Friction torque compensation method for surface-mounted permanent magnet synchronous motor based on sliding mode compound control

Abstract

A surface-mounted permanent magnet synchronous motor friction torque compensation method of sliding mode composite control, considering that the position information and speed information of the permanent magnet synchronous motor output can be accurately obtained through a high-precision encoder, therefore, a reduced dimension observer is used to observe the friction torque alone, and the disturbance caused by the friction torque is compensated in the form of current feedback. Meanwhile, the reduced dimension observer has less calculation amount compared with other observers, and the speed feedback by the photoelectric encoder is used as the input, which has higher precision of the friction torque value observed by other observers, and the compensated current value is more accurate. The present application can improve the position tracking accuracy of the system, and has strong robustness. The present application effectively reduces the position error caused by friction in the sliding mode control, and uses the reduced dimension observer to reduce the calculation amount of the observer algorithm, while ensuring the stability of the system, which is of great significance to the control accuracy of the servo system.

Description

Technical Field

[0001] This invention relates to a method for compensating for frictional torque in a motor. In particular, it relates to a method for compensating for frictional torque in a surface-mounted permanent magnet synchronous motor with sliding mode composite control. Background Technology

[0002] In recent years, high-precision CNC machine tools in advanced manufacturing have been widely used in the defense industry. As a crucial component of high-precision CNC machine tools and a control system that ensures accurate tracking of system outputs, the dynamic and static performance of servo systems significantly impacts the positioning accuracy of CNC machine tools. Permanent magnet synchronous motors (PMSMs), with their advantages of high efficiency and small size, are gradually replacing other motors and gaining widespread use in the servo field. However, in low-speed servo control of PMSMs, the strong nonlinearity of friction at low and zero speeds leads to instability in the servo system at low speeds. Specifically, when the system speed falls below a certain value, pulsation occurs in the system's motion, a phenomenon known as low-speed crawling. This phenomenon prevents the servo system from accurately following given commands and trajectories, resulting in significant positional errors and affecting the system's control accuracy.

[0003] Friction, being a nonlinear function, can lead to unintended behavior, performance degradation, stability issues, and suboptimal control when using traditional linear control strategies. Addressing these problems typically requires more complex nonlinear control methods. Therefore, sliding mode control is a viable approach. Sliding mode control can overcome system uncertainties and exhibits strong robustness to disturbances and unmodeled dynamics, particularly demonstrating good control performance for nonlinear systems. However, sliding mode control can cause chattering, and the controller cannot fully compensate for the nonlinear effect of frictional torque. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a sliding mode composite control method for compensating the friction torque of a surface-mounted permanent magnet synchronous motor during low-speed operation.

[0005] The technical solution adopted in this invention is: a method for compensating the friction torque of a surface-mounted permanent magnet synchronous motor with sliding mode composite control, comprising the following steps:

[0006] 1) Use the LuGre friction model to represent the frictional torque T present during the operation of the surface-mounted permanent magnet synchronous motor. f ;

[0007] 2) A novel sliding mode controller is designed based on an improved power-approach law;

[0008] 3) Set the rotor position angle reference value θ* and the rotor position angle feedback value θ of the photoelectric encoder m The reference value of the q-axis current is obtained after adjustment by the new sliding mode controller. Based on surface-mounted permanent magnet synchronous motor i d =0 control, obtain d-axis current reference value

[0009] 4) Construct the observation equations for a dimension-reduced observer used for friction torque compensation;

[0010] 5) The rotor mechanical angular velocity ω measured by the photoelectric encoder m , and the reference value of rotor mechanical angular velocity ω * and the feedback q-axis current i qm The current compensation amount corresponding to the friction torque is obtained by adjusting the observation equation of the dimension-reduced observer. The obtained q-axis current reference value i q * With current compensation amount Subtracting the two values ​​yields the compensated q-axis current reference value.

[0011] 6) The stator three-phase current i of the motor is detected by the sensor. A i B and i C The feedback motor stator d-axis and q-axis currents i obtained after the Parker transformation dm i qm Use d-axis current reference value and the compensated q-axis current reference value Subtract the feedback motor stator d-axis and q-axis currents i respectively dm i qm The two differences are passed through two proportional-integral (PI) controllers, and the outputs of the PI controllers are limited to obtain the reference values ​​of the d-axis and q-axis voltages, respectively.

[0012] 7) Employing a voltage space vector modulation strategy, the reference values ​​of the d-axis and q-axis voltages, after being output and limited by the proportional-integral controller, are used in the current cycle. and rotor position angle feedback value θ m The duty cycle of the six PWM pulses driving the voltage source two-level inverter is calculated. Then, the six PWM pulses are output from the drive circuit of the voltage source two-level inverter and sent to the gates of the six power devices of the voltage source two-level inverter, so that the reference values ​​of the d-axis and q-axis output voltages of the voltage source two-level inverter are obtained. Voltage reference value This effect on the motor effectively compensates for the motor's frictional torque.

[0013] This invention presents a method for compensating friction torque in surface-mounted permanent magnet synchronous motors (PMSMs) under sliding mode composite control. This method addresses the error in friction torque compensation caused by friction torque in sliding mode controllers. Considering that the position and speed information output by the PMSM can be accurately obtained through a high-precision encoder, a dimension-reduced observer is used to observe the friction torque separately and provide current feedback to compensate for the disturbance caused by the friction torque. Furthermore, using a dimension-reduced observer requires less computation compared to other observers, and the friction torque value observed using the rotational speed feedback from the photoelectric encoder has higher accuracy than that observed by other observers, resulting in more accurate compensation current values. This invention is based on the analysis of friction torque present in surface-mounted PMSMs during low-speed operation, improving the system's position tracking accuracy and exhibiting strong robustness. This invention effectively reduces the position error caused by friction in sliding mode control, and the use of a dimension-reduced observer reduces the computational load of the observer algorithm while ensuring system stability, which is of great significance to the control accuracy of servo systems. Attached Figure Description

[0014] Figure 1 This is a flowchart of the friction torque compensation method for a surface-mounted permanent magnet synchronous motor using sliding mode composite control according to the present invention;

[0015] Figure 2 This is a schematic diagram of the friction torque compensation method for a surface-mounted permanent magnet synchronous motor using sliding mode composite control according to the present invention.

