Motor adaptive backstepping controller design method for high self-locking force load

Abstract

The invention discloses a motor adaptive backstepping controller design method for a high self-locking force load, and the method comprises the steps: building a high self-locking force load torque mathematical model containing a time-varying unknown parameter and a DC motor mathematical model, and defining a virtual control quantity through a backstepping method control theory; designing an adaptive law to realize real-time estimation of time-varying unknown parameters; a self-adaptive backstepping controller is designed through a piecewise projection function and a quadratic Lyapunov function, the system convergence speed and actuator buffeting are optimized, and motor mute control is achieved; the method has the advantages that the time-varying unknown parameters can be estimated in real time, the mute control of the direct current motor is realized, and the hardware cost and the computing power cost are low.

Description

Technical Field

[0001] The invention relates to a motor control technology, and in particular to a design method of a motor adaptive backstepping controller for a high self-locking force load. Background Art

[0002] The self-locking force of the motor load is an important characteristic exhibited in its mechanical system. It allows the motor to maintain a certain position or angle after stopping without being disturbed by external forces. This characteristic is crucial in applications that require high-precision positioning, stable operation, and energy saving and consumption reduction. However, the high self-locking force characteristic of the motor load may affect the smoothness of the motor current when the load changes rapidly, thereby generating motor noise. In addition, the self-locking force of the motor load is affected by factors such as motor speed and mechanical lubrication, and there is a certain degree of uncertainty, which brings additional challenges to motor control. Therefore, it is of great significance to design a controller with slow current change for the self-locking force of time-varying unknown loads.

[0003] Existing motor control algorithms usually assume that the load model is known or time-invariant. For example, Chinese patent application No. 202410596409.8 and Chinese patent No. 202410866719.7 both propose motor control methods based on adaptive algorithms, but these methods require that the motor load is known. Time-varying unknown loads can cause large disturbances to the motor control system and increase the instability of the motor control system. If the motor control algorithm cannot effectively suppress these disturbances, it may cause oscillations, instability, and other phenomena in the motor control system, and in severe cases may even damage the motor or related equipment.

[0004] In order to cope with unknown load disturbances, the Chinese patent with patent number 202110015527.1 proposes a robust position control method for permanent magnet synchronous motors considering current limiting. However, the effectiveness of this method is based on the premise that the load disturbance and its first-order derivatives and second-order derivatives have known upper bounds and are relatively small, which limits its scope of application. For unknown time-varying load disturbances, the Chinese patent application with application number 202211635151.5 proposes a model-free coordinated adaptive optimal output regulator design method, but this method also requires that the load disturbance is bounded and the limits are known, which may be difficult to meet in practical applications.

[0005] In summary, there is no effective motor control algorithm for time-varying unknown high self-locking force loads in existing patents and scientific literature, especially for motor systems with current change rate constraints, there is still a lack of effective control algorithms. This shows that further research and innovation are still needed in the design of motor control systems to adapt to more complex and variable load conditions. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a design method for a motor adaptive backstepping controller for a high self-locking force load, which can estimate time-varying unknown parameters in real time and realize silent control of a DC motor.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a design method of a motor adaptive backstepping controller for high self-locking force loads, characterized by comprising the following steps:

[0008] Step 1: Based on the characteristics between the high self-locking force load and the angular velocity of the DC motor, a high self-locking force load torque mathematical model with time-varying unknown parameters is established based on the LuGre friction model as a high self-locking force load torque model; wherein the LuGre friction model has a time-varying unknown bristle minimum damping coefficient and a viscous friction coefficient;

[0009] Step 2: Based on the equivalent circuit and circuit principle of the DC motor, and combined with the mathematical model of high self-locking force load torque containing time-varying unknown parameters, a mathematical model of the DC motor is established;

[0010] Step 3: Based on the backstepping control theory, define the virtual control quantity, and combine the DC motor mathematical model to establish the error mathematical model between the system state and the control target and the virtual control quantity;

[0011] Step 4: Using the differential principle, design two piecewise projection functions;

