Adaptive parameter identification and control method for servo system with unknown backlash compensation

Abstract

The invention discloses a self-adaptive parameter identification and control method for a servo system with unknown backlash compensation, which relates to the technical field of servo system control and comprises the following steps of: establishing a position servo system model containing a backlash model, and initializing a system state and control parameters; taking parameter identification as a part of a controller, and designing an adaptive parameter method; and designing a sliding mode controller in combination with the identification parameters and the disturbance upper bound coefficient adaptive law. The designed online parameter identification and control algorithm has good identification and tracking control effects on the position servo system, system parameters can be accurately and rapidly identified, the control performance of the servo system is improved, and the influence caused by nonlinear factors is weakened.

Description

Technical Field

[0001] The present invention relates to the technical field of servo system control, and particularly to an online adaptive parameter identification and improved sliding mode control method, especially an adaptive parameter identification and control method for a servo system containing nonlinear disturbances and backlash clearances. Background Art

[0002] In the fields of modern industrial automation and precision machinery, as a core component of the actuator, the performance of the servo system directly affects the control accuracy and response speed of the entire system. To meet the growing demands of modern industrial systems for high-performance and high-precision motion control, researchers are committed to developing innovative control strategies and methods to improve the robustness and performance of the system. A large number of studies aim to research control strategies based on nonlinear characteristics and unknown system parameters, and among these studies, adaptive parameter identification and robust tracking control research stand out.

[0003] Currently, most algorithms for servo system parameter identification belong to offline identification methods. However, offline identification cannot timely reflect the changes in system parameters, which may further affect the control performance. Therefore, it is particularly important to develop an algorithm that can adaptively identify system parameters online and respond to external nonlinear characteristics and mechanical characteristics in real time.

[0004] Backlash and clearance are important nonlinear characteristics in the servo system. Their existence will lead to uncertainties and nonlinear behaviors in the dynamic response of the system, manifested as delays and instabilities in the relationship between input and output, which may cause problems such as reduced positioning accuracy, response lag, and oscillation. To solve these problems, compensation strategies, model identification, adaptive control, and sliding mode control and other methods are required in the design to improve the robustness and control accuracy of the system and ensure the stability and reliability of the servo system in a complex environment. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide an adaptive parameter identification and control method for a servo system with unknown clearance compensation, solve the parameter identification and control problems of a position servo system with backlash clearance, and enable the system to complete high-precision parameter identification and tracking control.

[0006] Technical Solution: An adaptive parameter identification and control method for a servo system with unknown clearance compensation according to the present invention includes the following steps:

[0007] Based on the inertial load dynamics model of the servo system, establish a position servo system model containing a backlash model, and initialize the system state and control parameters;

[0008] Take parameter identification as part of the controller, design an adaptive parameter method, and calculate the filter output and the dynamic variables associated with the filter output;

[0009] Design the control law of the system and calculate the disturbance boundary coefficient;

[0010] Calculate the unknown parameters of the system and the control signal;

[0011] After the system is asymptotically stable, output the actual signal trajectory.

[0012] The present invention identifies system parameters through an adaptive parameter identification method, and the designed disturbance coefficient boundary adaptive law can compensate for disturbances. At the same time, considering the backlash clearance of the system, a controller is designed to reduce the influence of nonlinear factors and ensure high-precision tracking control of the system in the presence of backlash clearance.

[0013] Preferably, the position servo system model with a backlash model is expressed as:

[0014]

[0015] Where, m represents mass; x1 represents the position signal of the motor, x2 represents the speed signal of the motor; u is the control input; b>0 is the slope of the backlash model; t represents the time variable; is a coefficient; K i represents the torque constant; B represents the viscous friction coefficient of the servo motor; f represents the disturbance of the system, including the influence of various uncertainties and disturbances; v1, v2, v3, v4 are all system parameters; b is the slope of the backlash model; Where, Bla is a smooth and differentiable function, and n1 is a positive adjustment parameter.

