k), and substituting it into formula (17) we get:

[0142] ΔV(x(k))=x T (k+1)Px(k+1)-x T (k)Px(k)

[0143] =x T (k)G k T X 1,1,T T PX 1,1,T G k x(k)-x T (k)Px(k)

[0144] =x T (k)[G k T X 1,1,T T PX 1,1,T G k -P]x(k) (18)

[0145] If ΔV(x(k))<0, the system can be stable. Correspondingly, the condition for system stability can be transformed into:

[0146] X 1,1,T G K PG K T X 1,1,T T -P<0 (19)

[0147] The proof is complete.

[0148] The invention uses an equivalent state space expression and provides design constraint conditions for ball-bar system state feedback control to meet the asymptotic stability requirements based on Lyapunov stability theory.

[0149] Let Q = G k P, the asymptotic stability of the system is equivalent to the existence of two matrices Q and P>0 that satisfy the following conditions (20), (21) and (22):

[0150] X 1,1,T QP -1 Q T X 1,1,T T -P<0 (20)

[0151] X 0,1,T Q=P (21)

[0152] U 0,1,T Q=KP (22)

[0153] The above equations (21) and (22) come from equation (12) and the equation relationship Q = G k The derivation of P,Equation (20) comes from the derivation result of equation (19).

[0154] By using the equation relationship X 0,1,T Q = P, and combined with equations (20), (21) and (22), the stability of the system is equivalent to the existence of a matrix Q that satisfies the following equations (23), (24) and (25):

[0155]

[0156] X 0,T Q>0 (24)

[0157] U 0,1,T Q=KX 0,1,T Q (25)

[0158] Formula (23) and Formula (25) are the equations that P = X 0,1,T Q is substituted into equation (20) and equation (22) respectively, and equation (24) is X 0,1,T Q=P obtained by substituting P>0.

[0159] From the perspective of controller design, we may first focus on the two inequality relationships between equations (23) and (24), and transform them into equation (26):

[0160]

[0161] Equivalent transformation of formula (25) yields formula (27):

[0162] K=U 0,1,T Q(X 0,1,T Q) -1 (27)

[0163] On the basis of satisfying equation (26), the controller obtained by equation (27) can ensure the stability of the system.

[0164] Here is another way to express formula (26). Considering formula (20), formula (21), and formula (22) and combining them with the condition of P>0, we can get formula (28) and formula (29):

[0165]

[0166] X 0,1,T Q=P (29)

[0167] Under the conditions of satisfying equations (28) and (29), the stable state feedback gain is expressed as:

[0168] K=U 0,1,T QP -1 (30)

[0169] The ball-bar system model refers to the literature: Liu Shiyu. Modeling of ball-bar system and design of its closed-loop controller [J]. Modern Machinery, 2018 (06): 1-8. DOI: 10.13667 / j.cnki.52-1046 / th.2018.06.001. The specific state space expression can be found in equations (1) to (9); the actual values ​​of the parameters of the ball-bar system experimental platform refer to the literature: Laboratory Experiment Ball and Beam BB50 [R]. Laboratory: Ingenieurbüro Gursk-Schramm. Mülheim ander Ruhr, Germany, 2013. After substituting the expression into the parameters to obtain the constant matrix of the system state space representation, the continuous model is discretized with a period of 0.05s to obtain:

[0170]

[0171]

[0172] Formula (31) and Formula (32) are only used to obtain input and output data and verify the effect of the designed controller, and are not involved in the data-driven controller design of the present invention.

[0173] In this embodiment, the specific solution process of the controller gain is:

[0174] In order to ensure the reliability of the designed controller, data with random initial conditions are generated as input. The input data is obtained using the command rand in MATLAB. Then, according to the reference system state space expression (31) and equation (32), a random input sequence with a length of T = 15 is applied to each input channel to obtain the output data.