[0012] Step 5: For the time-varying unknown parameters contained in the high self-locking force load torque mathematical model established in step 1, the piecewise projection function designed in step 4 is used to design an adaptive law to achieve real-time estimation of the time-varying unknown parameters;

[0013] Step 6: Based on the real-time estimation of the time-varying unknown parameters in step 5 and the error mathematical model established in step 3, a different quadratic Lyapunov function is designed for each error;

[0014] Step 7: Based on the quadratic Lyapunov function designed in step 6, design the expression of the adaptive backstepping controller with adjustable system convergence speed and actuator jitter;

[0015] Step 8: Based on the system convergence speed index, establish an optimization problem for solving the parameters of the adaptive backstepping controller;

[0016] Step 9: Use the gradient descent method to solve the optimization problem in step 8 in real time, minimize the current change rate, and obtain the value of the adaptive backstepping controller parameter;

[0017] Step 10: Substitute the values ​​of the adaptive backstepping controller parameters obtained in step 9 into the adaptive backstepping controller in step 7 to obtain the real-time control output of the adaptive backstepping controller to achieve motor silent control.

[0018] In step 1, the mathematical model of high self-locking force load torque with time-varying unknown parameters is described as:

[0019]

[0020] Wherein, t represents the time variable, T(t) represents the time-varying unknown torque of the high self-locking force load, e represents the force arm of the high self-locking force load, σ0 represents the elastic stiffness of the bristle, f(t) represents the micro-displacement of the bristle, a(t) represents the time-varying unknown minimum damping coefficient of the bristle of the LuGre friction model, and b(t) represents the time-varying unknown viscous friction coefficient of the LuGre friction model. represents the first-order derivative of f(t), g() represents the functional used to describe the Stribeck effect. ω m Indicates the angular velocity of the DC motor. The symbol “||” is the modulus operator. F c is the Coulomb friction force, F s represents the maximum static friction, e is a natural constant, ω s represents the Stribeck velocity, and n represents the Stribeck curve index.

[0021] In step 2, the DC motor mathematical model is described as:

[0022]

[0023] Wherein, J represents the comprehensive mechanical inertia of the high self-locking force transmission system, Represents ω m The first derivative of e It represents the electromagnetic torque of the DC motor, D represents the damping coefficient of the DC motor, and U d represents the input voltage of the DC motor, R represents the total resistance of the armature circuit, I d represents the input current of the DC motor, L represents the total inductance of the armature circuit, I d The first-order derivative of, E represents the induced electromotive force, C m It represents the torque coefficient of the DC motor at rated flux. Represents θ m The first derivative of m Indicates the rotation angle of the DC motor.

[0024] In step 3, the error mathematical model between the system state, the control target, and the virtual control amount is described as:

[0025] z1(t)=x1(t)-θ r

[0026] z2(t)=x2(t)-u2(t);

[0027] z3(t)=x3(t)-u3(t)

[0028] where [x1(t)x2(t)x3(t)] T represents the system state vector, x1(t) represents the first system state, x2(t) represents the second system state, x3(t) represents the third system state, [x1(t)x2(t)x3(t)] T =[θ m ω m I d ] T , the first-order derivative of x1(t) is The first-order derivative of x2(t) is The first-order derivative of x3(t) is u(t) represents the control output of the adaptive backstepping controller, θ r represents the control target, is the target rotation angle, u2(t) represents the virtual control amount of x2(t), u3(t) represents the virtual control amount of x3(t), z1(t) represents the virtual control amount of x1(t) and θ r , z2(t) represents the error between x2(t) and u2(t), z3(t) represents the error between x3(t) and u3(t), and the superscript “T” represents the transpose operation of the vector.

[0029] In step 4, the two segmented projection functions are and

[0030] in, represents the real-time estimated value of a(t), represents the real-time estimated value of b(t), λ represents the input of the piecewise projection function, express The projection upper bound of σ represents the upper bound of the projection, express The first derivative of express The projection upper bound of for The first derivative of .

