Servo motor control method based on nonsingular terminal sliding mode control

Abstract

The invention relates to the field of servo motor control, in particular to a servo motor control method based on nonsingular terminal sliding mode control. The method comprises the following steps: firstly, establishing a mathematical model of the servo motor according to the working principle of the servo motor; then, according to the mathematical model of the servo motor, designing an improved extended state observer, designing an anti-saturation input auxiliary system, and establishing an error function; thirdly, according to the error function, defining a sliding mode surface of nonsingular terminal sliding mode control, and according to the sliding mode surface, obtaining a nonsingular terminal sliding mode control law; and finally, according to the extended state observer, the auxiliary system and the nonsingular terminal sliding mode control law, obtaining the nonsingular terminal sliding mode control law based on the improved extended observer and the anti-saturation input auxiliary system.

Description

Technical Field

[0001] The present invention relates to the field of servo motor control, and in particular to a servo motor control method based on non-singular terminal sliding mode control. Background Art

[0002] Servo motor control systems play a core role in many fields such as industrial automation, robotics, and precision machinery. With the development of technology, the performance requirements for servo motor control systems are getting higher and higher, especially in terms of dynamic response, positioning accuracy, and robustness. However, in the field of servo motor control, conventional servo motor control methods are usually motor control technologies based on PID control. However, when system parameters change or loads change rapidly, PID control may not be able to respond quickly to system changes, resulting in large overshoot and oscillation in the system, which affects the dynamic response of the system and leads to poor anti-interference ability.

[0003] In addition, the servo motor will face parameter changes and interference when working. Since the PID controller is designed based on linear control theory and assumes that the system is time-invariant, and the design of the PID controller is usually based on the simplification and approximation of the system model, it will lead to insufficient robustness of the system and the PID controller cannot maintain stable performance.

[0004] In addition, servo motors will also face input saturation. When the control input reaches saturation, the control input cannot meet the needs of the system, and the system cannot obtain sufficient control torque to respond to external disturbances or track reference inputs. Therefore, input saturation will limit the dynamic response speed and anti-interference ability of the control system.

[0005] In this context, a servo motor control method based on non-singular terminal sliding mode control is proposed. This method uses the strong robustness and fast response of non-singular terminal sliding mode control, as well as the extended state observer and anti-saturation input auxiliary system to ensure that the system can respond quickly and accurately when subjected to external disturbances. When the input of the system exceeds the maximum input that the system can withstand, the auxiliary system plays a role in suppressing the impact of input signal saturation on the system, thereby maintaining the control performance and stability of the servo motor. Summary of the invention

[0006] The present invention provides a servo motor control method based on non-singular terminal sliding mode control, which is used to solve the above technical problems. First, according to the working principle of the servo motor, a mathematical model of the servo motor is established; then, according to the mathematical model of the servo motor, an improved extended state observer is designed, an anti-saturation input auxiliary system is designed and an error function is established; then, according to the error function, a sliding surface of non-singular terminal sliding mode control is defined, and according to the sliding surface, a non-singular terminal sliding mode control law is obtained; finally, according to the extended state observer, the anti-saturation input auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended observer and the anti-saturation auxiliary system is obtained.

[0007] A servo motor control method based on non-singular terminal sliding mode control comprises the following steps:

[0008] S1. According to the working principle of the servo motor, a mathematical model of the servo motor is established;

[0009] S2. According to the mathematical model, an improved extended state observer is designed, an anti-saturation input auxiliary system is designed, and an error function is established;

[0010] S3. According to the error function, a sliding surface of a non-singular terminal sliding mode control is defined, and according to the sliding surface, a non-singular terminal sliding mode control law is obtained;

[0011] S4. According to the improved extended state observer, the anti-windup input auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended state observer and the anti-windup auxiliary system is obtained.

[0012] Furthermore, according to the working principle of the servo motor, a frequency domain mathematical model of the servo motor is established, and the frequency domain mathematical model is:

[0013]

[0014] Among them, θ is the rotation angle of the motor, s is the Laplace operator, J is the equivalent moment of inertia of the system, m is the motor torque coefficient; u is the system input, and R is the total disturbance of the system;

[0015] The frequency domain mathematical model is converted into a time domain mathematical model, and the time domain mathematical model is:

[0016]

[0017] In the formula, b and f are intermediate variables, expressed as:

[0018]

[0019] Where θ is the rotation angle of the motor, is the first-order derivative of θ, ω is the angular velocity of the motor, is the first-order derivative of ω, u is the input of the system, m is the motor torque coefficient, J is the system equivalent moment of inertia, and R is the total disturbance of the system.