[0016] Preferably, the steps for establishing the position servo system model with a backlash model and initializing the system state and control parameters are as follows:

[0017] The inertial load dynamics model of the servo system is expressed as follows:

[0018]

[0019] Where, m represents mass; y represents the angular displacement; represents the angular velocity; K i represents the torque constant; B represents the viscous friction coefficient of the servo motor; f represents the disturbance of the system, including the influence of various uncertainties and disturbances;

[0020] Bl(u) represents the unknown brake backlash, and the relationship between the control input u and the backlash characteristic is given by the following formula:

[0021]

[0022] where \(b>0\) is the slope of the backlash model; \(s\) r is a parameter greater than zero; \(s\) l is a parameter less than zero; \(B_l(u(t_))\) represents the backlash output value at the previous moment;

[0023] Define \(x_1\) to represent the position signal of the motor and \(x_2\) to represent the speed signal of the motor, Rewrite equation (1) as:

[0024]

[0025] Define \(V\) I (·) represents the new backlash inverse function, and its expression is as follows:

[0026]

[0027] In the formula, \(B_l\) is a smooth differentiable function of equation (2), and where the smooth arctangent function ensures its continuity, and \(n_1\) is a positive adjustment parameter;

[0028] Parameterize the backlash nonlinearity linearly as:

[0029] \(B_{la}=bu - rrbs\) r \(-rlbs\) l (5)

[0030] Equation (3) is further expressed as:

[0031]

[0032] where,

[0033] Preferably, the method for designing the adaptive parameter includes the following steps:

[0034] Define represents the error of ·, represents the estimation of ·, and the parameter error Introduce the online estimation signal to represent the estimation of, and we can get:

[0035]

[0036] where, represents an intermediate variable, and the in equation (6) is rewritten as:

[0037]

[0038] Equation (6) is rewritten as:

[0039]

[0040] where, δ0 represents the boundary value of perturbation coefficient one; δ1 represents the boundary value of perturbation coefficient two; δ2 represents the boundary value of perturbation coefficient three; ||e|| represents the norm of the tracking error e; represents the norm of the derivative of the tracking error;

[0041] Define as:

[0042]

[0043] where, is automatically generated online through the adaptive law k w is a positive tuning parameter, w is the filter output, and its expression is as follows:

[0044]

[0045] x is expressed as:

[0046]

[0047] Define the auxiliary variable η:

[0048]

[0049] The derivative of η is:

[0050]

[0051] Define two dynamic equations Q and C as follows:

[0052]

[0053]

[0054] θ c = Q(t c ) T C(t c ) (17)

[0055] Through Equation (10), Equation (9) is expressed as:

[0056]

[0057] The information about the parameter error is obtained from Equations (11)-(15) as follows:

[0058]

[0059] Preferably, the control law of the design system includes the following steps:

[0060] Define the tracking error e as:

[0061] e = x1 - x d (20)

[0062] where, x1 represents the actual position; x d represents the desired trajectory; and

[0063] Define the sliding surface as Then the derivative of s is obtained as:

[0064]

[0065] The control law of the design system is:

[0066]

[0067] where, λ > 0, k > 0 are positive adjustment gains, and the disturbance boundary coefficients are the estimated values of δ0, δ1, δ2 respectively;

[0068] The estimation law of

[0069]

[0070]

[0071]

[0072] where, c i > 0, i = 1, 2, 3, 4, 5, 6, μ i > 0, i = 1, 2, 3 are adjustment parameters;

[0073] Define Γ = diag{r1, r2, r3, r4}, and the identification law of the system unknown parameters is redesigned as:

[0074]

[0075] Define the Lyapunov function as follows:

[0076]

[0077] Taking the derivative of Equation (26) gives:

[0078]

[0079] Substitute equations (21)-(26) into equation (28), we get The system is asymptotically stable.

[0080] On the other hand, the present invention provides a computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the above method is implemented.

[0081] On the third aspect, the present invention provides a computer storage medium, where instructions are stored in the computer storage medium, and when the instructions are executed on a computer, the computer is made to execute the above method.

[0082] Based on the parameter identification theory and the sliding mode control technology, the present invention designs an online parameter identification and sliding mode control algorithm for a servo system with backlash compensation, realizes the online identification of unknown parameters of the system and the high-precision control of the servo system, enhances the robustness of the system, and weakens the influence of non-linear factors on the system.

[0083] The technical concept of the present invention is as follows: for a position servo system with backlash, the present invention compensates for the gap by designing relevant function inputs, improves the adaptive parameter identification for system parameter identification, and combines the disturbance boundary coefficient adaptive rate to design the system control law to complete the high-precision tracking control of the system and the accurate online identification of parameters. The present invention provides a method capable of online adaptively identifying unknown parameters of the system, enabling the system parameters to effectively converge to the true values, and designs a sliding mode control algorithm capable of compensating for the backlash gap to ensure that the servo system can achieve a better control effect. At the same time, the robustness of the system is enhanced.

