Servo system Super-twisting fast nonsingular terminal sliding mode control method based on parameter error transformation

Abstract

The invention discloses a servo system Super-twisting rapid nonsingular terminal sliding mode control method based on parameter error transformation, and the method comprises the following steps: building a servo system model with nonlinear friction force, and initializing a system state and control parameters; extracting parameter error information, designing a parameter error conversion method based on a preset performance function, designing AESO and performing stability analysis, designing Super-twisting fast nonsingular terminal sliding mode control, identifying unknown parameters of the system on line, and proving the stability of the system. The designed parameter error conversion and AESO have good identification and tracking control effects on the position servo system, system parameters can be identified on line with high precision, the control performance of the servo system is improved, and buffeting of an input controller and parameter identification is weakened.

Description

Technical Field

[0001] The present invention belongs to the technical field of servo system control, and relates to a method for online adaptive parameter identification and adaptive extended state observer (AESO) based on parameter error conversion of a preset performance function, especially an adaptive parameter identification and control method for a servo system with nonlinear friction. Background Art

[0002] In the fields of automation and precision control, ensuring accurate position tracking in servo systems is crucial, especially for high-performance applications. However, these systems often encounter various disturbances, including nonlinear forces such as friction and parameter uncertainties, which may compromise accuracy and stability. Traditional control strategies are relatively difficult to address these challenges, especially in dynamic environments with unforeseen disturbances. This complexity drives the need for more advanced control algorithms.

[0003] Currently, many parameter identification algorithms for servo systems adopt offline methods. However, the offline identification method cannot update system parameters in real time, and this lag directly affects the control performance of the servo system and even causes system instability. Online adaptive parameter identification solves this problem, but online parameter identification has problems such as a slow convergence speed and chattering. Therefore, it is necessary to add a parameter error conversion method for compensation on this basis.

[0004] A key challenge in modern control systems is to manage inherent uncertainties and external disturbances. Over the past few decades, extended state observers (ESOs) have been widely used to estimate and compensate for unknown dynamics and disturbances. ESOs are generally divided into linear ESO (LESO) and nonlinear ESO (NESO). However, due to its static parameters, traditional ESO limits the ability to adapt to changing system or environmental conditions. To address this limitation, an adaptive extended state observer (AESO) is proposed, which realizes real-time adjustment of observer parameters by introducing an adaptive mechanism. This method significantly enhances the system's ability to handle uncertainties and disturbances and improves the robustness in dynamic or changing environments. The adaptability of AESO shows obvious advantages in highly dynamic systems or scenarios with fluctuating conditions. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a Super-twisting fast non-singular terminal sliding mode control method for a servo system based on parameter error transformation, to solve the problems of parameter identification and control of a position servo system with nonlinear friction, and enable the system to complete high-precision parameter identification and tracking control.

[0006] Technical solution: The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation of the present invention includes the following steps:

[0007] Establish a position servo system model with non-linear friction, and initialize the system state and control parameters;

[0008] Extract parameter error information;

[0009] Design parameter error conversion based on a preset performance function;

[0010] Design an adaptive extended state observer;

[0011] Design a controller for the system input.

[0012] The present invention provides a method for parameter error conversion based on a preset performance function. This method can extract the error information of the parameters themselves and the tracking error, and design an adaptive identification law based on this. By reducing the parameter error, the parameters converge to their own effective values. At the same time, considering other disturbances in the system, an AESO is designed to observe the system state, ensuring high-precision tracking control of the system.

[0013] Preferably, the establishment of the position servo system model with non-linear friction and the initialization of the system state and control parameters include the following steps:

[0014] The position servo system model is expressed as follows:

[0015]

[0016] Among them, y is the displacement of the system payload, and M is the total mass of the system payload; represents non-linear friction; F d represents other modeling errors and system disturbances, u represents the control input, and k represents the gain coefficient;

[0017] It is expressed as follows:

[0018]

[0019] Among them, f s is the static friction coefficient, f c is the Coulomb coefficient, f v is the viscous coefficient; (f s - f c ) f1 describes the Stribeck effect; f c f2 is the Coulomb friction force; β1 and β2 are coefficients used to approximate the shape of the Stribeck effect; β3 is a coefficient used to approximate the sig function;

[0020] When the parameters satisfy the following conditions, the friction model (2) is significantly continuously differentiable;

[0021] β1 >> 0, β1 > β2, β2 = 1 / v s , β3 >> 0 (22)

[0022] where v s is the Stribeck speed;

[0023] Define x1 = y, then the system model (1) can be reformulated in state - space form as:

[0024]

[0025] where f = θ2f1(x2)+θ3f2(x2)+θ4x2, d = F d / M; where θ1 = k / M, θ2 = (f s -f c ) / M, θ3 = f c / M, θ4 = f v / M;

[0026] Let denote the estimate of ·, and define as the parameter - estimation error;

[0027] Define the control input as:

[0028] θ1u = θ 10 u+Δθ 10 u (24)

[0029] where θ 10 is the nominal value of θ1, determined empirically; Δθ 10 represents the uncertain part of θ1.

