CN104638999B - Dual-servo-motor system control method based on segmentation neutral net friction model - Google Patents

Abstract

The invention relates to a control method for a dual-motor servo system based on a segmented neural network friction model, and belongs to the technical field of electromechanical control. Firstly, the friction-containing dual-motor drive servo system is analyzed, and according to the mechanism modeling method, the mathematical model of the friction-containing dual-motor drive servo system is established according to the structure and physical laws of the motor. Then the friction term f _i in the model is analyzed, and the friction model of friction nonlinearity f _i is established by using segmental neural network. The segmented neural network friction model is obtained, and the motor speed synchronous control law is obtained by using the terminal sliding mode control algorithm, and the synchronous tracking control of the dual-motor servo system is completed according to the control law. The method of the invention can eliminate the influence of friction on the dual-motor system, enable the dual-motor system to have better transient performance, effectively improve the tracking response speed of the dual-motor servo system, and ensure fast synchronization of the dual-motor system.

Description

Control Method of Dual Motor Servo System Based on Segmented Neural Network Friction Model

technical field

The invention relates to a dual-motor friction compensation synchronous tracking control method, which belongs to the technical field of electromechanical control.

Background technique

With the rapid development of modern science and technology, it is increasingly difficult for single-motor servo systems to meet the needs of high-power systems in terms of power and performance. Using multiple motors to jointly drive loads can solve this problem very well. In multi-motor servo systems, frictional nonlinearity leads to many negative effects, for example, Stribeck effect and speed dead zone, which seriously affects the tracking accuracy of the servo system at low speeds. This makes it difficult to ensure a good control effect for the multi-motor servo system using traditional controllers. How to ensure high-precision tracking and synchronous control of multi-motor servo systems has become a hot issue.

Friction is an unavoidable problem in motor servo systems. For high-precision servo tracking systems, the existence of frictional links is an obstacle to improving system performance. The impact of friction on the static performance of the system is manifested by a large static difference in the output response or steady-state limit cycle oscillation, and the impact on the dynamic performance of the system is manifested by crawling (jitter) at low speeds and waveform distortion when the speed crosses zero. Friction severely affects the low-speed performance and tracking accuracy of electromechanical servo systems. In order to solve the impact of friction on the positioning and tracking accuracy of the servo system, the friction should be modeled and the corresponding dynamic compensation scheme should be designed. Researchers have successively proposed a variety of friction models, such as the classic Coulomb friction + viscous friction model, Dahl model, Karnop model, LuGre model, Leuven model, Maxwell-slip model, etc. Among them, the LuGre model can accurately describe the complex dynamic and static characteristics in the friction process, such as crawling, limit cycle oscillation, deformation before sliding, friction memory, variable static friction and Stribeck curve, etc., and has become the most commonly used model-based friction compensation. A friction model.

Since the LuGre model can well describe complex friction phenomena, many scholars have done more research on the friction modeling and compensation control of the LuGre model. For example, Dr. Muvengei from Kenya studied the LuGre friction model and the identification method of model parameters. In order to better overcome the influence of friction and improve the control accuracy of the control system, Dr. Hoshino D of Japan used the observer for friction compensation control. Domestically, Dr. Xiang Hongbiao of Tianjin University of Technology used the inversion algorithm to propose an adaptive compensation control method based on the friction model.

In addition, with the continuous improvement of the control precision of the motor servo system, the high-precision control of the servo system has also become a hot spot in this field. In this regard, Dr. Wang Xiaojing of Harbin Institute of Technology proposed a tracking controller based on zero phase error, which effectively improved the anti-interference performance and frequency domain performance of the servo system; Liu Zhi of Central South University proposed an active disturbance based on BP neural network Inhibition control method; Zhang Zhen of the University of Hong Kong proposed a method that can achieve fast synchronization of multiple motor speeds.

However, most of these existing methods only study the tracking with friction compensation or multi-motor synchronization problems alone, and no inventions have been mentioned that can solve these two problems at the same time.

Contents of the invention

The purpose of the present invention is to propose a dual-motor servo system control method based on a segmented neural network friction model in order to realize high-precision tracking and synchronous control of the motors during the control process of the dual-motor servo system.