[0031] In step 5, for a(t) and b(t), the corresponding piecewise projection function is used to design an adaptive law, and the real-time estimation of a(t) and b(t) is achieved as follows:

[0032]

[0033] in, express The first derivative of replace The λ in is obtained, express The first derivative of for replace The λ in is obtained.

[0034] In step 6, the quadratic Lyapunov function V1(t) designed for z1(t) is described as: The quadratic Lyapunov function V2(t) designed for z2(t) is described as: The quadratic Lyapunov function V3(t) designed for z3(t) is described as: in, a is the upper bound of a(t), is the upper bound of b(t).

[0035] In step 7, the expression of the adaptive backstepping controller is:

[0036]

[0037] Where u(t) represents the control output of the adaptive backstepping controller, represents the first-order derivative of u3(t), represents the first-order derivative of u2(t), Represents θ r The first-order derivative of , k1, k2, k3 are the adaptive backstepping controller parameters for the convergence speed of the control system to be designed, ε1, ε2 are the adaptive backstepping controller parameters for the vibration of the control actuator to be designed.

[0038] In step 8, the optimization problem is described as:

[0039] Optimization goal:

[0040] Constraints:

[0041]

[0042]

[0043] ε1>0,ε2>0

[0044] in, is the expanded expression of the current change rate, s is the ratio of the square of the current change rate to ||x(t)||, and x(t) represents the system state vector, that is, x(t) = [x1(t) x2(t) x3(t)] T , the symbol “|| ||” is the symbol for finding the binary norm. It is the positive expected value of the system convergence speed indicator.

[0045] Compared with the prior art, the advantages of the present invention are:

[0046] 1) Considering the influence of mechanical lubrication degree, angular velocity of DC motor and other motion states and external environmental factors on the minimum bristle damping coefficient and viscous friction coefficient of LuGre friction model, the minimum bristle damping coefficient and viscous friction coefficient are modeled as time-varying unknown parameters, which improves the accuracy of LuGre friction model and solves the problem that the high self-locking force characteristics of motor load may affect the smoothness of motor current.

[0047] 2) Design an adaptive law of the piecewise projection function to achieve real-time estimation of the bristle minimum damping coefficient and viscous friction coefficient without the need for additional sensor detection or data-driven identification algorithm, reducing the hardware cost and computing power cost of estimating time-varying unknown parameters.

[0048] 3) By converting the parameter design problem of the adaptive backstepping controller into an optimization problem and solving it in real time using the gradient descent method, the system convergence speed and actuator jitter are optimized. By minimizing the current change rate, the vibration and noise of the DC motor are reduced, the control performance of the DC motor is improved, and silent control of the DC motor is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of a motor adaptive backstepping control system for high self-locking force loads;

[0050] Figure 2 Schematic diagram of the implementation process of the method of the present invention;

[0051] Figure 3 The figure is a tracking effect diagram of the angular velocity of the DC motor under the method of the present invention;

[0052] Figure 4 This is a diagram showing the tracking effect of the angular velocity of a DC motor under the existing PID control algorithm. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below with reference to the accompanying drawings.

[0054] Figure 1 The schematic diagram of the motor adaptive backstepping control system for high self-locking force load is given. The control system includes an adaptive backstepping controller, a high self-locking force load, a DC motor, and a sensor. The adaptive backstepping controller consists of an error model building module, a parameter adaptive estimation module, a controller expression design module, a controller parameter optimization module, and a controller output calculation module. The target rotation angle θ r Input the adaptive backstepping controller, which will get the estimated value of the time-varying unknown bristle minimum damping coefficient a(t) Estimation of the unknown time-varying viscous friction coefficient b(t) Provided to the high self-locking force load, the adaptive backstepping controller provides the control output u(t) to the DC motor, the torque T(t) of the high self-locking force load is provided to the DC motor, and the sensor collects the rotation angle θ of the DC motor m 、Angular velocity of DC motor ω m , DC motor input current I d , the sensor transmits the collected data to the adaptive backstepping controller.