[0030] Preferably, the step of extracting the parameter - error information includes the following steps:

[0031] From equations (4) and (5), we get:

[0032]

[0033] Define θ = [θ2 θ3 θ4] T then we have;

[0034]

[0035] where x 2f 、u f and are x2, u and The filtering variable; r is the filtered tuning parameter; x 2f (0), u f (0), are the initial values of x 2f , u f , respectively;

[0036] Obtained from equations (6) and (7):

[0037]

[0038] Define two dynamic equations for W and S:

[0039]

[0040] where l is the adjustment parameter; W(0) and S(0) are the initial values of W and S respectively; W represents the covariance matrix of the parameter estimation error; S represents the covariance matrix of the tracking error;

[0041] From equation (8), the solution is as follows:

[0042]

[0043] where t is the time variable and T is the sampling period;

[0044] According to equations (8) and (10), the information about the parameter error is obtained as follows:

[0045] S = Wθ (30)

[0046]

[0047] Preferably, the design of the parameter error conversion based on the preset performance function includes the following steps:

[0048] Define the preset performance function:

[0049] χ(t) = coth(γt + υ) - 1 + χ ∞ (32)

[0050] where γ, υ are positive constants; χ(t) represents the preset performance function, x ∞ represents the steady-state value of the preset performance function, and coth represents the hyperbolic cotangent function;

[0051] Define the parameter error conversion function:

[0052]

[0053] where ζ = [ζ1, ζ2, ζ3] T, ζ represents the conversion error, and D(ζ) is defined as a strictly monotonically increasing function; represents the parameter error;

[0054]

[0055] where, δ is a positive constant, represents the parameter error exponent;

[0056] The converted error ζ is expressed as:

[0057]

[0058] where, is the normalized parameter error;

[0059] The derivative of Equation (16) is:

[0060]

[0061] where is a bounded variable.

[0062] Preferably, the design of the adaptive extended state observer includes the following steps:

[0063] Define the state where φ(x2) = [f1(x2) f2(x2) x2] T , represents the time derivative of state x3; therefore, Equation (8) is reformulated as follows:

[0064]

[0065] The adaptive extended state observer is constructed as:

[0066]

[0067] where represents the state estimation, l i (t) > 0, i = 1, 2, are variable gains,

[0068] The adjustable gain l i (t), i = 1, 2, is constructed as:

[0069]

[0070] The dynamic gain w n (t) is defined as:

[0071]

[0072] where w1 is the initial gain and w2 is the final gain.

[0073] Preferably, the controller for the design system input includes the following steps:

[0074] The tracking error is defined as e = x1 - x d , and the derivative of the tracking error is defined as where x d represents the reference signal; the sliding surface is defined as:

[0075]

[0076] where λ > 0 and λ is a constant;

[0077] According to the parameter error transformation method, the sliding surface is defined as:

[0078] s2 = ζ1 + ζ2 + ζ3 (23)

[0079] The controller for the system input is designed as:

[0080] u = u eq + u stw (24)

[0081]

[0082] where k1, k2, k3, k4 are control gains, is the model uncertainty; μ is the auxiliary control variable;

[0083] The adaptive law for online parameter identification is:

[0084]

[0085] where ρ1 is a bounded variable of ρ2 is a bounded variable of

[0086] Define the Lyapunov function:

[0087]

[0088] Taking the derivatives of V1 and V2 and substituting the controller (24)-(26) and the parameter adaptive law (27) gives:

[0089]

[0090] Then the entire system is stable.

[0091] Based on the parameter error conversion theory of the preset performance function and the adaptive extended state observer technology, the present invention designs a Super-twisting fast non-singular terminal sliding mode control method for the servo system based on parameter error transformation, realizes the online identification of unknown system parameters and the high-precision control of the servo system, and simultaneously weakens the chattering problems of the sliding mode control input and the online parameter identification.

