Fixed time adaptive control method for dual-motor servo system containing nonlinear dead zone

Abstract

The invention discloses a fixed time adaptive control method for a dual-motor servo system containing a nonlinear dead zone. The method comprises the following steps: establishing a dynamic model of the dual-motor servo system, and describing the total transmission torque in the dynamic model of the dual-motor servo system by using a nonlinear dead zone function; estimating a nonlinear function in the dynamic model of the reconstructed dual-motor servo system by using a continuous piecewise linear neural network; based on a non-singular fixed time sliding mode surface, a continuous linear piecewise neural network, a virtual control law and a second-order sliding mode differentiator, a non-singular fixed time sliding mode controller based on an adaptive law is designed to serve as input torque of the dual-motor servo system, and tracking of desired signals by system output is achieved. Through the controller designed by combining the continuous piecewise linear neural network and the non-singular fixed time sliding mode surface, the effects of ensuring the load tracking precision and increasing the system response speed without being influenced by the initial state of the system can be achieved, and buffeting can be effectively suppressed.

Description

Technical Field

[0001] The invention relates to a fixed-time adaptive control method for a dual-motor servo system containing a nonlinear dead zone, and belongs to the technical field of load tracking of the dual-motor servo system. Background Art

[0002] Dual-motor servo systems are now widely used in various fields such as industry, medicine, and aviation. However, the dual-motor servo system itself has the characteristics of strong coupling, nonlinearity, uncertainty of some internal parameters, etc., and will also be affected by nonlinear dead zone disturbances during operation. These problems will affect the tracking accuracy of the load to the motor. Therefore, how to achieve fast and high-precision load tracking control of the dual-motor system under the influence of these problems is still a huge challenge. Many scholars have proposed and improved various advanced control methods to achieve the expected control effect, such as fuzzy control, anti-disturbance control, adaptive control, model predictive control, sliding mode control, etc. Among them, sliding mode control provides a high-quality control solution for dual-motor load tracking control due to its own robustness and simple implementation.

[0003] The design of sliding mode control includes sliding surface design and reaching law design. Traditional linear sliding mode control has problems such as uncertain convergence time and singularity. Therefore, scholars have proposed terminal sliding mode control, which can achieve system stability in a limited time. Furthermore, in view of the potential singularity problem that often exists in terminal sliding mode control, patent application CN117506908A discloses a non-singular terminal sliding mode control scheme for trajectory tracking control, which avoids potential singularities by reasonably adjusting the state variables of the sliding surface. However, when the system converges to the vicinity of the equilibrium point, the error convergence speed is slow. In view of the defects of non-singular terminal sliding mode control, patent application CN117762020A discloses a fast non-singular terminal sliding mode control scheme, which enhances the rapidity of tracking error convergence and control accuracy, but its error convergence time is affected by the initial state of the system. Therefore, it is still very important to improve the current control method.

[0004] In view of this, the present invention is proposed. Summary of the invention

[0005] The present invention provides a fixed-time adaptive control method for a dual-motor servo system with a nonlinear dead zone. By designing a controller by combining a continuous piecewise linear neural network with a non-singular fixed-time sliding surface, the method can achieve the effects of ensuring load tracking accuracy, accelerating system response speed and being unaffected by the initial state of the system. In addition, in the process of designing the controller, a sig(·) function is introduced, which can effectively suppress chattering.

[0006] The technical solution of the present invention is:

[0007] A fixed-time adaptive control method for a dual-motor servo system with a nonlinear dead zone comprises the following steps:

[0008] S1. Establishing a dynamic model of a dual-motor servo system and using a nonlinear dead zone function to describe the total transmission torque in the dynamic model of the dual-motor servo system;

[0009] S2, estimating the nonlinear function in the dynamic model of the reconstructed dual-motor servo system using a continuous piecewise linear neural network;

[0010] S3, based on the non-singular fixed-time sliding mode surface, virtual control law and second-order sliding mode differentiator, a non-singular fixed-time sliding mode controller based on adaptive law is designed as the input torque of the dual-motor servo system to achieve the system output x1 to the expected signal x d tracking.