[0175] Substituting the input and output data into equation (14), we get the equivalent representation of the closed-loop state feedback of the system; based on the equivalent representation, we write equation (15) to get the Lyapunov function that stabilizes the system. The control goal of this design is to make the ball finally stabilize at the preset equilibrium position, and the corresponding desired state is:

[0176] x finial =[0;0;0;0] T (33)

[0177] Set the initial state to:

[0178] x(0) = [1; 0; 1; 0] T (34)

[0179] That is, in the initial state, the ball is located 1m away from the equilibrium position and is moving away from the equilibrium point at a speed of 1m / s. The Lyapunov function is written according to the equivalent representation of the closed-loop state feedback of the system, and then based on it, the equations (28) and (29) are obtained by combining the equation relationship. Under the condition that the above ball-bar system is stable, that is, on the basis of the establishment of equations (28) and (29), the controller is obtained as follows:

[0180] K=U 0,1,T QP -1 (35)

[0181] According to the specific solution process of the controller gain mentioned above, using the mosek solver in Matlab, the steady-state feedback gain K of the system is obtained as:

[0182] K=[3.2347 -18.6502 5.4685 -6.0243] T (36)

[0183] According to the reference model of equations (31) and (32), under the action of the above controller gain, we get Figure 4 Output curves for various system states are shown.

[0184] like Figure 4As shown in the figure, it can be seen from the curve of the change of the ball position over time that the ball is far away from the set equilibrium position due to its own initial speed of 1m / s, resulting in the increase of the distance between the ball and the equilibrium position in the initial period. Then, under the action of the controller, the ball gradually approaches the target position and stabilizes at the designed target position around 100s; Figure 4 As shown in the figure, it can be seen from the curve of the change of the angle between the guide rail and the horizontal plane over time that the angle between the guide rail and the horizontal plane is positive in the initial period, which is to reduce the speed of the ball away from the equilibrium point, and then the ball slows down and stops and gives the ball a speed close to the equilibrium point; when it is about to reach the equilibrium point, the negative guide rail angle is used to consume the kinetic energy of the ball around 40s to achieve the stability of the ball in the equilibrium position; and the ball speed and the guide rail angular velocity are gradually in a stable state after the stabilization of the ball position. It can be seen that in the case of an unknown system model, the present invention can achieve the stability of the ball-bar system at any position by only using input and output parameters. The present invention not only effectively guarantees the control performance of the ball-bar system, but also the system does not need to include mathematical model information of the controlled process during the design of the controller, which solves the modeling problem of the system physical model and structural parameters that are difficult to obtain, and achieves the expected purpose.

[0185] like Figure 5 As shown, in the controller design concept of the present invention, firstly, the system input satisfies the continuous excitation and the input signal u of length T≥(m+1)n+m is input to obtain the corresponding system state sequence X 0,1,T With X 1,1,T ; Then list the design conditions of the model-free controller:

[0186] X 1,1,T QP -1 Q T X 1,1,T T -P<0 (37)

[0187] X 0,1,T Q=P (38)

[0188] U 0,1,T Q=KP (39)

[0189] Among them, the matrix P is a positive definite matrix, Q = G K P,U 0,1,T =[u(0),u(1),...,u(T-1)],X 0,1,T =[x(0),x(1),...,x(T-1)],X 1,1,T =[x(1),x(2),...,x(T)]. If equations (37), (38) and (39) hold, the corresponding controller gain can be obtained:

[0190] K=U0,1,T QP -1 (40)

[0191] The present invention uses the current K obtained in formula (40) as the stable state feedback gain of the system, which can ensure the asymptotic stability of the club system.

[0192] like Figure 6 As shown, it can be seen that the controller effect obtained based on data driving in the present invention is Figure 5 Based on the idea of ​​​​getting the controller gain k, combined with the system's current state x, the system is exerted with the control input u(k)=kx(k) to realize system state feedback control.

[0193] In summary, the present invention provides a data-driven ball-bar system controller (system stable state feedback gain) design, which effectively guarantees the ball-bar system control performance. At the same time, in the design process of the controller, the system does not need to include mathematical model information of the controlled process, which solves the modeling problem of the system physical model and structural parameters that are difficult to obtain, thereby greatly improving the controller design efficiency. For the ball-bar system in the present invention, the ball in the system can start from any initial state, and finally stabilize at the equilibrium point as the design goal. The technical problems of complex controller design, complex parameter adjustment, and poor control accuracy in the existing ball-bar system controller design technology are solved.