[0055] The present invention is directed to Figure 1 The adaptive backstepping controller in this paper provides a design method for a motor adaptive backstepping controller for high self-locking force loads. The implementation process is as follows: Figure 2 As shown, it includes the following steps:

[0056] Step 1: Aiming at the characteristics between the high self-locking force load and the angular velocity of the DC motor, a high self-locking force load torque mathematical model containing time-varying unknown parameters is established based on the LuGre friction model as a high self-locking force load torque model; wherein, the LuGre friction model has a time-varying unknown bristle minimum damping coefficient and a viscous friction coefficient, and the existing LuGre friction model has a time-invariant bristle minimum damping coefficient and a viscous friction coefficient. Here, the time-invariant bristle minimum damping coefficient and a viscous friction coefficient of the existing LuGre friction model are modified to time-varying unknown bristle minimum damping coefficient and a viscous friction coefficient. Improving the coefficient from time-invariant to time-varying unknown can be achieved through conventional technology.

[0057] Further defined, in step 1, the mathematical model of high self-locking force load torque with time-varying unknown parameters is described as:

[0058]

[0059] Wherein, t represents the time variable, T(t) represents the time-varying unknown torque of the high self-locking force load, l represents the force arm of the high self-locking force load, σ0 represents the elastic stiffness of the bristle, f(t) represents the micro-displacement of the bristle, a(t) represents the time-varying unknown bristle minimum damping coefficient of the LuGre friction model, b(t) represents the time-varying unknown viscous friction coefficient of the LuGre friction model, and both a(t) and b(t) are time-varying unknown parameters. represents the first-order derivative of f(t), g() represents the functional used to describe the Stribeck effect. ω m Indicates the angular velocity of the DC motor. The symbol “||” is the modulus operator. F c is the Coulomb friction force, F s represents the maximum static friction, e is a natural constant, e = 2.71…, ω s represents the Stribeck velocity, and n represents the Stribeck curve index.

[0060] Step 2: Based on the equivalent circuit and circuit principle of the DC motor, and combined with the mathematical model of high self-locking force load torque containing time-varying unknown parameters, a mathematical model of the DC motor is established.

[0061] Further defined, in step 2, the DC motor mathematical model is described as:

[0062]

[0063] Wherein, J represents the comprehensive mechanical inertia of the high self-locking force transmission system, Represents ω m The first derivative of e It represents the electromagnetic torque of the DC motor, D represents the damping coefficient of the DC motor, and U d represents the input voltage of the DC motor, R represents the total resistance of the armature circuit, I d represents the input current of the DC motor, L represents the total inductance of the armature circuit, Indicates I d The first-order derivative of, E represents the induced electromotive force, C m It represents the torque coefficient of the DC motor at rated flux. Represents θ m The first derivative of m Indicates the rotation angle of the DC motor.

[0064] Step 3: Based on the backstepping control theory, define the virtual control quantity, and combine the DC motor mathematical model to establish the error mathematical model between the system state and the control target and the virtual control quantity.

[0065] Further definition, in step 3, the error mathematical model between the system state and the control target and the virtual control quantity is described as:

[0066] z1(t)=x1(t)-θ r

[0067] z2(t)=x2(t)-u2(t);

[0068] z3(t)=x3(t)-u3(t)

[0069] where [x1(t)x2(t)x3(t)] T represents the system state vector, x1(t) represents the first system state, x2(t) represents the second system state, x3(t) represents the third system state, [x1(t)x2(t)x3(t)] T =[θ m ω m I d ] T , that is, the first system state x1(t) is θ m , the second system state x2(t) is ω m , the third system state x3(t) is I d , the first-order derivative of x1(t) is The first-order derivative of x2(t) is The first-order derivative of x3(t) is u(t) represents the control output of the adaptive backstepping controller, θ r represents the control target, is the target rotation angle, u2(t) represents the virtual control amount of x2(t), u3(t) represents the virtual control amount of x3(t), z1(t) represents the virtual control amount of x1(t) and θ r , z2(t) represents the error between x2(t) and u2(t), z3(t) represents the error between x3(t) and u3(t), and the superscript “T” represents the transpose operation of the vector.