[0011] Furthermore, the S2 specifically includes:

[0012] S2.1, reconstructing the dynamics model of the dual-motor servo system to obtain a reconstructed dynamics model of the dual-motor servo system;

[0013] S2.2. Divide the nonlinear dead zone function into N non-overlapping subdomains according to the continuous linear segmented neural network, and set σ0 = 1 to obtain the reconstructed nonlinear dead zone function:

[0014]

[0015] Among them, p r (z) and q r (z) are the lower and upper bounds of the rth subdomain of the nonlinear dead zone function; z is the angular position difference between the motor and the load; the weight W T =[ρ0…ρ N ], ρ0 represents the minimum lower bound of the unknown weights of the neural network, ρ N Represents the upper bound of the unknown weights of the neural network; the activation function vector σ N That is, the activation function σ N (a, b, c); Φ is the activation function vector;

[0016] S2.3. Nonlinear functions in the dynamic model of the reconstructed dual-motor servo system Estimation is performed using the reconstructed nonlinear dead zone function:

[0017]

[0018] in, J l is the load inertia; J mis the motor inertia; represents the reconstructed nonlinear dead zone function.

[0019] Furthermore, the S3 specifically includes the following steps:

[0020] S3.1, design a first non-singular fixed-time sliding surface s1; based on the first non-singular fixed-time sliding surface, design a first adaptive law; based on the first adaptive law, design a virtual control law η;

[0021] S3.2, introduce a second-order sliding mode differentiator into the virtual control law;

[0022] S3.3. Design a second non-singular fixed-time sliding surface s2; design a second adaptive law based on the second non-singular fixed-time sliding surface; design a non-singular fixed-time sliding mode controller u based on the adaptive law based on the second non-singular fixed-time sliding surface, the second adaptive law and the estimated value of the second-order derivative of the virtual control law.

[0023] Furthermore, the designing of the first non-singular fixed-time sliding surface specifically includes:

[0024] Define tracking error e1;

[0025] According to the tracking error and the estimated nonlinear function, the first non-singular fixed-time sliding surface s1 is designed:

[0026]

[0027] in, and The expression is:

[0028]

[0029] in, represents the first-order derivative of s1; represents the first and second order derivatives of e1; k s1 >0,l s1 >0, 0<α1<1, α2>1 are all constants; |e1| is the modulus of the tracking error e1; ε e1 is a constant; an intermediate variable x2 and x3 are defined system state variables, b l is the load viscous friction coefficient; W is the weight; J l is the load inertia; Φ is the excitation function vector; For x d The second derivative of .

[0030] Furthermore, the first adaptive law is designed based on the first non-singular fixed-time sliding mode surface s1 as follows:

[0031]

[0032] Among them, Γ1 and is a constant, is the estimated value of W1, for The first derivative of .

[0033] Furthermore, according to the first adaptive law, the virtual control law η is designed as:

[0034]

[0035] In the formula, is a normal number; R1∈(1 / 2,1), Q1∈(1,3 / 2); a1 is a constant.

[0036] Furthermore, the designing of the second non-singular fixed-time sliding surface specifically includes:

[0037] According to the designed virtual control law η, the tracking virtual error e2 is defined;

[0038] According to the tracking virtual error, the second non-singular fixed-time sliding surface s2 is designed as:

[0039]

[0040] in, and The expression is:

[0041]

[0042]

[0043] in, represents the first-order derivative of s2; represents the first and second order derivatives of e2; k s2 >0,l s2 >0, 0<α3<1, α4>1 are all constants; |e2| is the modulus of the tracking virtual error e2; ε e2 is a constant, an intermediate variable b mi is the motor viscous friction coefficient of the i-th motor, x4 is the system state variable; W is the weight, J mis the motor inertia; u is a non-singular fixed-time sliding mode controller based on the adaptive law; Φ is the excitation function vector.

[0044] Furthermore, according to the second non-singular fixed-time sliding mode surface s2, the second adaptive law is designed as:

[0045]

[0046] Among them, Γ2 and is a constant, is the estimated value of W2, for The first derivative of .

[0047] Furthermore, the estimated value of the second derivative of the second non-singular fixed time sliding surface s2, the second adaptive law and the virtual control law η Design a non-singular fixed-time sliding mode controller u based on the adaptive law as:

[0048]

[0049] in, is a normal number; R2∈(1 / 2,1), Q2∈(1,3 / 2); a2 is a constant.