[0084] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: the present invention can realize online parameter identification, reduce the influence brought by system non-linear factors, and realize high-performance tracking control of the servo system. Brief Description of the Drawings

[0085] Figure 1 is the control flow chart of the present invention;

[0086] Figure 2 is the tracking trajectory effect diagram when the reference signal is x 1d ;

[0087] Figure 3 is the tracking error effect diagram when the reference signal is x 1d ;

[0088] Figure 4 is the effect diagrams of the control input u and Blu when the reference signal is x 1d ;

[0089] Figure 5The reference signal is x 1d Identification effect diagrams of system parameters v1, v2, v3, v4 when

[0090] Figure 6 The reference signal is x 1d Estimation effect diagrams of disturbance coefficient boundary variables δ0, δ1, δ2 when

[0091] Figure 7 The reference signal is x 2d Tracking trajectory effect diagrams when

[0092] Figure 8 The reference signal is x 2d Tracking error effect diagrams when

[0093] Figure 9 The reference signal is x 2d Effect diagrams of control inputs u and Blu when

[0094] Figure 10 The reference signal is x 2d Identification effect diagrams of system parameters v1, v2, v3, v4 when

[0095] Figure 11 The reference signal is x 2d Estimation effect diagrams of disturbance coefficient boundary variables δ0, δ1, δ2 when

[0096] Figure 12 Picture of the physical experimental platform

[0097] Figure 13 The reference signal is x d Tracking trajectory effect diagrams when = πsin(t)

[0098] Figure 14 The reference signal is x d Tracking error effect diagrams when = πsin(t)

[0099] Figure 15 The reference signal is x d Effect diagrams of control inputs u and Blu when = πsin(t)

[0100] Figure 16 The reference signal is x d Identification effect diagrams of system parameters v1, v2, v3, v4 when = πsin(t)

[0101] Figure 17 The reference signal is x d Estimation effect diagrams of disturbance coefficient boundary variables δ0, δ1, δ2 when = πsin(t). Detailed implementation method

[0102] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

[0103] Referring to Figures 1 - 17 , an adaptive parameter identification and control method for a servo system with unknown backlash compensation includes the following steps:

[0104] Step 1, establish a position servo system model including a backlash model, and initialize the system state and control parameters. The process is as follows:

[0105] 1.1, The inertial load dynamics model of the servo system is expressed as follows:

[0106]

[0107] where m represents mass; represents acceleration; y represents angular displacement; represents angular velocity; K i represents the torque constant; B represents the viscous friction coefficient of the servo motor; t represents the time variable; u represents the control input; f represents the disturbance of the system, including the influence of various uncertainties and perturbations;

[0108] 1.2, Considering the influence of the backlash gap, Bl(u) represents the unknown brake backlash. Among them, the relationship between the control input u and the backlash characteristics is given by the following formula:

[0109]

[0110] where b > 0 is the slope of the backlash model; s r is a parameter greater than zero; s l is a parameter less than zero; Bl(u(t_)) represents the backlash output value at the previous moment; represents the derivative of the control law u;

[0111] 1.3, Define x1 to represent the position signal of the motor, x2 to represent the speed signal of the motor, T represents the transpose of the matrix, represents the angular velocity of the motor, represents the angular acceleration of the motor; Rewrite equation (1) as:

[0112]

[0113] 1.4, Define V I (·) represents the new backlash inverse function, and its expression is as follows:

[0114]

[0115] In the formula, Bla is a smooth differentiable function of model (2), and Among them, the smooth arctangent function ensures its continuity, and n1 is a positive adjustment parameter;

[0116] 1.5. Further considering the unknown parameters b and s r , s l , and the immeasurability of Bl(u), the backlash nonlinearity can be linearly parameterized as:

[0117] Bla = bu - rrbs r -rlbs l (5)

[0118] The system model (3) can be further expressed as:

[0119]

[0120] Among them, is the coefficient;

[0121] Step 2, Design of the adaptive parameter method, the process is as follows:

[0122] 2.1, Define to represent the error of ·, to represent the estimate of ●, and the parameter error Introduce an online estimation signal to represent the estimate of, and we can get:

[0123]

[0124] Among them, u represents an intermediate variable; then in equation (6) can be written as:

[0125]

[0126] is the coefficient;

[0127] Furthermore, the system model (6) can be rewritten as:

[0128]

[0129] Among them, δ0 represents the boundary value of the first perturbation coefficient; δ1 represents the boundary value of the second perturbation coefficient; δ2 represents the boundary value of the third perturbation coefficient; ||e|| represents the norm of the tracking error e; represents the norm of the derivative of the tracking error;

[0130] 2.2, Define as:

[0131]

[0132] wherein, is automatically generated online through the adaptation law k w is a positive adjustment parameter, w is the filter output, is the derivative of the filter output, and its expression is as follows:

[0133]

[0134] wherein, w(t0) is the initial value of the filter;

[0135] The derivative of the system error can be expressed as:

[0136]

[0137] 2.3. Define an auxiliary variable η:

[0138]

[0139] Its derivative is:

[0140]

[0141] wherein, η(t0) is the initial value of the auxiliary variable η; is the initial estimate of the system;

[0142] 2.4. Define two dynamic equations Q and C as follows:

[0143]

[0144] θ c = Q(t c ) T C(t c ) (17)

[0145] w T is the transpose of the filter matrix; Q(t0) is the initial value of the dynamic matrix Q; v 0 is the initial value of the system parameter;

[0146] C(t0) is the initial value of the dynamic matrix C; θ c is the value of the parameter at time c; t c represents the time at time c;

[0147] 2.5. Through equation (10), equation (9) can be written as:

[0148]

[0149] is the system state observer;

[0150] The information about the parameter error is obtained from (11)-(15) as follows:

[0151]

[0152] Adaptive rate; Γ is the adjustment gain matrix, Initial value of system parameter estimation;

[0153] Step 3, design the control law, the process is as follows:

[0154] 3.1, Define the tracking error e as:

[0155] e = x1 - x d (20)

[0156] where x1 represents the actual position; x d represents the desired trajectory; and

[0157] 3.2, Define the sliding surface as Then the derivative of s is:

[0158]

[0159] 3.3, Design the control law of the system as:

[0160]

[0161] where λ > 0, k > 0 are positive adjustment gains, are the estimated values of δ0, δ1, δ2 respectively; μ i > 0, i = 1, 2, 3; μ i is the adjustment parameter; i is the subscript; k is the positive adjustment gain;

[0162] 3.4, The estimation law of

[0163]

[0164]

[0165]

[0166] where c i > 0, i = 1, 2, 3, 4, 5, 6, μ i > 0, i = 1, 2, 3, are the adjustment parameters; ||s|| represents the norm of the sliding surface; denotes the norm of the sliding mode surface derivative; ||e|| denotes the norm of the tracking error; denotes the norm of the derivative of the tracking error;

[0167] 3.5, Define Γ = diag{r1, r2, r3, r4}, and the identification law of the system unknown parameters can be redesigned as:

[0168]

[0169] 3.6, Define the Lyapunov function as follows:

[0170]

[0171] where r1, r2, r3, r4 are respectively the values of the four numbers on the diagonal of the gain matrix, are respectively the squares of the errors of the four system parameters;

[0172] Differentiating Equation (26) gives:

[0173]

[0174] 3.7, Substituting Equations (21)-(26) into Equation (28) shows that, the system is asymptotically stable.

[0175] To verify the online identification performance and control effect of the proposed method, the present invention conducts a simulation experiment on it. Set the initial conditions of various parameters in the experiment as: system parameter K i = 5, m = 5, B = 4; the backlash model parameters are set as b = 1, s r = 0.5, s l = -0.5, n1 = 1; the identification and control parameters λ = 2, k w = 4, k1 = 15, μ1 = 0.8, μ2 = 0.4, μ3 = 0.7, c1 = 0.3, c2 = 2.8, c3 = 0.45, c4 = 0.0001, c5 = 0.0002, c6 = 0.0001, Γ = diag{0.001 0.4 4.2 3.1}; set the initial values of all other relevant parameters to 0. To ensure the fairness of comparison, the same set of data is used in two groups of simulations. In the experiment, the reference signal x d takes x 1d = 2sin(2t) and x 2d = sin(πt) + 0.4cos(t) respectively.