The basic principle of the method of the invention is: the friction model expressed based on the discontinuous segmented neural network is used to replace the LuGre steady-state friction model, thereby better approaching real friction and realizing friction compensation. In order to enable the dual-motor system to be synchronized quickly and controlled with high precision, a variable coefficient representing the synchronization rate is proposed in the method of fast terminal sliding mode, and friction compensation control is performed based on it.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

A method for controlling a dual-motor servo system based on a segmented neural network friction model, comprising the following steps:

Step 1: Analyze the friction-containing dual-motor drive servo system, and establish a mathematical model of the friction-containing dual-motor drive servo system according to the mechanism modeling method, according to the structure and physical laws of the motor. The purpose of establishing this model is to better understand the characteristics of the dual-motor system, and then design a synchronous tracking control method to achieve fast synchronization and precise tracking. details as follows:

According to the mechanism modeling method, according to the structure and physical laws of the motor, the mathematical model of the dual-motor drive servo system with friction is established, as follows:

Among them, θ _i (i=1,2) and θ _m represent the rotation angles of the driving end and the load end respectively; and Respectively represent the rotational speed of the drive end and the load end; and Respectively represent the acceleration of the drive end and the load end; J represents the moment of inertia of the driving motor; J _m represents the moment of inertia of the load end; b _m represents the viscosity coefficient of the connected gear; u _i represents the system input torque; ω represents the bias torque; τ _i (t) represents the transmission torque between the motor and the load; f _i represents the friction torque of the drive motor; t represents the time from the signal input; i=1, 2 represents the drive motor 1 and drive motor 2 of the dual-motor system.

In formula (1), assuming the backlash is 2α, the gear transmission torque τ _i (t) can be expressed as:

Among them, k represents the torque coefficient of the gear, c represents the damping coefficient of the gear, and f(z _i (t)) represents a nonlinear function with backlash dead zone, expressed as:

Wherein, z _i (t) = θ _i (t) - θ _m (t) is the angle difference between the driving end and the load end.

To facilitate the design of the controller, the nonlinear function f(z _i (t)) is rewritten as a continuously differentiable function:

Among them, r represents a normal number. Then the gear transmission torque τ _i (t) can be expressed as:

Define the following variables x ₁ , x ₂ , x _3i , x _4i to simplify the control algorithm design.

From the above, it can be obtained that the gear transmission torque is τ _i (t)=kx _3i +cx _4i , so formula (1) is rewritten from variables x ₁ , x ₂ , x _3i , x _4i to:

in,

Considering that in formula (7) Part, the friction force f _i is the resistance of the system input u _i (t).

The following discusses how to use the segmental neural network to approximate f _i to generate a moment of the same magnitude as the friction force f _i , and then use the compensation control mechanism to enable it to track the desired signal to meet the accuracy requirements.

Step 2, analyzing the friction item f _i in the model established in step 1, and utilizing the segmented neural network to establish a friction model of friction nonlinearity f _i ;

The friction torque seriously affects the tracking accuracy and control effect of the servo system. In order to eliminate the adverse effects of friction and improve the tracking ability and robustness of the system, it is necessary to analyze the friction phenomenon and carry out modeling and identification of characteristic parameters. The stage where the friction force has the greatest impact on the system is the low-speed stage. At this time, the system may vibrate or crawl due to the influence of friction. In classical PID control, the influence of low-speed friction on the system is overcome by increasing the gain of the control system, but the system is often unstable.

In the first step, the characteristics of the dual-motor object and the existing frictional nonlinearity are comprehensively analyzed, and in the second step, the frictional nonlinearity f _i is approximated using a segmented neural network. The piecewise neural network can approximate any piecewise continuous linear function, which can be represented by a linear parameterized expression. There is no need to make any assumptions about the unknown function, and the accuracy of the approximation can be controlled by adjusting several parameters in the formula, which is the biggest advantage of the piecewise neural network expression.

Given any l-dimensional piecewise linear function f(v,w), (v∈R ^l-1 ,w∈R), the domain of definition is Then it is expressed as follows:

Divide D into N non-overlapping subdomains D _G (G=1,...,N) and Then f(v,w) is expressed as:

Among them, α _G (ν) and β _G (ν) are the upper bound and lower bound of v∈R ^l-1 of the Gth subfield, respectively. α _G (ν) is the minimum lower bound on v relative to domain D. p _G is the unknown coefficient to be estimated in the expression, σ _G (0,w-α _G (ν), β _G (ν)-α _G (ν)) is the basis function, and its specific form is:

σ(a,b,c)=max(a,min(b,c)) (10)

As a special case of the above theory, the expression form of a one-dimensional segmented neural network is:

Among them, the basis function σ(0,h-α _G ,β _G -α _G ) is a special piecewise continuous linear function, expressed as: σ(0,h-α _G ,β _G -α _G )=max( 0,h-α _G )-max(0,h-max(α _G ,β _G )), α _G and β _G are the upper bound and lower bound of h∈R on the Gth subinterval respectively, p _G ( G=1,...,N) is the unknown coefficient that needs to be estimated; and the unknown coefficient p _G is actually the unknown slope of the local linear function σ _G =h-α _G when α _G ≤ h ≤ β _G , when h When <α _G , σ _G =0; when h≥β _G , σ _G =β _G -α _G . The sufficient condition for using equation (11) to approximate a 1-dimensional piecewise continuous linear function is that the domain of the independent variable h is divided into non-overlapping subintervals and the boundary points α _G and β _G satisfy α _G <β _G and β _G = α _G+1 .