[0050] The beneficial effects of the present invention are:

[0051] 1) A continuous linear segmented neural network is used to estimate the nonlinear dead zone function in the dual-motor servo system, and finally embedded in the controller for compensation, which can effectively eliminate the adverse effects caused by the nonlinear function in the motor operation.

[0052] 2) The present invention designs a non-singular fixed-time sliding mode, which, on the one hand, solves the singularity problem existing in sliding mode control, and on the other hand, can make the error signal converge to a minimum neighborhood of zero within a fixed time, thereby accelerating the convergence speed.

[0053] 3) The non-singular fixed-time sliding mode controller based on the adaptive law designed in the present invention, on the one hand, compensates for the nonlinear dead zone function existing in the system, and on the other hand, introduces the sig(·) function, which can effectively suppress the system chattering. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a control flow diagram of the method of the present invention;

[0055] Figure 2 It is a schematic diagram of the position tracking effect and tracking error of the load under the action of the expected signal involved in the present invention;

[0056] Figure 3A schematic diagram of motor dead zone estimation and estimation error of a dual-motor servo system according to the present invention;

[0057] Figure 4 The present invention is a schematic diagram of load dead zone estimation and estimation error of a dual-motor servo system. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0059] refer to Figure 1-Figure 4 The present invention provides a fixed-time adaptive control method for a dual-motor servo system with a nonlinear dead zone, comprising the following steps:

[0060] S1. Establish the dynamic model of the dual-motor servo system and initialize the state and parameters of the dual-motor servo system. The process is as follows:

[0061] The dynamic model of the dual-motor servo system is expressed as follows:

[0062]

[0063] Where: i = 1, 2 represent the two motors in the dual-motor servo system (i = 1 represents the first motor, i = 2 represents the second motor); J mi ,θ mi 、b mi are the motor inertia, motor angular position, and motor viscous friction coefficient of the i-th motor respectively; J l is the load inertia; θ l is the load angular position; b l is the load viscous friction coefficient, u i is the system input torque of the ith motor, τ i is the transmission torque when the i-th motor contacts the load, and defines the total transmission torque of the two motors

[0064] Because the transmission torque is nonlinear, the following nonlinear dead zone function is used to describe the total transmission torque τ, which is expressed as:

[0065]

[0066] Where: z = θ m -νθ lis the angular position difference between the motor and the load, ν is the transmission ratio, here ν = 1; k + and k - is the slope of the nonlinear death function, α + and α - is the dead zone width of the nonlinear dead zone function. In practical applications, the dead zone slope and dead zone width have upper and lower bounds.

[0067] S2. Estimating the nonlinear function in the dynamic model of the reconstructed dual-motor servo system using a continuous piecewise linear neural network; further comprising the following:

[0068] S2.1, reconstructing the dynamics model of the dual-motor servo system to obtain a reconstructed dynamics model of the dual-motor servo system;

[0069] Define the system state variables as The dynamic model of the dual-motor servo system is reconstructed to obtain the reconstructed dynamic model of the dual-motor servo system, which is expressed as:

[0070]

[0071] Among them, y is the system output,

[0072] S2.2, constructing a continuous linear piecewise neural network to estimate the nonlinear dead zone function, and obtaining a reconstructed nonlinear dead zone function;

[0073] The present invention reconstructs the nonlinear dead zone function shown in formula (2), specifically: the nonlinear dead zone function is divided into N non-overlapping subdomains D according to a continuous linear segmented neural network. r (r=0,…,N), then the reconstructed nonlinear dead zone function can be expressed as:

[0074]

[0075] Among them, p r (z) and q r (z) are the lower and upper bounds of the rth subdomain of the nonlinear dead zone function, respectively, and ρ r is the unknown weight of the neural network, ρ0 represents the minimum lower bound of the unknown weight of the neural network; σ r (0,zp r (z),q r (z)-p r (z) is used as the excitation function and is determined by the following formula:

[0076] σ r (a,b,c)=max(a,min(b,c)) (5)

[0077] Assuming σ0 = 1, the reconstructed nonlinear dead zone function is rewritten as follows:

[0078]