[0020] Furthermore, according to the mathematical model, an improved extended state observer is designed, and the improved extended state observer is:

[0021]

[0022] Where e0 is the error between the actual motor angular velocity and the observed motor angular velocity, expressed as:

[0023]

[0024] in, is the state estimation value of the motor rotation angular velocity ω; is the disturbance estimate of f, ω0 is the bandwidth of the extended state observer, is the first-order derivative of e0.

[0025] Furthermore, according to the time domain mathematical model, an anti-saturation input auxiliary system is designed, and the auxiliary system is:

[0026]

[0027] Among them, Δu is an intermediate variable, expressed as:

[0028]

[0029] Among them, u is the actual control input, expressed as:

[0030]

[0031] in, is the state variable of the auxiliary system, for The first-order derivative of , δ is the parameter to be designed, u is the actual control input, is the output signal of the controller, u max is the maximum input value, u min Enter the minimum value.

[0032] Furthermore, according to the time domain mathematical model, an error function is established, and the error function is:

[0033] e1=θ d -θ;

[0034] Among them, e1 is the rotation angle error, θ is the actual output angle of the motor, and θ dis the target angle.

[0035] Further, according to the error function, a sliding surface of non-singular terminal sliding mode control is defined, and the sliding surface is:

[0036]

[0037] Wherein, e1 is the rotation angle error, λ, p and a are the sliding surface design parameters, is the derivative of e1.

[0038] Furthermore, according to the sliding surface, a non-singular terminal sliding mode control is designed, and the non-singular terminal sliding mode control law is:

[0039]

[0040] Among them, ε and k1 are the parameters to be designed. is the desired motor rotation angle θ d The second-order derivative of , sgn(z) is the sign function, λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1.

[0041] Further, according to the improved extended state observer, the auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended observer and the anti-saturation auxiliary system is obtained, and the non-singular terminal sliding mode control law is:

[0042]

[0043] Among them, ε, k1 and k2 are the parameters to be designed. is the desired motor rotation angle θ d The second derivative of , sgn(z) and is a symbolic function, λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1, is the perturbation estimate of f, is the state variable of the auxiliary system.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. Design a nonlinear improved extended state observer to improve the dynamic response and anti-interference of the servo motor control system. This control method can calculate and compensate for unknown friction, saturation constraints and external interference in the system in real time, realize fast start and stop and speed change operation on the production line, thereby reducing the stagnation time in production and improving production efficiency.

[0046] 2. Combined with the anti-saturation input control strategy, the stability and accuracy of the system can be effectively optimized. The anti-saturation input control strategy can effectively avoid the problem of system performance degradation caused by input signal saturation, thereby ensuring that the system output can quickly and stably track the expected signal, reduce chattering, and improve the processing accuracy and quality of the product.

[0047] 3. By applying non-singular terminal sliding mode control, the servo motor control system can achieve higher control accuracy and faster response speed in dealing with uncertainty and nonlinear problems. This method can ensure that the servo motor can execute complex motion instructions quickly and accurately, thereby improving the processing accuracy and operating efficiency of the production process. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the process of the present invention;

[0049] Figure 2 It is a servo motor control system. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] With the continuous progress of industrial automation technology, servo motors have become indispensable components in key areas such as CNC machine tools and automated production lines due to their high precision and excellent performance. Despite this, servo motors often encounter various interference factors such as load fluctuations and mechanical friction in actual operation, which may reduce the performance of the motor and thus affect the accuracy and stability of its movement. To this end, the present invention provides a servo motor control method based on non-singular terminal sliding mode control. By adopting an anti-saturation input control strategy and non-singular terminal sliding mode control technology, the method not only effectively optimizes the stability and control accuracy of the system, but also improves the response speed and anti-interference of the servo motor, and achieves higher control accuracy and faster response speed in dealing with uncertainty and nonlinear problems. In order to illustrate the feasibility of the present invention, two specific embodiments will be described below.