[0092] The technical concept of the present invention is as follows: for a position servo system with non-linear friction, the present invention extracts the parameter error information and tracking error of the system, adds a parameter error conversion method based on online parameter identification to identify the unknown parameters of the system. At the same time, an AESO is built to observe the state of the system, improve the control accuracy, and combine the Super-twisting fast non-singular terminal sliding mode control 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 for parameter error conversion based on a preset performance function, enabling the system parameters to effectively converge to the true value. At the same time, the chattering problem of online parameter identification is solved. And an AESO is designed to observe the system state to ensure that the servo system can achieve a better control effect.

[0093] The present invention further discloses a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the above method is implemented.

[0094] The present invention further provides a computer storage medium, in which instructions are stored. When the instructions are executed on a computer, the computer is enabled to execute the above method.

[0095] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: the present invention can achieve effective online identification of parameters, reduce the chattering problems of the sliding mode input and online parameter identification, and realize high-performance tracking control of the servo system. Description of the Drawings

[0096] Figure 1 is the control flow chart of the present invention;

[0097] Figure 2 is the tracking trajectory effect diagram when the reference signal is x d1 ;

[0098] Figure 3 is the tracking error effect diagram when the reference signal is x d1 ;

[0099] Figure 4 is the control input u effect diagram when the reference signal is x d1 ;

[0100] Figure 5When the reference signal is x d1 The identification effect diagrams of the system parameters θ2, θ3, and θ4;

[0101] Figure 6 When the reference signal is x d1 The estimated effect diagram of the extended state x3;

[0102] Figure 7 When the reference signal is x d2 The tracking trajectory effect diagram;

[0103] Figure 8 When the reference signal is x d2 The tracking error effect diagram;

[0104] Figure 9 When the reference signal is x d2 The control input u effect diagram;

[0105] Figure 10 When the reference signal is x d1 The identification effect diagrams of the system parameters θ2, θ3, and θ4;

[0106] Figure 11 When the reference signal is x d2 The estimated effect diagram of the extended state x3.

[0107] Figure 12 When the reference signal is x d The tracking trajectory comparison diagram;

[0108] Figure 13 When the reference signal is x d The tracking error comparison diagram;

[0109] Figure 14 When the reference signal is x d The control input u effect diagram;

[0110] Figure 15 When the reference signal is x d The identification effect diagrams of the system parameters θ2, θ3, and θ4;

[0111] Figure 16 When the reference signal is x d The estimated effect diagram of the extended state x3. Specific implementation manner

[0112] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

[0113] Referring to Figure 1 As shown, the servo system Super-twisting fast nonsingular terminal sliding mode control based on parameter error transformation includes the following steps:

[0114] Step 1: Establish a position servo system model with non-linear friction, and initialize the system state and control parameters. The specific steps are as follows:

[0115] The position servo system model is expressed as follows:

[0116]

[0117] Where y is the displacement of the system payload, and M is the total mass of the system payload; represents non-linear friction; F d represents other modeling errors and system disturbances, u represents the control input, and k represents the gain coefficient;

[0118] It is expressed as follows:

[0119]

[0120] Where f s is the static friction coefficient, f c is the Coulomb coefficient, f v is the viscous coefficient; (f s -f c )f1 describes the Stribeck effect; f c f2 is the Coulomb friction; β1 and β2 are coefficients used to approximate the shape of the Stribeck effect; β3 is the coefficient used to approximate the sig function;

[0121] When the parameters satisfy the following conditions, the friction model (2) is significantly continuously differentiable;

[0122] β1 >> 0, β1 > β2, β2 = 1 / v s , β3 >> 0 (41)

[0123] Where v s is the Stribeck speed;

[0124] Define x1 = y, Then the system model (1) can be re-expressed in state space form as:

[0125]

[0126] Where f = θ2f1(x2)+θ3f2(x2)+θ4x2, d = F d / M; where θ1 = k / M, θ2 = (f s -f c ) / M, θ3 = f c / M, θ4 = f v / M;

[0127] Let denote the estimate of ·, and define as the parameter estimation error;

[0128] Define the control input as:

[0129] θ1u = θ 10 u + Δθ 10 u (43)

[0130] where θ 10 is the nominal value of θ1, determined empirically; Δθ 10 represents the uncertain part of θ1.

