Predetermined time control method for multi-motor servo system based on state and parameter estimation

Abstract

The present disclosure provides a method for predetermined time control of a multi-motor servo system based on state and parameter estimation, which aims to improve the control accuracy, dynamic responsiveness and robustness of the multi-motor servo system. First, a Gaussian neural network is used for nonlinear dynamic modeling to accurately approximate the unknown dynamic characteristics in the system. Secondly, an observer is designed for the multi-motor servo system, which can simultaneously estimate the unknown state and parameters of the system, significantly improving the adaptability and robustness of the system under complex working conditions. Finally, combined with the observer estimation results, a new variable gain predefined sliding mode control surface is proposed. This method can effectively overcome the state constraint problem existing in traditional sliding mode control and ensure that the system achieves fast and stable tracking control within a predetermined time. Through the technical solution of the present invention, the performance of the multi-motor servo system in terms of precise control, high-speed response and robustness can be significantly improved, and it is widely applicable to high-precision, multi-degree-of-freedom servo control systems.

Description

Technical Field

[0001] The present invention relates to the field of electromechanical control technology, and in particular to a method for controlling a multi-motor servo system in predetermined time based on state and parameter estimation. Background Art

[0002] Servo systems are widely used in fields such as industrial automation, robotics, and precision machining. Their high precision and rapid response are crucial to system performance. However, traditional single-motor servo systems, due to limitations in drive and load capacity, have struggled to meet the demands of high performance, multi-tasking, and complex operating conditions. Consequently, multi-motor linkage control strategies have emerged. By leveraging the coordinated operation of multiple low-power motors, they significantly enhance the system's drive capability and overload tolerance, reduce the power burden of a single motor, and improve control accuracy and response speed, while reducing design and manufacturing costs.

[0003] Currently, many tracking controllers for motor servo systems assume that the system's state and parameters are known. Control algorithms designed based on this assumption can achieve high tracking accuracy under ideal conditions. However, in real-world applications, especially in complex and dynamically changing environments, accurate system state and parameters are often difficult to obtain, resulting in reduced accuracy in existing algorithms when dealing with uncertainty. Therefore, achieving high-precision control in the absence of known system state and parameters has become a critical issue that needs to be addressed.

[0004] Furthermore, sliding mode control, as a classic robust control method, has excellent anti-interference capabilities and the ability to adapt to complex dynamic environments. However, traditional sliding mode control methods suffer from the unpredictability of the time required for the system state to reach the sliding surface, making it difficult to precisely control the convergence time. This is particularly true in multi-motor servo systems that require fast response and high-precision control. Excessive convergence time can affect response speed and control accuracy, and may even lead to system instability. Summary of the Invention

[0005] In view of this, and taking into account the technical bottlenecks of existing multi-motor servo systems in processing complex nonlinear dynamics, state estimation and parameter identification, the present invention proposes a predetermined time control method for a multi-motor servo system based on state observation and parameter estimation. This method can effectively estimate the state and parameters of the system at the same time, accurately compensate for unknown nonlinear dynamics in the system, and ensure that the tracking error in the control system converges quickly to zero within a predetermined time, thereby realizing high-precision and high-response speed multi-motor servo control.

[0006] In order to solve the above technical problems, the present invention is implemented as follows.

[0007] A method for pre-setting time control of a multi-motor servo system based on state and parameter estimation, comprising:

[0008] Step 1: Train a neural network to estimate the unknown dynamics of the multi-motor servo system; the unknown dynamics include friction and disturbance; the input of the neural network is the control quantity u and system output y of the multi-motor servo system, and the output of the neural network is the system dynamic estimation quantity d net ;

[0009] Step 2: During control, the control quantity u and system output y of the multi-motor servo system are input into the neural network, and the system dynamic estimation quantity d output by the neural network is net Provided to the adaptive observer and adaptive tracking controller;