[0079] Among them, the weight W T =[ρ0…ρ N ]; activation function vector σ N That is, σ N (a,b,c), the same for the others;

[0080] According to the characteristics of the nonlinear dead zone function, the parameter estimation of the nonlinear dead zone function is as follows:

[0081]

[0082] in, and They are α + , -α - , k + and k - The estimated value of + and r - They are the last and first r when f(z)=0 respectively; Indicates p r (z) where r is the value of r + The value of Indicates p r (z) where r is the value of r - The value of when

[0083] S2.3. Nonlinear functions in the dynamic model of the reconstructed dual-motor servo system Estimation is performed using the reconstructed nonlinear dead zone function:

[0084]

[0085] in,

[0086] S3, based on the non-singular fixed-time sliding mode surface, virtual control law and second-order sliding mode differentiator, a non-singular fixed-time sliding mode controller based on adaptive law is designed as the input torque of the dual-motor servo system to achieve the system output x1 to the expected signal x d Further, including the following:

[0087] S3.1. Design the first non-singular fixed-time sliding surface, the virtual control law η and the first adaptive law

[0088] Define the tracking error e1 as:

[0089] e1=x1-x d (9)

[0090] Among them, x1 is the system output, x d is the expected output signal.

[0091] According to the tracking error and the estimated nonlinear function, the first non-singular fixed-time sliding surface s1 is designed as:

[0092]

[0093] in, and The expression is:

[0094]

[0095]

[0096] in, k s1 >0,l s1 >0, 0<α1<1, α2>1 are all constants; |e1| is the modulus of the tracking error e1, ε e1 is a small constant, the intermediate variable

[0097] According to the first non-singular fixed-time sliding surface, the first adaptive law is designed as:

[0098]

[0099] Among them, Γ1 and is a constant, is the estimated value of W1.

[0100] According to the first adaptive law, the virtual control law η is designed as:

[0101]

[0102] In the formula, W is the weight; J l is the load inertia, is a positive constant; the general expression of the sig(·) function The same is true for other sig(·) functions in this article; R1∈(1 / 2,1), Q1∈(1,3 / 2); a1 is a constant; For x d The second derivative of

[0103] S3.2, Introducing the second-order sliding mode differentiator

[0104] Let the virtual control law η pass through the following second-order sliding mode differentiator to obtain the estimated values ​​of the virtual control law η and its first and second-order derivatives:

[0105]

[0106] Among them, sat(·) is a saturation function, which can be used to reduce the chattering problem; m0, m1, and m2 are positive constants. and are η, and The estimated value of and They are and The first derivative of ;

[0107] Filter Error I=0,1,2 satisfies:

[0108] in, for The model, is a constant; I = 0, η (I) Represents η; I=1,2, η (I) represents the I-order derivative of η;

[0109] S3.3, the second non-singular fixed-time sliding mode surface, the non-singular fixed-time sliding mode controller u based on the adaptive law, and the second adaptive law

[0110] According to the designed virtual control law, the tracking virtual error e2 is defined as:

[0111]

[0112] According to the tracking virtual error and the estimated nonlinear function, the second non-singular fixed-time sliding surface s2 is designed as:

[0113]

[0114] in, and The expression is:

[0115]

[0116]

[0117] in, k s2 >0,l s2 >0, 0<α3<1, α4>1 are all constants; |e2| is the modulus of the tracking virtual error e2, ε e2is a small constant, the intermediate variable

[0118] According to the second non-singular fixed-time sliding surface, the second adaptive law is designed as:

[0119]

[0120] Among them, Γ2 and is a constant, is the estimated value of W2.

[0121] According to the second non-singular fixed-time sliding mode surface, the second adaptive law and the estimated value ν2 of the second-order derivative of the virtual control law η, the non-singular fixed-time sliding mode controller u based on the adaptive law is designed as:

[0122]

[0123] in, W is the weight, J m is the motor inertia; is a positive constant; the general expression of the sig(·) function The same is true for other sig(·) functions in this article; R2∈(1 / 2,1), Q2∈(1,3 / 2); a2 is a constant.