[0131] Step 2: Extract parameter error information, which specifically includes the following steps: Obtained from Eqs. (4) and (5):

[0132]

[0133] Define θ = [θ2 θ3 θ4] T then there is;

[0134]

[0135] where, x2f, uf, and are the filtered variables of x2, u, and ; r is the filtered tuning parameter; x 2f (0), u f (0), are the initial values of x 2f , u f , respectively;

[0136] Obtained from Eqs. (6) and (7):

[0137]

[0138] Define two dynamic equations for W and S:

[0139]

[0140] where, l is the adjustment parameter; W(0), S(0) are the initial values of W and S respectively; W represents the covariance matrix of the parameter estimation error; S represents the covariance matrix of the tracking error;

[0141] From Eq. (8), the solution is as follows:

[0142]

[0143] where, t is the time variable, and T is the sampling period;

[0144] According to Equations (8) and (10), the information about the parameter error is obtained as follows:

[0145] S = Wθ (49)

[0146]

[0147] Step 3: Design the parameter error transformation based on a preset performance function, which specifically includes the following steps: Define the preset performance function:

[0148] χ(t) = coth(γt + υ) - 1 + χ ∞ (51)

[0149] where γ, υ are positive constants; χ(t) represents the preset performance function, and x ∞ represents the steady-state value of the preset performance function, and coth represents the hyperbolic cotangent function;

[0150] Define the parameter error transformation function:

[0151]

[0152] where ζ = [ζ1, ζ2, ζ3] T , ζ represents the transformation error, and D(ζ) is defined as a strictly monotonically increasing function; represents the parameter error;

[0153]

[0154] where δ is a positive constant, represents the parameter error exponent;

[0155] The transformed error ζ is expressed as:

[0156]

[0157] where is the normalized parameter error;

[0158] The derivative of Equation (16) is:

[0159]

[0160] where is a bounded variable.

[0161] Step 4: Design an adaptive extended state observer, which specifically includes the following steps:

[0162] Define the state where φ(x2) = [f1(x2) f2(x2) x2]T , represents the time derivative of state x3; thus, Equation (8) is reformulated as follows:

[0163]

[0164] The adaptive extended state observer is constructed as:

[0165]

[0166] where represents the state estimate, l i (t) > 0, i = 1, 2, are variable gains,

[0167] The adjustable gain l i (t), i = 1, 2, is constructed as:

[0168]

[0169] The dynamic gain w n (t) is defined as:

[0170]

[0171] where w1 is the initial gain and w2 is the final gain.

[0172] Step Five: Design the controller for the system input, which specifically includes the following steps:

[0173] The tracking error is defined as e = x1 - x d , and the derivative of the tracking error is defined as where x d represents the reference signal; the sliding surface is defined as:

[0174]

[0175] where λ > 0, λ is a constant;

[0176] According to the parameter error transformation method, the sliding surface is defined as:

[0177] s2 = ζ1 + ζ2 + ζ3 (23)

[0178] The controller for the system input is designed as:

[0179] u = u eq + u stw (24)

[0180]

[0181] where k1, k2, k3, k4 are control gains, is the model uncertainty; μ is the auxiliary control variable;

[0182] The adaptive law for online parameter identification is:

[0183]

[0184] where ρ1 is a bounded variable of ρ2 is a bounded variable of

[0185] Define the Lyapunov function:

[0186]

[0187] Taking the derivatives of V1 and V2 and substituting into the controller (24)-(26) and the parameter adaptive law (27) gives:

[0188]

[0189] Then the whole system is stable.

[0190] To verify the online identification performance and control effect of the proposed method, the present invention conducts simulation and physical experiments on it.

[0191] Set the initial conditions of various parameters in the simulation experiment as: system parameters β1 = 1000, β2 = 0.1, β3 = 3000, f s = 1.2, f c = 1, f v = 0.4; identification and control parameters x ∞ = 0.05, v = 1, w1 = 10, w2 = 32, t1 = 4, k1 = 2, k2 = 1, k3 = 1, k4 = 20, λ = 100, r = 0.001, l = diag{0.1, 0.1, 0.1}, θ 10 = 10, γ = 1. Initial conditions x 2f (0) = 0, u f (0) = 0, W(0) = 0, S(0) = 0, In the simulation experiment, the reference signal x d takes x d1 = sin(πt) and x d2 = 0.9sin(πt) + 0.6cos(t) respectively.