[0010] Step 3: The adaptive observer uses the system dynamics estimator d net As compensation for system friction and external disturbances, the system state quantities and parameters are observed and the state estimation is and parameter estimates Provided to the adaptive tracking controller;

[0011] Step 4: Using the error between the position of the multi-motor servo system and the desired position as input, an adaptive variable gain predetermined time sliding mode tracking controller is used to generate a control variable u, which is output to the multi-motor servo system; the adaptive variable gain predetermined time sliding mode tracking controller uses the system dynamic estimation quantity d net To compensate for the friction and external disturbances of the system, and to use the estimator of the adaptive observer and As the actual system state and parameters, and according to the actual needs to design the sliding surface of the predetermined time T f , ensuring that the system achieves tracking within that time.

[0012] Preferably, the neural network adopts a Gaussian neural network.

[0013] Preferably, the Gaussian neural network includes:

[0014] Input layer: The input layer contains two nodes, representing the system control variable u and the system output y respectively;

[0015] Hidden layer: There are three hidden layers; the first layer contains 10 nodes, the second layer contains 16 nodes, and the third layer contains 12 nodes. Each hidden layer converts the input features into a higher-dimensional representation through high-dimensional nonlinear mapping, enabling the network to effectively capture the complex nonlinear relationship between input and output.

[0016] Output layer: The output layer contains 1 node, which is used to output the approximated system dynamic estimate d net .

[0017] Preferably, in step 2, the system dynamics estimate d net The compensated adaptive observer is:

[0018] System dynamics estimator d net The compensated multi-motor servo system model is:

[0019]

[0020] where x(t) = [x1, x2] T , x1=θ L , θ L represents the angular position of the load of the multi-motor servo system; A is the system matrix, Ψ(t) is the regression matrix, C is the output matrix of the system, y(t) is the system output; θ is the system parameter to be estimated:

[0021] θ=[θ1θ2] T ,

[0022] Where ε is the load angular position θ without dead zone nonlinearity L and the motor angular position θ m The proportional coefficient between L and J m Represents the load and the rotational inertia of each motor respectively; b m Indicates the viscous friction coefficient of the motor;

[0023] Then, the auxiliary matrix is ​​designed based on the multi-motor servo system model:

[0024]

[0025] Then, the system dynamics estimate d net The compensated adaptive observer is:

[0026]

[0027] in, and are the state estimation and parameter estimation of the adaptive observer output respectively; (A-KC) is the Hurwitz matrix, K is the observation gain vector, and Γ is the learning gain matrix.

[0028] Preferably, in step 4, the adaptive variable gain predetermined time sliding mode tracking controller is designed as follows:

[0029] Get the multi-motor servo system position y and combine it with the expected signal x d , calculate the tracking error of the system as e1=x1-x d , get:

[0030]

[0031] Define the sliding surface s with variable gain:

[0032] s=(η1+μ)e1+(η2+E n )e2

[0033] By taking the derivative of the sliding surface s and combining it with the system dynamic estimation d net Compensated multi-motor servo system model, obtaining the sliding membrane surface derivative for:

[0034]

[0035] Where μ is the angular matrix, E n is the identity matrix; parameter and is a positive real number, csch represents the hyperbolic cosecant function;

[0036] Based on Lyapunov criterion and sliding surface derivative The adaptive variable gain scheduled time sliding mode tracking controller is designed as:

[0037]

[0038] in, is the sliding surface coefficient; is the feedback gain of the design; a, b, and p are positive parameters in the Lyapunov function, and p satisfies 0<p<1; T f >0 is the predetermined time of the sliding surface, which can be specified according to actual needs;

[0039] The adaptive law is modified as follows:

[0040]

[0041] Beneficial effects:

[0042] (1) The present invention uses a neural network for nonlinear dynamic modeling to accurately approximate the unknown dynamic characteristics in the system.

[0043] (2) Design an observer for the multi-motor servo system to estimate the system dynamics d net As compensation for system friction and external disturbances, the unknown state and parameters of the system are estimated at the same time. Due to the addition of the system dynamic estimator d net, 、 and It can accurately reconstruct the unmeasurable state and unknown parameters of the system, significantly improving the adaptability and robustness of the system under complex working conditions.