[0176] Figures 2 - 17 are the simulation experiment effect diagrams of the adaptive parameter identification and control of the servo system with unknown gap compensation. Figure 2 and Figure 3 respectively represent that the reference signal is x1d The tracking trajectory and tracking error at [time], these two figures show excellent tracking performance, and the tracking error e always fluctuates within a very small range. Figure 4 where the reference signal is x 1d The effect diagrams of the control input u and Blu at [time], it can be seen from the figure that the output performance of the control law Blu after backlash clearance treatment is slightly better than that of u. Figure 5 where the reference signal is x 1d The effect diagrams of the identification of system parameters v1, v2, v3, v4 at [time], it can be seen that the system parameters can quickly converge to the true values, showing excellent identification performance. Figure 6 where the reference signal is x 1d The effect diagrams of the estimation of the disturbance coefficient boundary variables δ0, δ1, δ2 at [time], it can be seen from the figure that the boundaries of the disturbance coefficients can be quickly identified. Figure 7 and Figure 8 where the reference signal is x 2d The effect diagrams of the tracking trajectory and tracking error at [time], this figure shows that the system still has good tracking effect when the reference signal changes. Figure 9 where the reference signal is x 2d The effect diagrams of the control input u and Blu at [time], showing a similar effect to the previous group of experiments, and the control output is relatively stable. Figure 10 where the reference signal is x 2d The effect diagrams of the identification of system parameters v1, v2, v3, v4 at [time], Figure 11 The reference signal is x 2d The effect diagrams of the estimation of the disturbance coefficient boundary variables δ0, δ1, δ2 at [time], the system parameters can quickly converge to the true values, and the disturbance coefficients can also be quickly identified.

[0177] Based on an open-source multi-motor drive control experimental platform, the correctness and effectiveness of the proposed method are verified. In this experiment, a permanent magnet synchronous motor and a DC brushed motor are used to conduct experiments on a counter-rotating platform. The equipment used includes an experimental box, motors, and a computer. The experimental equipment is as Figure 12 shown, and the motor parameters are shown in Table 1 and Table 2. The control parameters are set as: λ = 0.5, k w = 5, k1 = 1.8, μ1 = 0.1, μ2 = 0.005, μ3 = 0.07, c1 = 0.001, c2 = 0.2, c3 = 0.2, c4 = 1, c5 = 1000, c6 = 20, b = 1, s r = 0.5, s l = -0.5, n1 = 1, Γ = diag{0.03 0.03 0.0005 0.005}. In the experiment, the reference signal is x d = πsin(t).

[0178] Figure 13It is the tracking strategy diagram of the traditional PI controller and the controller in this paper. Figure 14 It is the tracking error diagram of the two controllers. It can be seen from the figure that both controllers show excellent tracking performance, but the controller in this paper is significantly better than the PI controller. The error of the controller proposed in this paper fluctuates within ±0.04, while the PI controller fluctuates within ±0.09. Figure 15 It is the effect diagram of the control input u and Blu, and its effect is similar to that in the simulation experiment. The effect of Blu is slightly better than that of u. Figure 16 It is the effect diagram of the identification of the system parameters v1, v2, v3, v4. It can be seen from the figure that the system parameters quickly converge to the true values, thus proving significant parameter identification performance. Figure 17 It is the effect diagram of the estimation of the disturbance coefficient boundary variables δ0, δ1, δ2. The disturbance coefficient can be quickly identified.

[0179] Table 1-1 Basic motor parameters of the permanent magnet synchronous motor

[0180]

[0181] Table 1-2 Parameter table of the DC brushed motor

[0182]

[0183]

[0184] The above describes the simulation experiment and the experiment on the experimental platform given by the present invention to show the effectiveness of the method designed by the present invention. However, it is obvious that the present invention is not limited to the above examples, and various deformations can be made and implemented on the premise of not deviating from the basic spirit of the present invention and not exceeding the scope involved in the substantial content of the present invention. The online parameter identification and control method designed by the present invention has good identification and tracking control effects on the position servo system with backlash, and can achieve high-precision parameter identification and tracking control of the servo system.

Claims

1. An adaptive parameter identification and control method for a servo system with unknown gap compensation, characterized in that, It includes the following steps: Based on the inertial load dynamics model of the servo system, establish a position servo system model with backlash model, and initialize the system state and control parameters; Take parameter identification as part of the controller, design an adaptive parameter method, and calculate the filter output and the dynamic variables associated with the filter output; Design the control law of the system and calculate the disturbance boundary coefficient; Calculate the unknown parameters and control signals of the system; Output the actual signal trajectory after the system is asymptotically stable.