[0194] The present invention utilizes an equivalent state space expression and, based on Lyapunov stability theory, provides design constraints for ball-bar system state feedback control to meet asymptotic stability requirements, and solves the system's stable state feedback gain based on the design constraints, thereby reducing the complexity of ball-bar system controller design.

[0195] The present invention uses the linear matrix inequality toolbox in Matlab to solve the design constraints of the state feedback control system that meet the asymptotic stability requirements, and then uses the relevant parameters that meet the constraints to solve the state feedback controller gain, thereby converting the controller design problem into a simple linear matrix inequality problem, reducing the algorithm complexity, so that the ball in the ball-bar system will eventually stabilize at the designed equilibrium position starting from any state and position. When in the equilibrium position, the guide rail inclination angle, the guide rail inclination angle change rate, and the ball speed are all close to 0.

[0196] The controller design of the present invention utilizes the online or offline historical I / O data of the controlled system and the knowledge obtained through data processing to design the controller, and realizes stable control in the case of unknown disturbances, and it is difficult to accurately obtain system parameters and precise models, and reduces the dependence of the controller design on the model while improving the design efficiency of the controller, and has the characteristics of high efficiency and universality. The present invention solves the technical problems of complex controller design, complex parameter adjustment, and poor control accuracy in the design technology of the existing ball bar system controller.