[0124] In the above, the non-singular fixed-time sliding mode controller based on the adaptive law shown in formula (22) is obtained by using the first non-singular fixed-time sliding mode surface shown in formula (10), the second non-singular fixed-time sliding mode surface shown in formula (18), the virtual control law shown in formula (14), the first adaptive law shown in formula (13), and the second adaptive law shown in formula (21). According to the reconstructed dynamic model of the dual-motor servo system shown in formula (3) and the non-singular fixed-time sliding mode controller based on the adaptive law, a closed-loop system is constructed. The stability of the closed-loop system is analyzed using the Lyapunov function. The following conclusions are obtained after analysis:

[0125] 1) Estimation error of the system dead zone by the neural network Bounded.

[0126] 2) The tracking error can be approached to zero under any initial conditions.

[0127] 3) According to the fixed time control principle, the closed-loop system can converge to the minimum neighborhood of the zero point within a fixed time.

[0128] Stability analysis: For the convenience of calculation, define j = 1, 2. Define a Lyapunov function as:

[0129]

[0130] Taking the derivative of V1, we get:

[0131]

[0132] For any scalar ν j >(1 / 2), we can get:

[0133]

[0134] Substituting the above formula into formula (24), we can obtain:

[0135]

[0136] in, So we can get is bounded, defined Is a normal number.

[0137] Formula (24) can be further expressed as:

[0138]

[0139] in, λ max (Γ j ) means taking the maximum value of the quantity in brackets;

[0140] If satisfied You can get:

[0141]

[0142] If satisfied You can get:

[0143]

[0144] in, l0=(Q j +1) / 2.

[0145] when You can get:

[0146]

[0147] The expression can be further expressed as:

[0148]

[0149] in,

[0150] According to the fixed time control principle, the closed-loop system is actually stable within a fixed time and can converge to the following zero minimum neighborhood within a fixed time:

[0151]

[0152] When ε∈(0,1), the convergence time satisfies:

[0153]

[0154] In order to verify the feasibility of the method described in the present invention, a control simulation experiment of the above control method in a dual-motor servo system is given. The simulation experiment uses a dual-motor servo system as the research object. The initial state of the dual-motor servo system is defined as: x1 = 0.2, x2 = 0, x3 = 0.3, x4 = 0.1; the parameters of the dual-motor servo system are: J m =0.185kg·m 2 , b m =1.2N·m·s / rad, J l =0.028kg·m 2 , b l =1.3N·m·s / rad. The desired output signal is defined as: x d = sin(t). The sampling time is set to 20s.

[0155] The specific parameters of the controller designed by the present invention are as follows: - =0.4, k + =0.6,α + =α - =0.1; Γ1=Γ2=100, k s1 =k s2 =600, l s1 = l s2 =800, α1=α3=0.3, α2=α4=1.6; m0=m1=m2=100; a1=25, a2=18, ε e1 =ε e2 =0.1.

[0156] Substituting the above parameters into the controller of the present invention and the reconstructed dynamic model, the simulation results are as follows: The tracking curve of the load to the motor and the tracking error curve in the dual-motor servo system are as follows: Figure 2 As shown; the estimation curve of the continuous linear segmented neural network for the nonlinear function of the motor side and the load side and the estimation error curve are shown in Figure 3 and Figure 4 shown.

[0157] pass Figure 2 It can be seen that the fixed-time adaptive control method for the dual-motor servo system with nonlinear dead zone proposed in the present invention can make the output signal track the expected signal well, with small tracking error and short response time, and has good control performance.

[0158] from Figure 3 and Figure 4 It can be seen that the continuous linear piecewise neural network can better estimate the nonlinear functions on the motor side and the load side within the allowable range of the estimation error, has a good estimation effect, and can be well embedded in the controller to compensate for the nonlinear function.

[0159] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone, characterized in that: The following steps are involved: S1. Establishing a dynamic model of a dual-motor servo system and using a nonlinear dead zone function to describe the total transmission torque in the dynamic model of the dual-motor servo system; S2, estimating the nonlinear function in the dynamic model of the reconstructed dual-motor servo system using a continuous piecewise linear neural network; S3, based on the non-singular fixed-time sliding mode surface, virtual control law and second-order sliding mode differentiator, a non-singular fixed-time sliding mode controller based on adaptive law is designed as the input torque of the dual-motor servo system to achieve the system output x1 to the expected signal x d tracking.

2. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 1, characterized in that: The S2 specifically includes: S2.1, reconstructing the dynamics model of the dual-motor servo system to obtain a reconstructed dynamics model of the dual-motor servo system; S2.

2. Divide the nonlinear dead zone function into N non-overlapping subdomains according to the continuous linear segmented neural network, and set σ0 = 1 to obtain the reconstructed nonlinear dead zone function: Among them, p r (z) and q r (z) are the lower and upper bounds of the rth subdomain of the nonlinear dead zone function; z is the angular position difference between the motor and the load; the weight W T =[ρ0…ρ N ], ρ0 represents the minimum lower bound of the unknown weights of the neural network, ρ N Represents the upper bound of the unknown weights of the neural network; the activation function vector σ N That is, the activation function σ N (a, b, c); Φ is the activation function vector; S2.

3. Nonlinear functions in the dynamic model of the reconstructed dual-motor servo system Estimation is performed using the reconstructed nonlinear dead zone function: in, J l is the load inertia; J m is the motor inertia; represents the reconstructed nonlinear dead zone function.

3. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 1, characterized in that: The S3 specifically includes the following steps: S3.1, design a first non-singular fixed-time sliding surface s1; based on the first non-singular fixed-time sliding surface, design a first adaptive law; based on the first adaptive law, design a virtual control law η; S3.2, introduce a second-order sliding mode differentiator into the virtual control law; S3.

3. Design a second non-singular fixed-time sliding surface s2; design a second adaptive law based on the second non-singular fixed-time sliding surface; design a non-singular fixed-time sliding mode controller u based on the adaptive law based on the second non-singular fixed-time sliding surface, the second adaptive law and the estimated value of the second-order derivative of the virtual control law.

4. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 3 is characterized in that: The designing of the first non-singular fixed-time sliding surface specifically includes: Define tracking error e1; According to the tracking error and the estimated nonlinear function, the first non-singular fixed-time sliding surface s1 is designed: in, and The expression is: in, represents the first-order derivative of s1; represents the first and second order derivatives of e1; k s1 >0,l s1 >0, 0<α1<1, α2>1 are all constants; |e1| is the modulus of the tracking error e1; ε e1 is a constant; an intermediate variable x2 and x3 are defined system state variables, b l is the load viscous friction coefficient; W is the weight; J l is the load inertia; Φ is the excitation function vector; For x d The second derivative of .

5. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 4 is characterized in that: The first adaptive law is designed based on the first non-singular fixed-time sliding surface s1: Among them, Γ1 and is a constant, is the estimated value of W1, for The first derivative of .

6. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 5, characterized in that: According to the first adaptive law, the virtual control law η is designed as: In the formula, is a normal number; R1∈(1 / 2,1), Q1∈(1,3 / 2); a1 is a constant.

7. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 3, characterized in that: The designing of the second non-singular fixed-time sliding surface specifically includes: According to the designed virtual control law η, the tracking virtual error e2 is defined; According to the tracking virtual error, the second non-singular fixed-time sliding surface s2 is designed as: in, and The expression is: in, represents the first-order derivative of s2; represents the first and second order derivatives of e2; k s2 >0,l s2 >0, 0<α3<1, α4>1 are all constants; |e2| is the modulus of the tracking virtual error e2; ε e2 is a constant, an intermediate variable b mi is the motor viscous friction coefficient of the i-th motor, x4 is the system state variable; W is the weight, J m is the motor inertia; u is a non-singular fixed-time sliding mode controller based on the adaptive law; Φ is the excitation function vector.

8. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 7, characterized in that: According to the second non-singular fixed-time sliding mode surface s2, the second adaptive law is designed as: Among them, Γ2 and is a constant, is the estimated value of W2, for The first derivative of .

9. The fixed-time adaptive control method for a dual-motor servo system with nonlinear dead zone according to claim 8, characterized in that: The estimated value of the second derivative of the second non-singular fixed time sliding surface s2, the second adaptive law and the virtual control law η Design a non-singular fixed-time sliding mode controller u based on the adaptive law as: in, is a normal number; R2∈(1 / 2,1), Q2∈(1,3 / 2); a2 is a constant.

Images