[0052] Embodiment 1

[0053] In the embodiment of the present application, a servo motor control method based on non-singular terminal sliding mode control is adopted; the specific implementation process is as follows Figure 1 As shown, first, according to the working principle of the servo motor, the mathematical model of the servo motor is established; then, according to the mathematical model of the servo motor, an improved extended state observer is designed, an anti-saturation input auxiliary system is designed and an error function is established; then, according to the error function, a sliding surface of a non-singular terminal sliding mode control is defined, and according to the sliding surface, a non-singular terminal sliding mode control law is obtained; finally, according to the extended state observer, the anti-saturation input auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended observer and the anti-saturation auxiliary system is obtained.

[0054] Furthermore, in the embodiment of the present application, the servo motor parameters are selected as follows: J = 1.5194 × 10 -4 kg·m 2 , m = 0.0866N·s / m; where J is the system equivalent moment of inertia, m is the motor torque coefficient, and the expected value is set to unit step response, that is, θ d =10deg; According to the working principle of the servo motor, a frequency domain mathematical model of the servo motor is established, and the frequency domain mathematical model of the servo motor is:

[0055]

[0056] Among them, θ is the rotation angle of the motor, s is the Laplace operator, and R is the total disturbance of the system.

[0057] The frequency domain mathematical model is converted into a time domain mathematical model, and the time domain mathematical model is:

[0058]

[0059] Among them, θ is the rotation angle of the motor, ω is the angular velocity of the motor, α is the angular acceleration of the motor, u is the input of the system, and R is the total disturbance of the system.

[0060] In the embodiment of the present application, by analyzing the working principle of the servo motor, a mathematical model of the servo motor is established, and a dynamic model of the servo motor is described. The model takes into account the basic parameters of the servo motor and the disturbances to the servo motor system, comprehensively reflects the actual operation of the servo motor, and is conducive to achieving high-precision control of the servo motor.

[0061] Furthermore, according to the time domain mathematical model, an improved extended state observer is designed, and the extended state observer is:

[0062]

[0063] Where e0 is the error between the actual motor angular velocity and the observed motor angular velocity, expressed as:

[0064]

[0065] in, is the state estimation value of the motor rotation angular velocity ω, is the disturbance estimate of f, ω0 is the bandwidth of the extended state observer, is the first-order derivative of e0.

[0066] In the embodiment of the present application, a new state variable is defined, and an extended state observer is established to expand the unknown interference signal of the system into a new state variable. By considering the interference signal as part of the system, the control system can respond quickly to external interference, thereby improving the response speed of the control system and achieving stable and rapid control of the servo motor by the control system.

[0067] Furthermore, according to the time domain mathematical model, an anti-saturation input auxiliary system is designed, and the auxiliary system is:

[0068]

[0069] Among them, Δu is an intermediate variable, expressed as:

[0070]

[0071] Among them, u is the actual control input, expressed as:

[0072]

[0073] in, is the state variable of the auxiliary system; Δu is the difference between the actual control input u and the estimated value of the input disturbance.

[0074] In the embodiment of the present application, an error function is established according to the state observer and an auxiliary system with anti-saturation input is designed to solve the input saturation problem. By designing the auxiliary system and setting the corresponding input, the influence of the saturation phenomenon on the controller is effectively suppressed, thereby reducing the influence of the actuator saturation on the control system performance, which helps to improve the stability and precise control of the control system.

[0075] Furthermore, according to the time domain mathematical model, an error function is established, and the error function is:

[0076] e1 = 10-θ;

[0077] Among them, e1 is the rotation angle error, and θ is the actual output angle of the motor.

[0078] In the embodiment of the present application, the error function of the servo motor is obtained according to the mathematical model of the servo motor. By calculating the angle estimation error, angular velocity estimation error and disturbance estimation error in real time, the deviation of the system can be adjusted promptly and quickly, ensuring the control of the servo motor by the control system, which helps to improve the control accuracy of the system.

[0079] Further, according to the error function, a sliding surface of non-singular terminal sliding mode control is defined, and the sliding surface is:

[0080]

[0081] Wherein, e1 is the rotation angle error, λ, p and q are the sliding surface design parameters, and is the derivative of e1.