[0070] Step 4: Using the differential principle, design two piecewise projection functions so that the adaptive parameter estimate has an upper bound.

[0071] Further definition, in step 4, the two segmented projection functions are and

[0072] in, represents the real-time estimated value of a(t),

[0073] represents the real-time estimated value of b(t), λ represents the input of the piecewise projection function, express The projection upper bound of h a Generally, it is taken as 0.1, σ represents the upper limit of the projection allowance, express The first derivative of express The projection upper bound of h b Generally, 0.01 is taken. for The first derivative of .

[0074] Step 5: For the time-varying unknown parameters contained in the high self-locking force load torque mathematical model established in step 1, the piecewise projection function designed in step 4 is used to design an adaptive law to achieve real-time estimation of the time-varying unknown parameters.

[0075] Further defined, in step 5, for a(t) and b(t), the corresponding piecewise projection function is used to design the adaptive law, and the real-time estimation of a(t) and b(t) is achieved as follows:

[0076]

[0077] in, express The first derivative of for replace The λ in is obtained, express The first derivative of for replace The λ in is obtained.

[0078] Step 6: Based on the real-time estimation of the time-varying unknown parameters in step 5 and the error mathematical model established in step 3, a different quadratic Lyapunov function is designed for each error.

[0079] Further defined, in step 6, the quadratic Lyapunov function V1(t) designed for z1(t) is described as: The quadratic Lyapunov function V2(t) designed for z2(t) is described as: The quadratic Lyapunov function V3(t) designed for z3(t) is described as: in, is the upper bound of a(t), is the upper bound of b(t).

[0080] Step 7: Based on the quadratic Lyapunov function designed in step 6, design the expression of the adaptive backstepping controller with adjustable system convergence speed and actuator jitter.

[0081] Further defined, in step 7, the expression of the adaptive backstepping controller is:

[0082]

[0083] Where u(t) represents the control output of the adaptive backstepping controller, represents the first-order derivative of u3(t), represents the first-order derivative of u2(t), Represents θ r The first-order derivative of , k1, k2, k3 are the adaptive backstepping controller parameters for the convergence speed of the control system to be designed, ε1, ε2 are the adaptive backstepping controller parameters for the vibration of the control actuator to be designed.

[0084] Step 8: Based on the system convergence speed index, establish the optimization problem of solving the parameters of the adaptive backstepping controller.

[0085] Further limiting, in step 8, the optimization problem is described as:

[0086] Optimization goal:

[0087] Constraints:

[0088]

[0089]

[0090] ε1>0,ε2>0

[0091] in, is the expanded expression of the current change rate, min is the minimum value function, s is the ratio of the square of the current change rate to ||x(t)||, and x(t) represents the system state vector, that is, x(t) = [x1(t)x2(t) x3(t)] T , the symbol “|| ||” is the symbol for finding the binary norm. Is the positive expected value of the system convergence speed index, generally All are taken as 0.01. This optimization problem means minimizing s while satisfying the constraints by optimizing the controller parameters k1, k2, k3, ε1, ε2.

[0092] Step 9: Use the gradient descent method to solve the optimization problem in step 8 in real time, minimize the current change rate, and obtain the values ​​of the adaptive backstepping controller parameters k1, k2, k3, ε1, ε2.

[0093] Step 10: Substitute the values ​​of the adaptive backstepping controller parameters obtained in step 9 into the adaptive backstepping controller in step 7 to obtain the real-time control output of the adaptive backstepping controller to achieve motor silent control.

[0094] In order to further illustrate the feasibility and effectiveness of the method of the present invention, a simulation experiment was carried out.