2. The servo system adaptive parameter identification and control method with unknown gap compensation according to claim 1, characterized in that The position servo system model with backlash model is expressed as: Among them, m represents mass; x1 represents the position signal of the motor, and x2 represents the speed signal of the motor; u is the control input; b > 0 is the slope of the backlash model; t represents the time variable; is a coefficient; K i represents the torque constant; B represents the viscous friction coefficient of the servo motor; f represents the disturbance of the system, including the influence of various uncertainties and perturbations; v1, v2, v3, v4 are all system parameters; b is the slope of the backlash model; Among them, Bla is a smooth differentiable function, and n1 is a positive regulation parameter.

3. The servo system adaptive parameter identification and control method with unknown gap compensation according to claim 1, characterized in that The steps of establishing the position servo system model with backlash model and initializing the system state and control parameters include the following: The inertial load dynamics model of the servo system is expressed as follows: where m represents mass; y represents angular displacement; represents angular velocity; K i represents torque constant; B represents the viscous friction coefficient of the servo motor; f represents the disturbance of the system, including the effects of various uncertainties and perturbations; Bl(u) represents the unknown brake backlash, and the relationship between the control input u and the backlash characteristics is given by the following formula: where b > 0 is the slope of the backlash model; s r is a parameter greater than zero; s l is a parameter less than zero; Bl(u(t_)) represents the backlash output value at the previous moment; Define that x1 represents the position signal of the motor and x2 represents the speed signal of the motor. Rewrite Equation (1) as: Define V I (·) represents the new backlash inverse function, and its expression is as follows: where Bl is a smooth and differentiable function of Equation (2), and the smooth arctangent function ensures its continuity, and n1 is a positive adjustment parameter; Linearly parameterize the backlash nonlinearity as: Bla = bu-rrbs r -rlbs l (5) Equation (3) is further expressed as: Among them, 4. The servo system adaptive parameter identification and control method with unknown gap compensation according to claim 3, characterized in that, The steps of designing the adaptive parameter method include the following: Definition Denote the error of · Denote the estimate of ·, and the parameter error Introduce the online estimation signal To represent The estimate of, we can get: Among them, represents an intermediate variable, and in formula (6) is rewritten as: Equation (6) is rewritten as: Among them, δ0 represents the boundary value of the first disturbance coefficient; δ1 represents the boundary value of the second disturbance coefficient; δ2 represents the boundary value of the third disturbance coefficient; ||e|| represents the norm of the tracking error e; represents the norm of the derivative of the tracking error; Definition is defined as: Among them, generated automatically online through the adaptation law k w is a positive adjustment parameter, w is the filter output, and its expression is as follows: Expressed as: Define the auxiliary variable η: The derivative of η is: Define two dynamic equations Q and C as follows: θ c = Q(t c ) T C(t c )(17) Through Equation (10), Equation (9) is expressed as: The information about the parameter error is obtained from Equations (11)-(15) as follows:

5. The servo system adaptive parameter identification and control method with unknown gap compensation according to claim 1, characterized in that The steps of designing the control law of the system include the following: Define the tracking error e as: e = x1 - x d (20) where x1 represents the actual position; x d represents the desired trajectory; and Define the sliding mode surface as Then, the derivative of s is obtained as follows: The control law of the system is designed as: where λ > 0 and k > 0 are positive adjustment gains, and the disturbance boundary coefficients are the estimated values of δ0, δ1, and δ2, respectively; The estimation law is designed as follows: Among them, c i > 0, i = 1, 2, 3, 4, 5, 6, μ i > 0, i = 1, 2, 3 are adjustment parameters; Define Γ = diag{r1, r2, r3, r4}, and the identification law of the unknown parameters of the system is redesigned as: Define the Lyapunov function as follows: Taking the derivative of Equation (26) gives: Substituting Eqs. (21)-(26) into Eq. (28), we get The system is asymptotically stable.

6. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the method described in any one of claims 1-5.

7. A computer storage medium, characterized in that, The computer storage medium stores instructions, and when the instructions are executed on the computer, the computer is caused to execute the method described in any one of claims 1-5.

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