[0082] In an embodiment of the present application, a sliding surface is designed, which can guide the system state to the sliding surface and maintain the system state on the sliding surface after reaching the sliding surface. The system state can converge to an equilibrium point or a desired trajectory within a limited time, thereby achieving rapid and stable control of the system.

[0083] Furthermore, according to the sliding surface, a non-singular terminal sliding mode control is designed, and the non-singular terminal sliding mode control law is:

[0084]

[0085] Among them, sgn(z) is the sign function, expressed as:

[0086]

[0087] Among them, ε and k are the parameters to be designed, sgn(z) is the sign function, λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1.

[0088] In the embodiment of the present application, a non-singular terminal sliding mode control law is obtained, and the servo motor control system can achieve higher control accuracy and faster response speed in dealing with uncertainty and nonlinear problems. The system state is forced to slide onto the sliding mode surface, so that the control can effectively resist the influence of external disturbances and changes in system parameters, and the system has stronger robustness.

[0089] Further, according to the extended state observer, the anti-saturation input auxiliary system and the sliding mode control law, a non-singular terminal sliding mode control law is obtained, and the non-singular terminal sliding mode control law is:

[0090]

[0091] Among them, λ, p and q are sliding surface design parameters, k is the control gain, sgn(z) is the sign function, λ1, λ2, p and q are sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1, is the perturbation estimate of f, is the state variable of the auxiliary system. The servo motor control system finally established is as follows: Figure 2 As shown, saturation limiting is the maximum input that the system can withstand.

[0092] In the embodiment of the present application, the non-singular terminal sliding mode control introduces an extended state observer, sets the disturbance as a new state variable, can accurately and clearly observe the change of the disturbance, so that it can respond quickly and effectively improve the stability of the system. Secondly, an auxiliary system that resists saturation input is designed to effectively suppress the impact of input saturation on the control system, which can effectively improve the dynamic response of the system and enhance the robustness of the system. Finally, by designing a dynamic sliding surface, the convergence speed of the system is improved, and the system is guaranteed to suppress chattering, thereby improving the tracking accuracy of the system.

[0093] Embodiment 2

[0094] In the present embodiment, the servo motor parameters are selected to be the same as those in the first embodiment. The expected value is set to θ d =20deg.

[0095] The frequency domain mathematical model of the servo motor is:

[0096]

[0097] Among them, θ is the rotation angle of the motor, s is the Laplace operator, and R is the total disturbance of the system.

[0098] The frequency domain mathematical model is converted into a time domain mathematical model, and the time domain mathematical model is:

[0099]

[0100] Among them, θ is the rotation angle of the motor, ω is the angular velocity of the motor, is the first-order derivative of ω, u is the input of the system, and R is the total disturbance of the system.

[0101] Furthermore, according to the time domain mathematical model, an improved extended state observer is designed, and the extended state observer is:

[0102]

[0103] Where e0 is the error between the actual motor angular velocity and the observed motor angular velocity, expressed as:

[0104]

[0105] in, is the state estimation value of the motor rotation angular velocity ω, is the disturbance estimate of f, ω0 is the bandwidth of the extended state observer, is the first-order derivative of e0.

[0106] Furthermore, according to the time domain mathematical model, an anti-saturation input auxiliary system is designed, and the auxiliary system is:

[0107]

[0108] Among them, Δu is an intermediate variable, expressed as:

[0109]

[0110] Among them, u is the actual control input, expressed as:

[0111]

[0112] in, is the state variable of the auxiliary system, and Δu is the difference between the actual control input u and the estimated value of the input disturbance.

[0113] Furthermore, according to the mathematical model, an error function is established, and the error function is:

[0114] e1 = 20-θ;

[0115] Among them, e1 is the rotation angle error, and θ is the actual output angle of the motor.

[0116] Further, according to the error function, a sliding surface of non-singular terminal sliding mode control is defined, and the sliding surface is:

[0117]

[0118] Wherein, e1 is the rotation angle error, λ, p and q are the sliding surface design parameters, and is the derivative of e1.