[0197] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data-driven control method for a club system, characterized in that: The method comprises: S1, applying a continuous excitation of not less than n+1 order to the ball-bar system, and collecting the excitation response information of the ball-bar system to obtain input and output data, thereby obtaining an equivalent state space expression of the state feedback of the ball-bar system, wherein n is the system order, and the step S1 comprises: S11, generating data of random initial conditions; S12, applying a random input sequence of a fixed length to each input channel of the system, thereby sequentially obtaining output data and input data of a preset length; S13, when the input data satisfies the continuous excitation condition and satisfies T≥(m+1)n+m, obtaining continuous excitation condition data to ensure that the data encodes all information to achieve direct design of the control law; S14, when the input data of the system meets the continuous excitation condition, obtaining an equivalent representation of the closed-loop state feedback u=Kx; Among them, in step S14, the state feedback equivalent representation of the system closed loop is: x(k+1)=Ax(k)+Bu(k)=(A+BK)x(k)=X 1,1,T G K x(k) (2) In the formula (2), A∈R n×n and B∈R n×m is the system coefficient matrix, x(k) is the system state in the kth period, u(k) is the system input in the kth period, K is the state feedback gain of the system, X 1,1,T =[x(1),x(2),...,x(T)] represents starting from the system state x(1), and taking the system state at the subsequent input time by one cycle, and taking the T-th system state x(T) in total, and forming a large matrix by these state sequences. The matrix G with T rows and n columns in formula (2) is K satisfy: In the above formula, I n represents the n-order identity matrix, U 0,1,T It means starting from the first system input u(0), the sampling time is then increased by one cycle to take the system input, a total of T system inputs are taken until u(T-1), and the matrix U is obtained 0,1,T =[u(0),u(1),...,u(T-1)],X 0,1,T It means starting from the first system state x(0), and then sampling time is added to the system state in turn, taking T system inputs until x(T-1), and getting the matrix X 0,1,T =[x(0),x(1),...,x(T-1)]; Wherein, under the condition that the formula (3) is established, the formula (2) is deduced by the following logic: S2. On the basis of the equivalent state space expression, based on the Lyapunov stability theory, the Lyapunov function is listed on the basis of the equivalent representation of the closed-loop state feedback of the system, and the design constraint conditions of the state feedback control system of the club system and the stable state feedback gain expression of the system are obtained, wherein the design constraint conditions satisfy the asymptotic stability of the system. The step S2 comprises: S21, under the condition of satisfying the continuous excitation, write the Lyapunov function based on the equivalent representation of the state feedback of the system closed loop in step S14; Wherein, in the step S21, for the state feedback equivalent representation of the closed loop of the system in the formula (2), if and only if there exists a matrix P>0, the Lyapunov function is listed, and the condition that the closed loop system satisfying u=Kx is asymptotically stable is: X 1,1,T G K PG K T X 1,1,T T -P<0 (5) The following logic is used to prove that the equation (5) is established to satisfy the asymptotic stability of the ball-bar system: The Lyapunov function is designed as follows: V(x(k))=x T (k)Px(k) (6) Where P matrix is ​​a positive definite matrix, let ΔV(x(k)) be: ΔV(x(k))=V(x(k+1))-V(x(k)) =x T (k+1)Px(k+1)-x T (k)Px(k) (7) Since x(k+1)=X 1,1,T G k Substituting x(k) into equation (7) yields: ΔV(x(k))=x T (k+1)Px(k+1)-x T (k)Px(k) =x T (k)G k T X 1,1,T T PX 1,1,T G k x(k)-x T (k)Px(k) =x T (k)[G k T X 1,1,T T PX 1,1,T G k -P]x(k) (8) If ΔV(x(k))<0, the system is considered stable and the system stability condition is transformed into: X 1,1,T G K PG K T X 1,1,T T -P<0 (9); S22, based on the Lyapunov function obtained in step S21, combined with the preset equation relationship, obtain the first constraint condition to ensure the stability equivalence of the system; Wherein, in step S22, based on the Lyapunov function obtained in step S21, on the basis of the existence of equation (5), let Q = G K P, the system stability condition is equivalent to: there are two matrices Q and P>0, satisfying the following logic equations (10), (11) and (12), X 1,1,T QP -1 Q T X T 1,1,T -P<0 (10) X 0,1,T Q=P (11) U 0,1,T Q=KP (12) In which, the equation condition Q=G K Substitute P into the formula (5) to obtain the formula (10), and derive the formula (11), the formula (12) and the following formula (13) according to the formula (3): Taking the equation (10), the equation (11), the equation (12) and the equation (13) as the first constraint condition for ensuring the stability of the system; S23, using a preset equivalent conversion condition to equivalently convert the first constraint condition to obtain the design constraint condition, and obtaining an applicable constraint condition by equivalent processing; Wherein, the step S23 further includes: S231, in the equation (12): X 0,1,T On the basis that Q=KP holds true, the system stability condition is equivalent to: there exists a matrix Q that satisfies the following equations (14), (15) and (16): X 1,1,T Q(X 0,1,T Q) -1 Q T X T 1,1,T -X 0,1,T Q<0 (14) X 0,1,T Q>0 (15) U 0,1,T Q=KX 0,1,T Q (16) Where P = X 0,1,T Substituting Q into equation (10) and equation (12) respectively, we obtain equation (14) and equation (16), and replacing P = X 0,1, T Substitute Q into P>0 to derive equation (15); S232, equivalently transform the formula (14) and the formula (15) to obtain the following formula (17): S24. Under the condition that the applicable constraint condition is satisfied, a steady-state feedback gain expression of the system is obtained; Wherein, in the step S24, on the basis of the establishment of equation (17), the expression of the steady-state feedback gain K of the system satisfies the following equation (18): K=U 0,1,T Q(X 0,1,T Q) -1 (18); S3, using the linear matrix inequality toolbox in Matlab to solve the design constraints, and using the constraints that satisfy the system stability to solve the steady-state feedback gain of the system; Wherein, the step S3 comprises: S31. According to formula (10), formula (12) and the condition of P>0, the following equivalent transformation conditions are obtained: X 0,1,T Q=P (20) S32, obtaining the steady-state feedback gain of the system according to the conditions of the formula (19) and the formula (20); Wherein, in the step S32, when the equations (19) and (20) are satisfied, according to equation (16) U 0,1,T Q=KP, and the steady-state feedback gain K of the system satisfies: K=U 0,1,T QP -1 (21)。 2. The data-driven control method of a club system according to claim 1, characterized in that: In step S13, the system inputs the sequence U 0,1,T = [u(0), u(1), ..., u(T-1)] satisfies the continuous excitation condition of order n+1, where the positive integer n represents the state order of the system, and u(i) is the system input of the i-th cycle, where i is a non-negative integer, U 0,1,T It means starting from the first system input u(0), then the sampling time is added to one cycle to take the system input, a total of T system inputs are taken until u(T-1), and these state sequences form a new matrix, the positive integer T is the number of input sequences, T satisfies the relationship T≥(m+1)n+m, and the positive integer m represents the input order of the system; the continuous excitation condition data is obtained by this logic to ensure that the data encodes all information to realize the direct design of the control law: In the formula (1), U 0,1,T =[u(0),u(1),...,u(T-1)], μ∈R m is the system input, X 0,1,T =[x(0),x(1),...,x(T-1)] means starting from the system state x(0), the system state is taken one cycle at each subsequent input moment, and the T-th system state x(T-1) is taken, and these state sequences form a large matrix, where x∈R n Represents the state of the system, rank represents the order of the matrix to be calculated, n represents the order of the system state x, and m represents the order of the system input μ.