[0095] In the simulation, the force arm of the high self-locking load is l = 0.1 m, the bristle elastic stiffness σ0 = 10000 N / m, and the Coulomb friction force F c =0.1 Newton, maximum static friction F s = 0.15 Newton, Stribeck speed ω s = 0.001 rad / s, Stribeck curve index n = 2, and the angular velocity ω of the DC motor m As the second system state x2(t), the mathematical model of high self-locking force load torque with time-varying unknown parameters is: The comprehensive mechanical inertia of the high self-locking force transmission system J = 0.02 kg × square meters, the DC motor's torque damping coefficient D = 0.2, the total resistance of the armature circuit R = 2 ohms, the total inductance of the armature circuit L = 0.5 Henry, the torque coefficient of the DC motor at rated magnetic flux C m =0.1, that is:

[0096]

[0097] Matlab software was used to perform simulation and compare the angular velocity of the DC motor under the method of the present invention with the angular velocity of the DC motor under the existing PID control algorithm. Figure 3 The tracking effect diagram of the angular velocity of the DC motor under the method of the present invention is given. Figure 4 The tracking effect diagram of the angular velocity of the DC motor under the existing PID control algorithm is given. Figure 3 and Figure 4 The horizontal axis represents time (in seconds), and the vertical axis represents the angular velocity of the DC motor (in radians per second). Figure 3 and Figure 4 By comparison, it can be clearly found that the angular velocity of the DC motor (i.e., the actual motor speed) is closer to the target speed under the method of the present invention, that is, the control accuracy is higher, while the angular velocity of the DC motor (i.e., the actual motor speed) is much different from the target speed under the PID control algorithm. In addition, the trajectory of the angular velocity of the DC motor is smoother under the method of the present invention, that is, the motor runs more smoothly and quietly.

Claims

1. A design method for a motor adaptive backstepping controller for high self-locking force loads, characterized in that The following steps are involved: Step 1: Based on the characteristics between the high self-locking force load and the angular velocity of the DC motor, a high self-locking force load torque mathematical model with time-varying unknown parameters is established based on the LuGre friction model as a high self-locking force load torque model; wherein the LuGre friction model has a time-varying unknown bristle minimum damping coefficient and a viscous friction coefficient; Step 2: Based on the equivalent circuit and circuit principle of the DC motor, and combined with the mathematical model of high self-locking force load torque containing time-varying unknown parameters, a mathematical model of the DC motor is established; Step 3: Based on the backstepping control theory, define the virtual control quantity, and combine the DC motor mathematical model to establish the error mathematical model between the system state and the control target and the virtual control quantity; Step 4: Using the differential principle, design two piecewise projection functions; Step 5: For the time-varying unknown parameters contained in the high self-locking force load torque mathematical model established in step 1, the piecewise projection function designed in step 4 is used to design an adaptive law to achieve real-time estimation of the time-varying unknown parameters; Step 6: Based on the real-time estimation of the time-varying unknown parameters in step 5 and the error mathematical model established in step 3, a different quadratic Lyapunov function is designed for each error; Step 7: Based on the quadratic Lyapunov function designed in step 6, design the expression of the adaptive backstepping controller with adjustable system convergence speed and actuator jitter; Step 8: Based on the system convergence speed index, establish an optimization problem for solving the parameters of the adaptive backstepping controller; Step 9: Use the gradient descent method to solve the optimization problem in step 8 in real time, minimize the current change rate, and obtain the value of the adaptive backstepping controller parameter; Step 10: Substitute the values ​​of the adaptive backstepping controller parameters obtained in step 9 into the adaptive backstepping controller in step 7 to obtain the real-time control output of the adaptive backstepping controller to achieve motor silent control.

2. The design method of a motor adaptive backstepping controller for a high self-locking force load according to claim 1 is characterized in that In step 1, the mathematical model of high self-locking force load torque with time-varying unknown parameters is described as: Wherein, t represents the time variable, T(t) represents the time-varying unknown torque of the high self-locking force load, e represents the force arm of the high self-locking force load, σ0 represents the elastic stiffness of the bristle, f(t) represents the micro-displacement of the bristle, a(t) represents the time-varying unknown minimum damping coefficient of the bristle of the LuGre friction model, and b(t) represents the time-varying unknown viscous friction coefficient of the LuGre friction model. represents the first-order derivative of f(t), g() represents the functional used to describe the Stribeck effect. ω m Indicates the angular velocity of the DC motor. The symbol "||" is the modulus operator. F c is the Coulomb friction force, F s represents the maximum static friction, e is a natural constant, ω s represents the Stribeck velocity, and n represents the Stribeck curve index.