[0119] Furthermore, according to the sliding surface, a non-singular terminal sliding mode control is designed, and the non-singular terminal sliding mode control law is:

[0120]

[0121] Among them, sgn(z) is the sign function, expressed as:

[0122]

[0123] Among them, ε and k are the parameters to be designed, sgn(z) is the sign function, λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1.

[0124] Furthermore, according to the extended state observer, the auxiliary system and the sliding mode control law, a non-singular terminal sliding mode control law is obtained, and the non-singular terminal sliding mode control law is:

[0125]

[0126] Among them, λ, p and q are the sliding surface design parameters, k is the control gain, sgn(z) and is a symbolic function, λ1, λ2, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1, is the perturbation estimate of f, is the state variable of the anti-saturation auxiliary system. The servo motor control system finally established is as follows: Figure 2 shown.

[0127] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A servo motor control method based on non-singular terminal sliding mode control, characterized in that: The following steps are involved: S1. According to the working principle of the servo motor, a mathematical model of the servo motor is established; S2. According to the mathematical model, an improved extended state observer is designed, an anti-saturation input auxiliary system is designed, and an error function is established; S3. According to the error function, a sliding surface of a non-singular terminal sliding mode control is defined, and according to the sliding surface, a non-singular terminal sliding mode control law is obtained; S4. According to the improved extended state observer, the anti-windup input auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended state observer and the anti-windup auxiliary system is obtained.

2. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the working principle of the servo motor, a frequency domain mathematical model of the servo motor is established, and the frequency domain mathematical model is: Among them, θ is the rotation angle of the motor, s is the Laplace operator, J is the equivalent moment of inertia of the system, m is the motor torque coefficient; u is the system input, and R is the total disturbance of the system; The frequency domain mathematical model is converted into a time domain mathematical model, and the time domain mathematical model is: In the formula, b and f are intermediate variables, expressed as: Where θ is the rotation angle of the motor, is the first-order derivative of θ, ω is the angular velocity of the motor, is the first-order derivative of ω, u is the input of the system, m is the motor torque coefficient, J is the system equivalent moment of inertia, and R is the total disturbance of the system.

3. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the time domain mathematical model, an improved extended state observer is designed, and the improved extended state observer is: Where e0 is the error between the actual motor angular velocity and the observed motor angular velocity, expressed as: in, is the state estimation value of the motor rotation angular velocity ω; is the disturbance estimate of f, ω0 is the bandwidth of the extended state observer, is the first-order derivative of e0.

4. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the time domain mathematical model, an anti-saturation input auxiliary system is designed, and the auxiliary system is: in, is the state variable of the auxiliary system, for The first-order derivative of , δ is the parameter to be designed, Δu is the intermediate variable, expressed as: Among them, u is the actual control input, expressed as: in, is the output signal of the controller, u max is the maximum input value, u min Enter the minimum value.

5. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the time domain mathematical model, an error function is established, and the error function is: e1=θ d -θ; Among them, e1 is the rotation angle error, θ is the rotation angle of the motor, θ d is the target angle.

6. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the error function, the sliding surface of the non-singular terminal sliding mode control is defined, and the sliding surface is: Among them, e1 is the rotation angle error, λ, p and q are the sliding surface design parameters, and is the derivative of e1.

7. The servo motor control method based on non-singular terminal sliding mode control according to claim 6, characterized in that: According to the sliding surface, a non-singular terminal sliding mode control is designed, and the non-singular terminal sliding mode control law is: Among them, sgn(z) is the sign function, expressed as: Among them, ε and k are the parameters to be designed. is the desired motor rotation angle θ d The second-order derivative of , λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1.

8. The servo motor control method based on non-singular terminal sliding mode control according to claim 1, characterized in that: According to the improved extended state observer, the anti-saturation input auxiliary system and the non-singular terminal sliding mode control law, a non-singular terminal sliding mode control law based on the improved extended observer and the anti-saturation auxiliary system is obtained, and the non-singular terminal sliding mode control law is: Among them, ε, k1 and k2 are the parameters to be designed. is the desired motor rotation angle θ d The second-order derivative of , sgn(z) is the sign function, λ, p and q are the sliding surface design parameters, e1 is the rotation angle error, is the first-order derivative of e1, is the perturbation estimate of f, is the state variable of the auxiliary system.

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