Considering the special nature of friction, the above segmentation neural network expression to establish a friction model needs to do the following processing. Due to the segmental characteristics of the friction dynamics, the method of establishing the friction model in Eq. (11) only considers that the friction force has an approximate linear relationship with the speed in the high-speed region, and ignores the influence of the low-speed stage. Considering that in the low-speed stage, Coulomb friction and Stribeck effect become the main factors affecting friction, which have strong non-smooth nonlinear characteristics, especially when the friction is near zero speed, there is still a jump phenomenon when turning. In order to solve the problem that the segmented neural network cannot describe the friction force well in the low-speed stage, the following processing is done in formula (11): adding jump term h ₁ (v) and exponent term h ₂ (v). Among them, the jump term h ₁ (v) is related to the maximum static friction force and is used to solve the friction force jump phenomenon when changing directions; the exponential term h ₂ (v) is used to solve the approximation of the low-speed Stribeck effect. Therefore, no matter in the high-speed section or the low-speed section, the segmented neural network can completely approximate the friction force, and the expression (11) can be rewritten as:

Among them, v and f(v) are velocity and friction force respectively; N(≥2) represents the number obtained by dividing the variation range of velocity v; α _G and β _G are the upper and lower bounds of the Gth subinterval, h ₁ (v ) is a transition item in the form of: h ₂ (v) describes the Stribeck effect in the form: Among them, F _s represents the static friction force, and v _c represents the speed when the friction torque is minimum.

For the convenience of processing, formula (12) is rewritten as a compact expression:

Among them, D=[d ₀ ,d ₁ ,…,N,d _N+1 ] ^T represents the parameter vector, Represents a vector of basis functions. The parameter D can be calculated by recursive least square estimation method.

In order to verify that the segmented neural network has a good approximation ability for discontinuous functions with jumping points such as friction nonlinearity, the segmented neural network is used to approximate the commonly used LuGre model:

The result is shown in Figure 2. It can be concluded from the figure that the segmented neural network can approximate the frictional nonlinearity very well.

The acquisition method of the speed interval _vc is:

Select no less than 10 different speed values in the positive and negative directions of the dual-motor servo system; at the same time, use PI control for the motor to keep the motor running speed constant; when the motor moves at a constant speed, the friction force is equal to the output torque of the motor The size of the motor output torque is proportional to the size of the controller output control voltage. By recording the size of the controller output control value, the size of the motor friction force at the current speed can be obtained; each speed sample point is not less than After 3 times of the above processing, take the average value of all the friction results obtained as the actual friction force of the system at the current speed; finally obtain the magnitude of the friction force at least 10 different speeds in the positive and negative directions, and then compare the positive and negative two directions. Each group of data in each direction is fitted by the least square method, and the velocity interval v _c can be obtained.

The acquisition method of the maximum static friction force F _s is:

Make the dual-motor servo system work in an open-loop environment, and gradually increase the control voltage of the dual-motor until the motor starts to rotate. At this time, it is the maximum static friction of the system; repeat the operation at least 10 times, and take the average value as the maximum static friction torque F _s .

Step 3: According to the segmental neural network friction model obtained in Step 2, the terminal sliding mode control algorithm is used to perform synchronous tracking control on the dual-motor servo system.

In step 2, the friction model is represented by a segmented neural network model, that is, Change f(v) into f _i and substitute it into the algorithm to design the controller. The following uses the fast terminal sliding mode algorithm for the present invention to design a control algorithm for a dual-motor system based on segmental neural network friction compensation, so that the dual-motor system can not only ensure the speed synchronization of the two motors, but also ensure that the load end has a large Good tracking performance.

Considering the tracking performance of the system, let y( _t )=θm be the output signal of the system, y _d (t) be the reference signal of the system, then the error e(t)=y(t)-y _d (t), get The differential, quadratic and cubic differentials of the error are:

Using the fast terminal sliding mode algorithm to get:

Wherein, p _i (i=0,1) is a positive odd number and satisfies p _i >q _i , and α _i >0, β _i >0.

In order to enable the dual-motor system to synchronize quickly and achieve high-precision tracking control, a variable coefficient representing the degree of synchronization of the dual-motor is proposed in the method of fast terminal sliding mode, and friction compensation control is performed based on it, and the original control law is divided into In order to ensure the two parts of speed synchronization u _si and tracking u _ti . Based on the piecewise neural network friction model, the control law u _i is expressed as

u _i =u _si +ψu _ti (18)

in,

Among them, f _i in the control law u _si that guarantees speed synchronization is the friction model obtained by the segmental neural network in the third step, and an input quantity that can offset the influence of friction force is generated at the input end u _i ; while b is a normal number, η is an optional constant, h ₁ (x _3i , x _4i ) is the state feedback item of the system, is the sliding mode term of the system, expressed as

h ₁ (x _3i ,x _4i )＝a ₂ cρ _i τ _i (t)+a ₂ cρ _i (-1) ⁱ ω+ca ₁ ρ _i (τ ₁ (t)+τ ₂ (t))-kx _4i (22)

According to the control law u _i , the dual-motor servo system is synchronously tracked and controlled, thereby realizing the purpose and original intention of the present invention.