[0044] (3) By using the system dynamics estimate dnet To compensate for friction and external disturbances, the controller is designed based on the Lyapunov criterion of predetermined time stability, and T is selected according to actual needs. f This not only ensures that the system state converges quickly within the preset time, but also significantly improves the tracking accuracy and dynamic response performance of the multi-motor system.

[0045] In summary, the technical solution of the present invention can effectively overcome the influence of system parameter uncertainty and external interference, and can significantly improve the performance of multi-motor servo systems in terms of precise control, high-speed response and robustness, and is widely applicable to high-precision, multi-degree-of-freedom servo control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a control block diagram of a method for pre-setting time control of a multi-motor servo system based on state observation and parameter estimation according to the present invention;

[0047] Figure 2 A schematic diagram of the structure of the multi-motor servo system considered in the present invention;

[0048] Figure 3 This is the Gaussian neural network approximation result graph;

[0049] Figure 4 This is a graph showing the observed values ​​of the system position under the action of the Gaussian neural network compensation and adaptive tracking controller proposed in the present invention;

[0050] Figure 5 This is a graph showing the observed value of the system speed under the action of the Gaussian neural network compensation and adaptive tracking controller proposed in the present invention;

[0051] Figure 6 This is a diagram showing the estimation results of the unknown parameters of the system under the action of the Gaussian neural network compensation and adaptive tracking controller proposed in the present invention;

[0052] Figure 7 This is a diagram showing the position tracking results of the system based on Gaussian neural network and adaptive observer compensation proposed in the present invention;

[0053] Figure 8 This is the result diagram of the observed value of the system position under PD control without compensation;

[0054] Figure 9 This is the observed value result diagram of the system speed under PD control without compensation;

[0055] Figure 10 This is the estimation result diagram of system parameters under PD control without compensation;

[0056] Figure 11 This is the system position tracking result diagram under PD control without compensation. DETAILED DESCRIPTION

[0057] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0058] This paper proposes a time-scheduled control method for a multi-motor servo system based on state observation and parameter estimation. The basic concept is to accurately reconstruct the system's unmeasurable states and unknown parameters by constructing a high-precision state observer and an adaptive parameter estimator. Combined with a time-scheduled control strategy, this method not only ensures rapid convergence of the system state within a preset time, but also significantly improves the tracking accuracy and dynamic response performance of the multi-motor system. This control scheme effectively overcomes the effects of system parameter uncertainty and external disturbances, ensuring excellent dynamic performance and robust stability.

[0059] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0060] like Figure 1 The design process of a predetermined time control method for a multi-motor servo system based on state observation and parameter estimation specifically includes:

[0061] S1: Based on the structure and physical laws of the multi-motor servo system, a mathematical model of the multi-motor servo system with unknown system states, parameters, and nonlinear dynamics is established as follows:

[0062]

[0063] Among them, θ L represents the angular position of the load, θ m represents the angular position of each motor, and Represent the load and the angular velocity of each motor respectively, and Represent the angular acceleration of the load and each motor respectively. L and J m Represent the load and the rotational inertia of each motor respectively, represents the unknown friction at the load end, b m Represents the viscous friction coefficient of the motor, u i Represents the control input of the i-th motor in the system. l and d m are the external total disturbances at the load end and the motor end respectively. n means that the multi-motor servo system includes n motors, τ i represents the transmission torque between the i-th motor and the load, specifically:

[0064]

[0065] Here the angular position difference between the motor and the load is δi =θ mi -θ L , k1 is the torsion coefficient, k2 is the damping coefficient. f(δ i )and The f(δ) used is a dead zone function, which can be expressed as:

[0066]

[0067] Where α is the gear backlash width parameter.