[0192] Figure 2-11It is the simulation experiment effect diagram of the Super-twisting fast non-singular terminal sliding mode control of the servo system based on parameter error transformation. Figure 2 and Figure 3 respectively represent the tracking trajectory and tracking error when the reference signal is x d1 . These two figures show that the trajectory of the system quickly coincides with the desired trajectory, and the tracking error can be controlled within a very small range [-2×10 -4 , 2×10 -4 . Figure 4 is the control input of the system when the reference signal is x d1 . Figure 5 is the system parameter identification result diagram when the reference signal is x d1 , indicating that the estimation of the parameters quickly and smoothly converges to their true values within a very short time. Figure 6 is the estimation diagram of the extended state x3 when the reference signal is x d1 . It can be seen from the figure that AESO can well track the disturbances and parameter estimation errors in the system. Figure 7 and Figure 8 are the tracking trajectory and tracking error effect diagrams when the reference signal is x d2 , which shows that the system still has a good tracking effect when the reference signal changes. Figure 9 is the system input when the reference signal is x d2 . As mentioned above, the super-twisting fast non-singular terminal sliding mode control method adopted in this paper has no jitter phenomenon. Figure 10 is the system parameter identification result diagram when the reference signal is x d2 . Although the trajectory has changed, the adopted parameter error transformation method ensures that the system parameters quickly and accurately converge to the actual values. Figure 11 is the estimation diagram of the extended state x3 when the reference signal is x d2 , which shows that this method has strong estimation performance. From the results of the simulation experiment, the method of parameter error conversion based on the preset performance function proposed in the present invention can online identify the unknown parameters of the system with high precision and achieve high-performance tracking control of the system.

[0193] Set the initial conditions of various parameters in the physical experiment as: system parameters β1 = 1000, β2 = 0.1, β3 = 3000, f s = 1.2, f c = 1, f v = 0.4; identification and control parameter C1: x ∞= 0.01, v = 0.5, w1 = 0.4, w2 = 1, t1 = 1, k1 = 0.005, k2 = 0.005, k3 = 0.005, k4 = 16, λ = 0.01, r = 0.001, l = diag{0.1, 0.1, 0.1}, θ 10 = 10, γ = 1. Initial condition x 2f (0) = 0, u f (0) = 0, W(0) = 0, S(0) = 0, In the physical experiment, the reference signal x d Take x d = 0.8πsin(t).

[0194] The PI control is adopted for the comparative experiment. The identification and control parameters C2:k p = 0.8, k i = 0.00001.

[0195] Figure 12 - Figure 16 It is the physical experiment effect diagram of the Super-twisting fast non-singular terminal sliding mode control of the servo system based on the parameter error transformation. Figure 12 It shows the comparison diagram of the tracking trajectories when the reference signal is x d , indicating that the trajectories of the proposed system and the PI control system quickly converge to the desired trajectory. However, in terms of the convergence accuracy, the control method proposed in this paper has significantly higher accuracy compared with the PI control method. Figure 13 It shows the comparison diagram of the tracking errors when the reference signal is x d , indicating that the tracking errors of the proposed system and the PI control system are both within the control range [-0.1, 0.1] of the controller. However, compared with the PI control method, the error of the control method proposed in this paper is significantly smaller. Figure 14 It is the control input of the system when the reference signal is x d , Figure 15 It is the parameter identification result when the reference signal is x d , indicating that the estimation of the parameters can converge to their true values within a very short time, and proves the effectiveness of the parameter error transformation method. Figure 16 It is the estimation diagram of the extended state x3 when the reference signal is x d . From the results of the physical experiment, the method of parameter error conversion based on the preset performance function proposed in the present invention can accurately identify the unknown parameters of the system online in the physical object and achieve high-performance tracking control of the system. As described above, the Super-twisting fast non-singular terminal sliding mode control method of the servo system based on the parameter error transformation adopted in this paper can be applied to the physical object.

[0196] The simulation and physical experiments described above are given by the present invention to demonstrate 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. Various deformations can be 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 parameter error conversion and AESO designed by the present invention have good identification and tracking control effects on the non-linear position servo system, and can achieve high-precision parameter identification and tracking control of the servo system.

Claims

1. A Super-twisting fast non-singular terminal sliding mode control method for a servo system based on parametric error transformation, characterized in that, It includes the following steps: Establish a position servo system model with non - linear friction, and initialize the system state and control parameters; Extract parameter error information; Design parameter error conversion based on a preset performance function; Design an adaptive extended state observer; Design a controller for the system input.