Beneficial effect

Control method of the present invention has following beneficial effect:

1. For the dual-motor servo system, the friction model of the segmented neural network has better nonlinear approximation ability, and can describe the friction characteristics with high precision. Therefore, the present invention designs a friction compensation controller based on the segmented neural network, which is compatible with the friction belt The resulting nonlinear effects cancel each other out, and finally achieve the purpose of compensation and eliminate the influence of friction on the dual-motor system.

2. While performing friction compensation, the synchronization and tracking control of the dual-motor servo system with a segmented neural network friction model is considered. Using the fast terminal sliding mode algorithm, it can not only ensure the rapidity of tracking, but also ensure the steady-state accuracy of the system . The invention can make the double-motor system have better transient performance, and effectively improve the tracking response speed of the double-motor servo system.

3. Aiming at the characteristics that the dual-motor servo system is not easy to synchronize, the present invention designs a fast terminal sliding mode controller based on the segmental neural network friction compensation, and proposes a variable coefficient to represent the degree of synchronization. This method can ensure the rapid synchronization of the dual-motor system , the control algorithm of the present invention has strong robustness.

In the fast terminal sliding mode algorithm, a variable coefficient ψ is designed to solve the coordination problem of dual-motor synchronization and tracking control well. The variable coefficient ψ is adjusted by the speed difference of the two drive motors to ensure the dual-motor Synchronization and tracking effect: when the speed difference between the two driving motors is large, the variable coefficient ψ is small, so that the speed synchronization control law u _si plays a major role, firstly, the speed of the two driving motors is synchronized as fast as possible; synchronization Finally, the speed difference between the two driving motors becomes smaller, and the variable coefficient ψ is close to 1, which ensures that the tracking control law u _ti plays a major role, making the dual-motor system have high tracking accuracy. Therefore, the control scheme of the present invention can ensure that the dual-motor system simultaneously achieves the effects of synchronization and tracking.

Description of drawings

Figure 1 is a typical structural diagram of a dual-motor servo control system;

Fig. 2 is a segmental neural network approximation friction model figure;

Fig. 3 is the dual motor speed-friction curve figure in the specific embodiment;

Fig. 4 is a curve diagram of the friction force test of two motors in the specific embodiment;

Fig. 5 is a tracking effect diagram utilizing a fast terminal sliding mode controller under segmented neural network friction compensation in a specific embodiment;

Fig. 6 is the tracking error diagram utilizing the fast terminal sliding mode controller under the segmented neural network friction compensation in the specific embodiment;

7 is a synchronous effect diagram of two drive motors in a dual-motor servo system using a fast terminal sliding mode controller in a specific embodiment;

Fig. 8 is a graph of synchronization errors in a dual-motor servo system using a fast terminal sliding mode controller in a specific embodiment.

Detailed ways

The method of the present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments.

A method for controlling a motor servo system based on a segmented neural network friction model, comprising the following steps:

Step 1. Analyze the friction-containing dual-motor drive servo system, and establish a mathematical model of the friction-containing dual-motor drive servo system according to the mechanism modeling method, according to the structure and physical laws of the motor, as follows:

in,

In formula (24), formula (25) and formula (26), θ _i (i=1, 2) and θ _m represent the rotation angles of the driving end and the load end respectively; and Respectively represent the rotational speed of the drive end and the load end; and Respectively represent the acceleration of the drive end and the load end; J represents the moment of inertia of the driving motor; J _m represents the moment of inertia of the load end; b _m represents the viscosity coefficient of the connected gear; u _i represents the system input torque; ω represents the bias torque; τ _i (t) represents the transmission torque between the motor and the load; f _i represents the friction torque of the driving motor; t represents the time from the signal input; i=1,2 represents the driving motor 1 and driving motor 2 of the dual-motor system; z _i (t)=θ _i (t)-θ _m (t) represents the angle difference between the drive end and the load end;

Step 2. Analyze the friction item f _i in the model established in step 1, and use the segmented neural network to establish a friction model of friction nonlinearity f _i , as follows:

The expression form of a one-dimensional segmented neural network is:

Among them, the basis function σ(0,h-α _G ,β _G -α _G ) is a special piecewise continuous linear function, expressed as: σ(0,h-α _G ,β _G -α _G )=max( 0,h-α _G )-max(0,h-max(α _G ,β _G )), α _G and β _G are the upper bound and lower bound of h∈R on the Gth subinterval respectively, p _G ( G=1,...,N) are unknown coefficients that need to be estimated;