3. The design method of the motor adaptive backstepping controller for high self-locking force load according to claim 2 is characterized in that In step 2, the DC motor mathematical model is described as: Wherein, J represents the comprehensive mechanical inertia of the high self-locking force transmission system, Represents ω m The first derivative of e It represents the electromagnetic torque of the DC motor, D represents the damping coefficient of the DC motor, and U d represents the input voltage of the DC motor, R represents the total resistance of the armature circuit, I d represents the input current of the DC motor, L represents the total inductance of the armature circuit, Indicates I d The first-order derivative of, E represents the induced electromotive force, C m It represents the torque coefficient of the DC motor at rated flux. Represents θ m The first derivative of m Indicates the rotation angle of the DC motor.

4. The design method of a motor adaptive backstepping controller for a high self-locking force load according to claim 3 is characterized in that In step 3, the error mathematical model between the system state, the control target, and the virtual control amount is described as: where [x1(t)x2(t)x3(t)] T represents the system state vector, x1(t) represents the first system state, x2(t) represents the second system state, x3(t) represents the third system state, [x1(t)x2(t)x3(t)] T =[θ m ω m I d ] T , the first-order derivative of x1(t) is The first-order derivative of x2(t) is The first-order derivative of x3(t) is u(t) represents the control output of the adaptive backstepping controller, θ r represents the control target, is the target rotation angle, u2(t) represents the virtual control amount of x2(t), u3(t) represents the virtual control amount of x3(t), z1(t) represents the virtual control amount of x1(t) and θ r , z2(t) represents the error between x2(t) and u2(t), z3(t) represents the error between x3(t) and u3(t), and the superscript "T" represents the transpose operation of the vector.

5. The design method of the motor adaptive backstepping controller for high self-locking force load according to claim 4 is characterized in that In step 4, the two segmented projection functions are and in, represents the real-time estimated value of a(t), represents the real-time estimated value of b(t), λ represents the input of the piecewise projection function, express The projection upper bound of σ represents the allowed upper bound of the projection, express The first derivative of express The projection upper bound of for The first derivative of .

6. The design method of a motor adaptive backstepping controller for high self-locking force loads according to claim 5 is characterized in that In step 5, for a(t) and b(t), the corresponding piecewise projection function is used to design an adaptive law, and the real-time estimation of a(t) and b(t) is achieved as follows: in, express The first derivative of for replace The λ in is obtained, express The first derivative of for replace The λ in is obtained.

7. The design method of a motor adaptive backstepping controller for a high self-locking force load according to claim 6, characterized in that In step 6, the quadratic Lyapunov function V1(t) designed for z1(t) is described as: The quadratic Lyapunov function V2(t) designed for z2(t) is described as: The quadratic Lyapunov function V3(t) designed for z3(t) is described as: in, is the upper bound of a(t), is the upper bound of b(t).

8. The design method of a motor adaptive backstepping controller for a high self-locking force load according to claim 7, characterized in that In step 7, the expression of the adaptive backstepping controller is: Where u(t) represents the control output of the adaptive backstepping controller, represents the first-order derivative of u3(t), represents the first-order derivative of u2(t), Represents θ r The first-order derivative of , k1, k2, k3 are the adaptive backstepping controller parameters for the convergence speed of the control system to be designed, ε1, ε2 are the adaptive backstepping controller parameters for the vibration of the control actuator to be designed.

9. The design method of a motor adaptive backstepping controller for high self-locking force loads according to claim 8, characterized in that In step 8, the optimization problem is described as: Optimization goal: Constraints: ε1>0,ε2>0 in, is the expanded expression of the current change rate, s is the ratio of the square of the current change rate to ||x(t)||, and x(t) represents the system state vector, that is, x(t) = [x1(t) x2(t) x3(t)] T , the symbol "|| ||" is the symbol for finding the binary norm. It is the positive expected value of the system convergence speed indicator.

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