2. The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation according to claim 1, characterized in that, The establishment of the position servo system model with non - linear friction and the initialization of the system state and control parameters include the following steps: The position servo system model is expressed as follows: where y is the displacement of the system payload, and M is the total mass of the system payload; represents the non-linear frictional force; F d represents other modeling errors and system disturbances, u represents the control input, and k represents the gain coefficient; It is described as follows: where, f s is the static friction coefficient, f c is the Coulomb coefficient, f v is the viscous coefficient; (f s - f c ) f1 describes the Stribeck effect; f c f2 is the Coulomb friction force; β1 and β2 are coefficients used to approximate the shape of the Stribeck effect; β3 is the coefficient used to approximate the sig function; When the parameters satisfy the following conditions, the friction model (2) is significantly continuously differentiable; β1＞＞0，β1＞β2,β2＝1 / v s ,β3＞＞0 (3) where v s is the Stribeck speed; Define \(x_1 = y\), Then the system model (1) can be reformulated in the state - space form as follows: where \(f = \theta_2f_1(x_2)+\theta_3f_2(x_2)+\theta_4x_2\), \(d = F\) d / M; where \(\theta_1 = k / M\), \(\theta_2=(f s -f c ) / M, \(\theta_3 = f c / M, \(\theta_4 = f v / M; Let denote the estimate of ·, and define as the parameter estimation error; Define the control input quantity as: θ1u = θ 10 u + Δθ 10 u (5) where θ 10 is the nominal value of θ1, determined empirically; Δθ 10 represents the uncertain part of θ1.

3. The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation according to claim 2, characterized in that, The extraction of the parameter error information includes the following steps: Obtained from equations (4) and (5): Definition θ = [θ2 θ3 θ4] T There is; where x 2f , u f and are the filtering variables of x2, u, and ; r is the filtered tuning parameter; x 2f (0), u f (0), are the initial values of x 2f , u f , respectively; Obtained from equations (6) and (7): Define two dynamic equations regarding W and S: Where l is an adjustment parameter; W(0) and S(0) are the initial values of W and S respectively; W represents the covariance matrix of the parameter estimation error; S represents the covariance matrix of the tracking error; From equation (8), the solution is as follows: Where t is the time variable and T is the sampling period; According to equations (8) and (10), the information about the parameter error is obtained as follows: S = Wθ (11) 4. The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation according to claim 3, characterized in that, The design of the parameter error conversion based on the preset performance function includes the following steps: Define the preset performance function: χ(t) = coth(γt + υ) - 1 + χ ∞ (13) where γ and υ are positive constants; χ(t) represents a predefined performance function, and x ∞ represents the steady-state value of the predefined performance function, and coth represents the hyperbolic cotangent function; Define the parameter error conversion function: where ζ = [ζ1, ζ2, ζ3] T , ζ represents the conversion error, and D(ζ) is defined as a strictly monotonically increasing function; represents the parameter error; wherein, δ is a positive constant, representing the parameter error exponent; The converted error ζ is expressed as: Among them, is the normalized parameter error; The derivative of equation (16) is: wherein is a bounded variable.

5. The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation according to claim 3, characterized in that The design of the adaptive extended state observer includes the following steps: Define the state where represents the time derivative of state x3; thus, Equation (8) is reformulated as follows: The adaptive extended state observer is constructed as: Among them represents state estimation, l i (t) > 0, i = 1, 2, are variable gains, Adjustable gain l i (t), i = 1, 2, is configured as: Dynamic gain w n (t) is defined as: Where w1 is the initial gain and w2 is the final gain.

6. The servo system Super-twisting fast non-singular terminal sliding mode control method based on parameter error transformation according to claim 5, characterized in that, The design of the controller for the system input includes the following steps: The tracking error is defined as e = x1 - x d , and the derivative of the tracking error is defined as where x d represents the reference signal; the sliding surface is defined as: Where λ > 0 and λ is a constant; Define the sliding surface according to the parameter error transformation method as: s2 = ζ1 + ζ2 + ζ3 (23) The controller for the system input is designed as: u = u eq + u stw (24) where k1, k2, k3, k4 are control gains, is the model uncertainty; μ is the auxiliary control variable; The adaptive law for online parameter identification is: wherein ρ1 is a bounded variable of, ρ2 is a bounded variable of, ρ3 is a bounded variable of; Define the Lyapunov function: Deriving the derivatives of V1 and V2 and substituting them into the controllers (24)-(26) and the parameter adaptation laws (27) gives: Then the whole system is stable.

7. 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 - 6.

8. A computer storage medium, characterized in that, The computer storage medium stores instructions, which when executed on a computer, cause the computer to execute the method described in any one of claims 1 - 6.

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