The sufficient condition for using equation (27) to approximate a one-dimensional piecewise continuous linear function is that the domain of the independent variable h is divided into non-overlapping subintervals and the boundary points α _G and β _G satisfy α _G < β _G and β _G =αG ₊₁ ;

Formula (27) is further processed as follows:

Add jump term h ₁ (v) and exponent term h ₂ (v) to formula (27); among them, jump term h ₁ (v) is related to the maximum static friction force, which is used to solve the friction force jump when changing direction variable phenomenon; the exponential term h ₂ (v) is used to solve the approximation of the low-speed Stribeck effect; equation (27) becomes as follows:

Among them, v and f(v) are velocity and friction force respectively; N(≥2) represents the number obtained by dividing the variation range of velocity v; α _G and β _G are the upper and lower bounds of the Gth subinterval, h ₁ (v ) is a transition item in the form of: h ₂ (v) describes the Stribeck effect in the form: Among them, F _s represents the static friction force, v _c represents the speed when the friction torque is minimum;

The formula (28) is further converted as follows:

Among them, D=[d ₀ ,d ₁ ,…,N,d _N+1 ] ^T represents the parameter vector, Indicates the basis function vector; the parameter D is calculated by the recursive least squares estimation method;

The acquisition method of the speed interval _vc is:

Select 15 different speed values in the positive and negative directions of the dual-motor servo system; at the same time, use PI control for the dual-motor system to keep the speed of the system constant; when the motor moves at a uniform speed, the output torque of the motor is the friction force The size of the motor output torque is proportional to the size of the controller output control voltage. By recording the size of the controller output control amount, the size of the motor friction force at the current speed can be obtained; 5 times for each speed sample point The above processing, take the average value of all the friction results obtained, as the actual friction force of the system at the current speed; finally get the magnitude of the friction force at 15 different speeds in the positive and negative directions, and then compare the positive and negative directions respectively The group data is fitted by the least square method, and the velocity interval v _c can be obtained. The velocity-friction curve obtained by fitting the least squares algorithm is shown in Fig. 3.

The acquisition method of the maximum static friction force F _s is:

Make the dual-motor servo system work in an open-loop environment, and gradually increase the control voltage of the dual-motor until the motor starts to rotate, which is the maximum static friction of the system; repeat the operation 10 times, and take the average value as the maximum static friction torque F _s . The collected speed signal and the output voltage signal of the controller are drawn into a graph, as shown in Figure 4, and the magnitude of the static friction can be observed.

Step 3. According to the segmented neural network friction model obtained in Step 2, use the terminal sliding mode control algorithm to perform synchronous tracking control on the dual-motor servo system. The method is as follows:

Let y(t)=θ _m be the system output signal, y _d (t) be the system reference signal, then the error e(t)=y(t)-y _d (t), get error differential, quadratic differential and cubic The differentials are:

Using the fast terminal sliding mode algorithm to get:

Wherein, p _i (i=0,1) is a positive odd number and satisfies p _i >q _i , and α _i >0, β _i >0;

At this time, the original control law is divided into two parts that ensure the speed synchronization u _si and ensure the tracking u _ti , and the control law u _i is expressed as

u _i =u _si +ψu _ti (34)

in,

Among them, f _i in the control law u _si that guarantees speed synchronization is the friction model obtained by the segmental neural network in step 2, and an input quantity that can offset the influence of friction force is generated at the input end u _i ; both b and η are positive numbers, h ₁ (x _3i ,x _4i ) is the system state feedback item, is the sliding mode item of the system, expressed as

h ₁ (x _3i ,x _4i )＝a ₂ cρ _i τ _i (t)+a ₂ cρ _i (-1) ⁱ ω+ca ₁ ρ _i (τ ₁ (t)+τ ₂ (t))-kx _4i (38)

According to the control law u _i , the dual-motor servo system can be synchronously tracked and controlled.

The above processing results are simulated, and the tracking effect and synchronization effect diagrams are obtained. It can be seen from the comparison simulation diagram that the segmental neural network friction compensation controller has high output tracking accuracy. In the dual-motor servo system segment neural network compensation synchronous tracking simulation experiment, the parameters of the drive motor, load and friction are shown in Table 1.

Table 1 Simulation parameters

Under the above motor parameters, the segmented neural network friction compensation algorithm is simulated, and the tracking effect and tracking error of the sinusoidal input signal are shown in the figure. Figure 5 and Figure 6 are the effect diagrams of sinusoidal signal tracking, and Figure 7 and Figure 8 are the effect diagrams of dual-motor synchronization. It can be seen from the simulation results that the control algorithm of the present invention has high tracking performance and synchronization performance, and can make the double motor system synchronize quickly and track the input signal with high precision.