3. A data-driven control system for a ball club system, used to execute the data-driven control system method for a ball club system according to any one of claims 1 to 2, characterized in that: The system comprises: An equivalent state space processing module is used to apply continuous excitation of no less than n+1 order to the ball-bar system and collect the excitation response information of the ball-bar system to obtain input and output data, thereby obtaining an equivalent state space expression of the ball-bar system state feedback, wherein n is the system order, and the equivalent state space processing module includes: Initialization module, used to generate random initial condition data; An input-output data module, for applying a random input sequence of a fixed length to each input channel, thereby obtaining output data of a preset length and input data in sequence; An input coding module, used for obtaining continuous excitation condition data when the input data satisfies the continuous excitation condition and satisfies T≥(m+1)n+m, ensuring that the data encodes all information to directly implement the design of the control law, and the input coding module is connected to the input-output data module; An equivalent representation module, used for obtaining an equivalent representation form of a closed-loop state feedback u=Kx when the input data satisfies the continuous excitation condition, the equivalent representation module being connected to the input encoding module and the input-output data module; An asymptotic stability constraint condition processing module is used to process the equivalent state space expression using Lyapunov stability theory to obtain the design constraint condition of the state feedback control system of the club system, wherein the design constraint condition satisfies asymptotic stability. The asymptotic stability constraint condition processing module is connected to the equivalent state space processing module, and the asymptotic stability constraint condition processing module includes: A Lyapunov function processing module, for processing the design constraint conditions of the closed-loop system under the state feedback u=Kx when the continuous excitation condition is met, and obtaining the Lyapunov function inequality by processing with a positive definite matrix P when the closed-loop system meets a specific system state condition; an asymptotic stabilization module, used for determining whether the state feedback control system achieves asymptotic stability when the Lyapunov function inequality is satisfied, the asymptotic stabilization module being connected to the Lyapunov function processing module; The first constraint module is used to make Q = G K P, converting the Lyapunov function inequality according to the system state at time k, thereby obtaining a first constraint condition, wherein the first constraint module is connected to the Lyapunov function processing module; An applicable constraint module, used for equivalently converting the first constraint condition by using a preset equivalent conversion condition to obtain a stable design constraint condition, and obtaining an applicable constraint condition by equivalent processing, and the applicable constraint module is connected to the first constraint module; A stabilization controller module, used for processing to obtain a controller satisfying system stability when the applicable constraint condition is satisfied, the stabilization controller module being connected to the first constraint module; A conversion module is used to solve the design constraints using the linear matrix inequality toolbox in Matlab, and to solve the steady-state feedback gain of the system using the constraints that satisfy the system stability. The conversion module is connected to the applicable constraint module and the stable controller module.

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