[0068] In the absence of gear backlash nonlinearity, the transmitted torque τ i It can be approximated as:

[0069]

[0070] In the absence of dead zone nonlinearity, there is a proportional relationship, namely θ m =εθ L Therefore, system (1) can be simplified to:

[0071]

[0072] In the above formula, reflects the unknown dynamics of the system, is the friction amount, d l +d m is the disturbance amount.

[0073] Define the state variable as x(t)=[x1,x2] T , x1=θ L , A is the system matrix, Ψ(t) is the regression matrix, C is the output matrix of the system, y(t) is the system output; θ is the system parameter to be estimated, then the mathematical model of the multi-motor servo system is expressed as:

[0074]

[0075] in Here f d (t) is the unknown dynamics of the system. Figure 2 The structural diagram of the multi-motor servo system is given.

[0076] S2: Nonlinear Friction Analysis: Numerical simulation is used to model the unknown nonlinear friction. Stribeck discovered through experiments that friction changes continuously from maximum static friction to Coulomb friction, a phenomenon known as the Stribeck effect. Based on this conclusion, the Stribeck friction model was designed as follows:

[0077]

[0078] Where f is the friction force, F c is the Coulomb friction coefficient, F s is the static friction coefficient; ω s is the Stribeck velocity, ω is the angular velocity, F v is the viscous friction coefficient.

[0079] The unknown dynamic f in step S2 d (t) includes not only the friction part but also the disturbance part, so the friction model cannot fully represent the unknown dynamics of the system.

[0080] S3: In order to accurately approximate the unknown dynamics in the control system, this paper proposes an approximation method based on a neural network. The input of the neural network is the control quantity u and the system output y of the multi-motor servo system, and the output of the neural network is the system dynamic estimation quantity d net .

[0081] The neural network preferably uses a Gaussian neural network. By introducing the Gaussian kernel function, the Gaussian neural network can efficiently map and approximate complex nonlinear dynamics. The structural design of the network takes into account both efficiency and expressiveness. The specific structure is as follows:

[0082] Input layer: The input layer contains 2 nodes, representing the system control variable u and the system output y respectively; therefore, the dimension of the input layer is 2 to adapt to the input characteristics of the system.

[0083] Hidden Layers: The network has three hidden layers, with the following design: 10 nodes in the first layer, 16 nodes in the second layer, and 12 nodes in the third layer. Each hidden layer transforms input features into a higher-dimensional representation through high-dimensional nonlinear mapping, enabling the network to effectively capture the complex nonlinear relationships between input and output.

[0084] Output layer: The output layer contains one node, which is mainly used to output the approximated nonlinear dynamic terms. This output represents the nonlinear characteristics of the system and serves as dynamic feedback in the control system.

[0085] The output d of the Gaussian neural network net Calculated by the following formula:

[0086]

[0087] Among them, π=[x1,u] is the neural network input, ω i is the weight coefficient of the i-th neuron, κ i is the center of the i-th Gaussian basis function, σ i 2is the width of the Gaussian kernel, and N represents the total number of Gaussian basis functions, which directly influences the network's complexity and approximation capabilities. Compared to traditional neural networks, Gaussian neural networks, due to their local response characteristics, are more efficient in handling nonlinearities in control systems. If the weights of a neural network gradually approach a constant value during training, it means that the network has found an effective strategy to minimize the loss function. Therefore, this phenomenon can be used to indirectly evaluate the training results.

[0088] S4: Based on the system output signal and combined with the approximation result of Gaussian neural network d net , construct an adaptive observer. The adaptive observer uses the system dynamics estimator d net As compensation for system friction and external disturbances, the system state quantities and parameters are observed and the state estimation is and parameter estimates Provided to the adaptive tracking controller.

[0089] First, the results of training the friction model using Gaussian neural network can be used to calculate the unknown nonlinear dynamics f in the multi-motor servo system (6). d (t) Use d net Instead, restructure the multi-motor servo system as follows:

[0090]

[0091] Based on the system model (9), the auxiliary matrix is ​​designed:

[0092]

[0093] Here (A-KC) is the Hurwitz matrix and K is the observation gain vector.