The invention considers the synchronous and tracking control problems of the dual-motor servo system with a segmented neural network friction model. Establishing a segmented neural network friction model can well approximate the friction nonlinearity of the servo system. This model can not only describe the friction characteristics of the high-speed section, but also has a good effect in the low-speed section. The controller is designed based on the segmental neural network friction model, and the variable coefficient representing the degree of synchronization is proposed in the algorithm of the fast terminal sliding mode, which can make the dual-motor system synchronize quickly and achieve high-precision tracking control. It can be seen from simulation experiments that the method of the invention has good control performance.

Claims (2)

1. based on the double-motor servo system control method of subsection neural network friction model, it is characterized in that, comprising the following steps: Step 1. Analyze the friction-containing dual-motor drive servo system, and establish a mathematical model of the friction-containing dual-motor drive servo system according to the mechanism modeling method, according to the structure and physical laws of the motor, as follows: in, <mrow><msub><mi>&amp;tau;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>k</mi><mrow><mo>(</mo><msub><mi>z</mi><mi>i</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>&amp;alpha;</mi><mo>(</mo><mrow><mfrac><mn>2</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>-</mo><msub><mi>rz</mi><mi>i</mi></msub></mrow></msup></mrow></mfrac><mo>-</mo><mn>1</mn></mrow><mo>)</mo><mo>)</mo><mo>+</mo><mi>c</mi><msub><mover><mi>z</mi><mo>&amp;CenterDot;</mo></mover><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mn>2</mn><mi>&amp;alpha;</mi><mfrac><msup><mi>e</mi><mrow><mo>-</mo><msub><mi>rz</mi><mi>i</mi></msub></mrow></msup><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>-</mo><msub><mi>rz</mi><mi>i</mi></msub></mrow></msup><mo>)</mo></mrow><mn>2</mn></msup></mfrac><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow> In formula (1), formula (2) and formula (3), θ _i (i=1, 2) and θ _m represent the rotation angles of the driving end and the load end respectively; and Respectively represent the rotational speed of the drive end and the load end; and Respectively represent the acceleration of the drive end and the load end; J represents the moment of inertia of the driving motor; J _m represents the moment of inertia of the load end; b _m represents the viscosity coefficient of the connected gear; u _i represents the system input torque; ω represents the bias torque; τ _i (t) represents the transmission torque between the motor and the load; f _i represents the friction torque of the driving motor; t represents the time from the signal input; i=1,2 represents the driving motor 1 and driving motor 2 of the dual-motor system; z _i (t)=θ _i (t)-θ _m (t) represents the angle difference between the drive end and the load end; α is the backlash between the motors, and γ represents a normal number; Step 2. Analyze the friction item f _i in the model established in step 1, and use the segmented neural network to establish a friction model of friction nonlinearity f _i , as follows: The expression form of a one-dimensional segmented neural network is: <mrow><mi>f</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>G</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>p</mi><mi>G</mi></msub><msub><mi>&amp;sigma;</mi><mi>G</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>h</mi><mo>-</mo><msub><mi>&amp;alpha;</mi><mi>G</mi>mi></msub><mo>,</mo><msub><mi>&amp;beta;</mi><mi>G</mi></msub><mo>-</mo><msub><mi>&amp;alpha;</mi><mi>G</mi></msub><mo>)</mo></mrow><mo>&amp;ForAll;</mo><mi>h</mi><mo>&amp;Element;</mo><mi>R</mi><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow> Among them, the basis function σ(0,h-α _G ,β _G -α _G ) is a special piecewise continuous linear function, expressed as: σ(0,h-α _G ,β _G -α _G )=max( 0,h-α _G )-max(0,h-max(α _G ,β _G )), α _G and β _G are the upper bound and lower bound of h∈R on the Gth subinterval respectively, p _G ( G=1,...,N) are unknown coefficients that need to be estimated; The sufficient condition for using equation (4) to approximate a one-dimensional piecewise continuous linear function is that the domain of the independent variable h is divided into non-overlapping subintervals and the boundary points α _G and β _G satisfy α _G < β _G and β _G =αG ₊₁ ; Formula (4) is further processed as follows: Add jump term h ₁ (v) and exponent term h ₂ (v) to formula (4); among them, the jump term h ₁ (v) is related to the maximum static friction force, which is used to solve the friction force jump when changing direction. variable phenomenon; the exponent term h ₂ (v) is used to solve the approximation of the low-speed Stribeck effect; formula (4) becomes as follows: <mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>d</mi><mn>0</mn></msub><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>G</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mo>&amp;lsqb;</mo><msub><mi>d</mi><mi>G</mi></msub><msub><mi>&amp;rho;</mi><mi>G</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>v</mi><mo>-</mo><msub><mi>&amp;alpha;</mi><mi>G</mi></msub><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>,</mo><msub><mi>&amp;beta;</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>&amp;alpha;</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>)</mo><mo>+</mo><msub><mi>h</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>&amp;rsqb;</mo><mo>+</mo><msub><mi>d</mi><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mi>h</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mrow> Among them, v and f(v) are velocity and friction force respectively; N(≥2) represents the number obtained by dividing the variation range of velocity v; d ₀ and d _G (G=1,…,N) are estimated Unknown coefficients; α _G and β _G are the upper and lower bounds of the Gth subinterval, h ₁ (v) is the jump term, the form is: h ₂ (v) describes the Stribeck effect in the form: Among them, F _s represents the static friction force, v _c represents the speed when the friction torque is minimum; The formula (5) is further converted as follows: Among them, D=[d ₀ ,d ₁ ,…,N,d _N+1 ] ^T represents the parameter vector, Indicates the basis function vector; the parameter D is calculated by the recursive least squares estimation method; Step 3. According to the segmented neural network friction model obtained in Step 2, use the terminal sliding mode control algorithm to perform synchronous tracking control on the dual-motor servo system. The method is as follows: Let y(t)=θ _m be the system output signal, y _d (t) be the system reference signal, then the error e(t)=y(t)-y _d (t), get error differential, quadratic differential and cubic The differentials are: <mrow><mover><mi>e</mi><mo>&amp;CenterDot;</mo></mover><mo>=</mo><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mover><mi>y</mi><mo>&amp;CenterDot;</mo></mover><mi>d</mi></msub><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mo>mn><mo>)</mo></mrow></mrow> <mrow><mover><mi>e</mi><mo>&amp;CenterDot;&amp;CenterDot;</mo></mover><mo>=</mo><msub><mover><mi>x</mi><mo>&amp;CenterDot;</mo></mover><mn>2</mn></msub><mo>-</mo><msub><mover><mi>y</mi><mo>&amp;CenterDot;&amp;CenterDot;</mo></mover><mi>d</mi></msub><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub><msubsup><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>2</mn></msubsup><msub><mi>&amp;tau;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mi>m</mi></msub><msub><mi>&amp;theta;</mi><mi>m</mi></msub><mo>-</mo><msub><mover><mi>y</mi><mo>&amp;CenterDot;&amp;CenterDot;</mo></mover><mi>d</mi></msub><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mrow> Among them, k represents the torque coefficient of the gear, and c represents the damping coefficient of the gear; Using the fast terminal sliding mode algorithm to get: <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>s</mi><mn>0</mn></msub><mo>=</mo><mi>e</mi></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>s</mi><mn>1</mn></msub><mo>=</mo><msub><mover><mi>s</mi><mo>&amp;CenterDot;</mo></mover><mn>0</mn></msub><mo>+</mo><msub><mi>&amp;alpha;</mi><mn>0</mn></msub><msub><mi>s</mi><mn>0</mn></msub><mo>+</mo><msub><mi>&amp;beta;</mi><mn>0</mn></msub><msubsup><mi>s</mi><mn>0</mn><mrow><msub><mi>q</mi><mn>0</mn></msub><mo>/</mo><msub><mi>p</mi><mn>0</mn></msub></mrow></msubsup></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>s</mi><mn>2</mn></msub><mo>=</mo><msub><mover><mi>s</mi><mo>&amp;CenterDot;</mo></mover><mn>1</mn></msub><mo>+</mo><msub><mi>&amp;alpha;</mi><mn>1</mn></msub><msub><mi>s</mi><mn>1</mn></msub><mo>+</mo><msub><mi>&amp;beta;</mi><mn>1</mn></msub><msubsup><mi>s</mi><mn>1</mn><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>/</mo><msub><mi>p</mi><mn>1</mn></msub></mrow></msubsup></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow> Among them, e is the abbreviation of error e(t), p _i (i=0,1) is a positive odd number and satisfies p _i >q _i , and α _i >0, β _i >0; At this time, the original control law is divided into two parts that ensure the speed synchronization u _si and ensure the tracking u _ti , and the control law u _i is expressed as u _i =u _si +ψu _ti (11) in, <mrow><msub><mi>u</mi><mrow><mi>s</mi><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>a</mi><mn>2</mn></msub><msub><mi>c&amp;rho;</mi><mi>i</mi></msub></mrow></mfrac><mo>&amp;lsqb;</mo><msub><mi>h</mi><mn>1</mn></msub><mrow><mo>(</mo><msub><mi>x</mi><mrow><mn>3</mn><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>x</mi><mrow><mn>4</mn><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><mi>c</mi><mrow><mo>(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mi>m</mi></msub><msub><mover><mi>&amp;theta;</mi><mo>&amp;CenterDot;</mo></mover><mi>m</mi></msub><mo>-</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>f</mi><mi>i</mi></msub><mo>)</mo></mrow><msub><mi>&amp;rho;</mi><mi>i</mi></msub><mo>&amp;rsqb;</mo><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow> <mrow><mi>&amp;psi;</mi><mo>=</mo><mfrac><mn>1</mn><msup><mi>e</mi><mrow><mi>&amp;eta;</mi><mo>|</mo><msub><mover><mi>z</mi><mo>&amp;CenterDot;</mo></mover><mn>1</mn></msub><mo>-</mo><msub><mover><mi>z</mi><mo>&amp;CenterDot;</mo></mover><mn>2</mn></msub><mo>|</mo></mrow></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>14</mn><mo>)</mo></mrow></mrow> Among them, f _i in the control law u _si that guarantees speed synchronization is the friction model obtained by the segmental neural network in step 2, and an input quantity that can offset the influence of friction force is generated at the input end u _i ; both b and η are positive numbers, h ₁ (x _3i ,x _4i ) is the system state feedback item, is the sliding mode item of the system, expressed as h ₁ (x _3i ,x _4i )＝a ₂ cρ _i τ _i (t)+a ₂ cρ _i (-1) ⁱ ω+ca ₁ ρ _i (τ ₁ (t)+τ ₂ (t))-kx _4i (15) <mrow><mtable><mtr><mtd><mrow><msub><mi>h</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>s</mi><mn>0</mn></msub><mo>,</mo><msub><mover><mi>s</mi><mo>&amp;CenterDot;</mo></mover><mn>0</mn></msub><mo>,</mo><msub><mover><mi>s</mi><mo>&amp;CenterDot;&amp;CenterDot;</mo></mover><mn>0</mn></msub><mo>,</mo><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msub><mover><mi>s</mi><mo>&amp;CenterDot;</mo></mover><mn>1</mn></msub><mo>)</mo></mrow><mo>=</mo><msub><mi>&amp;alpha;</mi><mn>0</mn></msub><msub><mover><mi>s</mi><mo>&amp;CenterDot;&amp;CenterDot;</mo></mover><mn>0</mn></msub><mo>/</mo><mrow><mo>(</mo><mn>2</mn><msub><mi>a</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>+</mo><msup><mrow><mo>(</mo><msub><mi>&amp;beta;</mi><mn>0</mn></msub><msubsup><mi>s</mi><mn>0</mn><mrow><msub><mi>q</mi><mn>0</mn></msub><mo>/</mo><msub><mi>p</mi><mn>0</mn></msub></mrow></msubsup><mo>)</mo></mrow><mrow><mo>&amp;prime;</mo><mo>&amp;prime;</mo></mrow></msup><mo>/</mo><mrow><mo>(</mo><mn>2</mn><msub><mi>a</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>+</mo><msup><mrow><mo>(</mo><msub><mi>&amp;beta;</mi><mn>1</mn></msub><msubsup><mi>s</mi><mn>1</mn><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>/</mo><msub><mi>p</mi><mn>1</mn></msub></mrow></msubsup><mo>)</mo></mrow><mo>&amp;prime;</mo></msup><mo>/</mo><mrow><mo>(</mo><mn>2</mn><msub><mi>a</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><msub><mi>&amp;alpha;</mi><mn>1</mn></msub><msub><mover><mi>s</mi><mo>&amp;CenterDot;</mo></mover><mn>1</mn></msub><mo>//</mo><mrow><mo>(</mo><mrow><mn>2</mn><msub><mi>a</mi><mn>1</mn></msub></mrow><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow> According to the control law u _i , the dual-motor servo system is synchronously tracked and controlled. 2. a kind of dual-motor servo system control method based on segmental neural network friction model as claimed in claim 1, is characterized in that, the acquisition method of speed interval _v in the step 2 is: Select no less than 10 different speed values in the positive and negative directions of the dual-motor servo system; at the same time, use PI control for the dual-motor system to keep the speed of the system constant; when the motor moves at a uniform speed, the output torque of the motor is The size of the friction force, and the size of the motor output torque is proportional to the size of the controller output control voltage, by recording the size of the controller output control amount, the size of the motor friction force at the current speed can be obtained; for each speed sample point Carry out the above processing no less than 3 times, and take the average value of all the friction results obtained as the actual friction force of the system at the current speed; finally obtain the friction force at least 10 different speeds in the positive and negative directions, and then The least squares method is used to fit each set of data in the positive and negative directions, and the velocity v _c when the friction torque is minimum can be obtained; The acquisition method of the maximum static friction force F _s is: Make the dual-motor servo system work in an open-loop environment, and gradually increase the control voltage of the dual-motor until the motor starts to rotate. At this time, it is the maximum static friction of the system; repeat the operation at least 10 times, and take the average value as the maximum static friction torque F _s .