[0094] Then the adaptive observer with Gaussian neural network compensation is designed as:

[0095]

[0096] in is the learning gain matrix.

[0097] S5: Design an adaptive variable gain scheduled time sliding mode tracking controller, which uses the system dynamic estimate d net As compensation for system friction and external disturbances, the predetermined time T is designed based on the Lyapunov criterion. f The sliding surface is specified as needed to ensure that the system can achieve tracking within the predetermined time.

[0098] Specifically, the system output y = x1 of the multi-motor servo system is obtained and combined with the desired signal x d , calculate the tracking error of the system as e1=x1-xd , Further we get:

[0099]

[0100] Next, define a sliding surface with variable gain:

[0101] s=(η1+μ)e1+(η2+E n )e2 (13)

[0102] In formula (13), μ = diag (μ1, μ2) is the designed diagonal matrix, E n is the identity matrix. η1,η2 are defined as follows:

[0103]

[0104] The parameters csch is the hyperbolic cosecant function.

[0105] Taking the derivative of the sliding surface and combining it with formula (9) we can get:

[0106]

[0107] According to formula (15), we can get:

[0108]

[0109] Where coth represents the hyperbolic cotangent function.

[0110] Substituting formula (16) into formula (15), we can obtain:

[0111]

[0112] in, is the synovial surface coefficient.

[0113] S6: The design time stability evaluation criteria are:

[0114]

[0115] Where V is a radial basis function greater than zero. a, b, and p are all positive numbers, and p satisfies 0<p<1. f >0 is the predetermined time, which can be determined arbitrarily according to actual needs.

[0116] According to (18), the adaptive variable gain scheduled time sliding mode tracking controller is designed as:

[0117]

[0118] here is the designed feedback gain, Where sign(s) is the sign function.

[0119] Next, the adaptive law (11) is modified as follows:

[0120]

[0121] In the above formula, the term Ψs is added to the conventional adaptive law.

[0122] Based on the above design process, the following Figure 1 The control system shown in the figure has the following working process:

[0123] Step 1: Train a Gaussian neural network to estimate the unknown dynamics of the multi-motor servo system; the unknown dynamics include friction and disturbance; the input of the neural network is the control quantity u and system output y of the multi-motor servo system, and the output of the neural network is the system dynamic estimation quantity d net .

[0124] Step 2: During control, the control quantity u and system output y of the multi-motor servo system are input into the neural network, and the system dynamic estimation quantity d output by the neural network is net Provided to the adaptive observer and adaptive tracking controller.

[0125] Step 3: The adaptive observer uses the system dynamics estimator d net As compensation for system friction and external disturbances, the system state quantities and parameters are observed and the state estimation is and parameter estimates Provided to the adaptive tracking controller. The formula of the adaptive observer is the above formula (11).

[0126] Step 4: Taking the error between the position and the desired position of the multi-motor servo system as input, an adaptive variable gain predetermined time sliding mode tracking controller is used to generate the control quantity u, which is output to the multi-motor servo system; the adaptive variable gain predetermined time sliding mode tracking controller is the above formula (19) (20), and the system dynamic estimation quantity d net To compensate for the friction and external disturbances of the system, and to use the estimator of the adaptive observer and As the actual system state and parameters, and according to the actual needs to design the sliding surface of the predetermined time T f , ensuring that the system achieves tracking within that time.

[0127] The technical solution disclosed in the present invention is simulated and verified as follows:

[0128] Step 1: The mathematical model of the multi-motor servo system is

[0129]

[0130] where x(0) =

[00] T .

[0131] Step 2: Design the Stribeck friction model as

[0132] Step 3: The present invention constructs a six-layer Gaussian neural network model, in which the input layer contains two nodes, the output layer is one node, and the hidden layer has three layers, with the number of nodes being 10, 16, and 12 respectively. By collecting training data (including state vectors and control inputs) from the control system, the data set is divided into a training set (70%) and a validation set (30%). Initialize the weight matrix, kernel center, and width of the Gaussian neural network, where the kernel center can be randomly selected from the training set data. Use the stochastic gradient descent optimization algorithm to train the neural network, and the optimization goal is to minimize the network output. The error between the true nonlinear dynamics f. The error function is defined as Use the trained weight matrix and bias matrix to verify the remaining 30% of the data, and judge the training effect by the change of the loss function. Finally, save the trained weight matrix and bias matrix. The training results are as follows: Figure 3 shown.

[0133] Step 4: Design an adaptive observer based on the results of Gaussian neural network training:

[0134]

[0135] in K = [502000] T ,Ψ(0)=

[00] .

[0136] Step 4: Select the reference signal, set the sampling period to dt = 0.001s, and the simulation time to 10s.

[0137] Step 5: The design parameters of the sliding surface with a given variable gain are The limiting parameters of the system state are chosen as

[0138] Step 5: Select the controller parameters as a=b=1,p=0.5,T f =2s. The simulation results are as follows Figure 4-7 shown.

[0139] Figure 4 and Figure 5 The results of the adaptive observer observing the position and velocity of the system under the action of Gaussian neural network compensation and adaptive tracking controller are shown respectively. Figure 4It can be seen that the state of the adaptive observer It can quickly follow the actual position x1 of the system, and the error graph below further proves that Observation performance. Figure 5 It shows the observer's observation results of the system speed, the speed observation value The curve also highly coincides with the system speed x2, verifying the efficiency of the observer in speed estimation.

[0140] Figure 6 The estimated results of the unknown parameters of the system are given. As can be seen from the figure, the estimated values ​​of the system parameters θ1 and θ2 and It can quickly approach the true value. This fast convergence shows that the adaptive observer can effectively adjust its parameter estimates. Figures 4 to 6 The effectiveness of the adaptive observer in estimating unknown states and parameters of the system has been demonstrated. Through compensation using a Gaussian neural network, the adaptive observer can rapidly estimate states and parameters, reducing errors and improving system robustness. This capability is crucial for the control and optimization of complex systems, especially in environments with high state and parameter uncertainty.

[0141] Figure 7 The system position tracking results based on Gaussian neural network and adaptive observer compensation are shown. It can be seen that the adaptive tracking controller is able to f = 2 seconds to accurately track the desired trajectory. By combining a Gaussian neural network with an adaptive observer, the system is able to maintain accurate tracking of the desired trajectory in the presence of unknown system states, parameters, and nonlinear dynamics. This capability is crucial for control applications requiring high precision and fast response.

[0142] In order to verify the superiority of the proposed compensation algorithm based on Gaussian neural network, this paper also conducted a simulation verification of PD tracking control without using Gaussian neural network compensation. The simulation results are shown in Figure 8 , Figure 9 , Figure 10 and Figure 11 middle.

[0143] Figure 8 Figure 2 shows the evolution of the system position observation value and observation error under the PD controller. The system position observation curve and the system position signal curve are basically consistent, but the peaks and troughs do not overlap. The position observation error is large and is not within the expected error range. Figure 9 The figure shows the variation of the system velocity observation value and observation error under the action of the PD controller. The system position observation curve lags behind the system position signal curve, and the position observation error is large and is not within the expected error range. Figure 10The observed values ​​of the system parameters change under the action of the PD controller. The observed values ​​of the system parameters have a convergence trend, but the convergence is slow and cannot converge to the true value in a short time. In addition, there is a problem of vibration in the observed value curve during the convergence process. Figure 11 Figure 3 shows the position tracking and position tracking error of the system under the PD controller. The system position signal does not coincide with the position reference signal, significantly lagging behind it. Furthermore, the position tracking error is much larger than that under the adaptive controller, far exceeding the design tolerance.

[0144] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for pre-setting time control of a multi-motor servo system based on state and parameter estimation, characterized in that: include: Step 1: Train a neural network to estimate the unknown dynamics of the multi-motor servo system; the unknown dynamics include friction and disturbance; the input of the neural network is the control quantity u and system output y of the multi-motor servo system, and the output of the neural network is the system dynamic estimation quantity d net ; Step 2: During control, the control quantity u and system output y of the multi-motor servo system are input into the neural network, and the system dynamic estimation quantity d output by the neural network is net Provided to the adaptive observer and the adaptive variable gain scheduled time sliding mode tracking controller; Step 3: The adaptive observer uses the system dynamics estimator d net As compensation for system friction and external disturbances, the system state quantities and parameters are observed and the state estimation is and parameter estimates Provided to an adaptive variable gain predetermined time sliding mode tracking controller; Step 4: Using the error between the position of the multi-motor servo system and the desired position as input, an adaptive variable gain predetermined time sliding mode tracking controller is used to generate a control variable u, which is output to the multi-motor servo system; the adaptive variable gain predetermined time sliding mode tracking controller uses the system dynamic estimation quantity d net To compensate for the friction and external disturbances of the system, and to use the estimator of the adaptive observer and As the actual system state and parameters, and according to the actual needs to design the sliding surface of the predetermined time T f , ensuring that the system can achieve tracking within this time; The adaptive observer contains the system dynamics estimator d net The compensated adaptive observer is constructed as follows: Construct system dynamic estimator d net The compensated multi-motor servo system model is: where x(t) = [x1, x2] T , x1=θ L , θ L represents the angular position of the load of the multi-motor servo system; A is the system matrix, Ψ(t) is the regression matrix, C is the output matrix of the system, y(t) is the system output; θ is the system parameter to be estimated: Where ε is the load angular position θ without dead zone nonlinearity L and the motor angular position θ m The proportional coefficient between L and J m Represents the load and the rotational inertia of each motor respectively; b m Indicates the viscous friction coefficient of the motor; Then, the auxiliary matrix is ​​designed based on the multi-motor servo system model: Then, the system dynamics estimate d net The compensated adaptive observer is: in, and are the state estimation and parameter estimation of the adaptive observer output respectively; (A-KC) is the Hurwitz matrix, K is the observation gain vector, and Γ is the learning gain matrix.

2. The method according to claim 1, wherein The neural network adopts Gaussian neural network.

3. The method according to claim 2, wherein The Gaussian neural network comprises: Input layer: The input layer contains two nodes, representing the system control variable u and the system output y respectively; Hidden layer: There are three hidden layers; the first layer contains 10 nodes, the second layer contains 16 nodes, and the third layer contains 12 nodes. Each hidden layer converts the input features into a higher-dimensional representation through high-dimensional nonlinear mapping, enabling the network to effectively capture the complex nonlinear relationship between input and output. Output layer: The output layer contains 1 node, which is used to output the approximated system dynamic estimate d net .

4. The method according to claim 1, wherein In step 4, the design of the adaptive variable gain scheduled time sliding mode tracking controller is: Get the multi-motor servo system position y and combine it with the expected signal x d , calculate the tracking error of the system as e1=x1-x d , get: Define the sliding surface s with variable gain: s=(η1+μ)e1+(η2+E n )e2 By taking the derivative of the sliding surface s and combining it with the system dynamic estimation d net Compensated multi-motor servo system model, obtaining the sliding membrane surface derivative for: Where μ is the angular matrix, E n is the identity matrix; parameter and is a positive real number, csch represents the hyperbolic cosecant function; Based on Lyapunov criterion and sliding surface derivative The adaptive variable gain scheduled time sliding mode tracking controller is designed as: in, is the sliding surface coefficient; is the feedback gain of the design; a, b, and p are positive parameters in the Lyapunov function, and p satisfies 0<p<1; T f >0 is the predetermined time of the sliding surface, which is specified according to actual needs; coth represents the hyperbolic cotangent function; The adaptive law is modified as follows:

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