[0016] Figure 3 This is a schematic diagram of the structure of the novel sliding mode observer in this invention;

[0017] In the diagram, u represents the input quantity of the block diagram;

[0018] Figure 4 This is a schematic diagram of the observation equation of the dimension reduction observer in this invention. Detailed Implementation

[0019] The friction torque compensation method for surface-mounted permanent magnet synchronous motors with sliding mode composite control according to the present invention will be described in detail below with reference to embodiments and accompanying drawings.

[0020] This invention addresses the issue of reduced control accuracy in sliding mode controllers of servo systems operating at low speeds due to friction, and proposes a friction compensation method that incorporates a dimension-reduced observer.

[0021] like Figure 1 , Figure 2 As shown, the friction torque compensation method for a surface-mounted permanent magnet synchronous motor with sliding mode composite control of the present invention includes the following steps:

[0022] 1) Use the LuGre friction model to represent the frictional torque T present during the operation of the surface-mounted permanent magnet synchronous motor.f ;

[0023] The mathematical model of the LuGre friction model is as follows:

[0024]

[0025] In the formula, T f σ is the frictional torque; σ0 is the stiffness coefficient of the bristles; σ1 is the damping coefficient of the bristles; σ2 is the viscosity coefficient; ζ is the bristle deformation between the two contact surfaces; ω is the mechanical angular velocity of the motor; ω s For Stribeck velocity; g(ω) is a nonlinear function used to represent the Stribeck characteristic; F c For Coulomb friction; F s It is static friction.

[0026] 2) Design a novel sliding mode controller based on an improved power-approach law; such as... Figure 3 As shown, the equations for the novel sliding mode controller are as follows:

[0027]

[0028] In the formula, γ is the control output quantity, and satisfies i q * q is the reference value for the q-axis current; J is the moment of inertia of the motor; K t It is the electromagnetic torque coefficient, and satisfies K t =1.5ψ f p, ψ f θ is the flux linkage constant, p is the number of pole pairs; e is the difference between the rotor position angle reference value and the feedback value, e = θ * -θ m θ * θ is the reference value for the rotor position angle. m Here is the rotor position angle feedback value; here is the friction torque T. f ;T L k1|s| represents the load torque of the motor. α sgn(s) is the power term of the approach law. Here, k1, k2, and α are the variable terms of the reaching law, with values ​​ranging from k1 > 0 to α > 1. sgn() is the sign function, and s is the sliding surface that satisfies the following conditions: c1 is a constant.

[0029] 3) Set the rotor position angle reference value θ * and the rotor position angle feedback value θ of the photoelectric encoder m The reference value of the q-axis current is obtained after adjustment by the new sliding mode controller. Based on surface-mounted permanent magnet synchronous motor id =0 control, obtain d-axis current reference value

[0030] 4) Construct the observation equations for a dimension-reduced observer used for friction torque compensation, considering the presence of a friction torque term T in the control law. f Furthermore, frictional torque is a nonlinear function, which reduces the control accuracy of the controller during low-speed motor startup. An observer can effectively detect disturbances such as frictional torque. Traditional extended state observers involve significant computational loads, and high-precision encoders can provide more accurate speed and position information. Therefore, we consider using a reduced-dimensional observer's observation equation to observe the frictional torque and compensate for it in the form of current. For example... Figure 4 As shown, the process of constructing the observation equations for the dimensionality reduction observer is as follows:

[0031] Based on the PMSM kinematic equations, the system state equations are obtained as follows:

[0032]

[0033] In the formula, x1=ω m Let x be the speed of the motor output, x2 be the total disturbance, and let... Where is the flux linkage constant; J is the moment of inertia of the motor; i qm Let e1 and e2 be the feedback stator q-axis current of the motor; define e1 and e2 as observation errors, and satisfy:

[0034]

[0035] In the formula, z1 and z2 are the observed values ​​of x1 and x2, respectively;

[0036] The state equation of the reduced-dimensional observer is obtained as follows:

[0037]

[0038] In the formula, p1 and p2 are the observer gains;

[0039] The observation equation of the dimension-reduced observer is derived from the state equation of the dimension-reduced observer as follows:

[0040]

[0041] Thus, the current compensation amount for the frictional torque is obtained. for:

[0042]

[0043] In the formula, Kt is the electromagnetic torque coefficient.

[0044] 5) The rotor mechanical angular velocity ω measured by the photoelectric encoderm , and the reference value of rotor mechanical angular velocity ω * and the feedback q-axis current i qm The current compensation amount corresponding to the friction torque is obtained by adjusting the observation equation of the dimension-reduced observer. The obtained q-axis current reference value i q * With current compensation amount Subtracting the two values ​​yields the compensated q-axis current reference value.

[0045] 6) The stator three-phase current i of the motor is detected by the sensor. A i B and i C The feedback motor stator d-axis and q-axis currents i are obtained after Park transformation (transformation from the ABC three-phase stationary coordinate system to the dq two-phase rotating coordinate system). dm i qm Use d-axis current reference value and the compensated q-axis current reference value Subtract the feedback motor stator d-axis and q-axis currents i respectively dm i qm The two differences are passed through two proportional-integral (PI) controllers respectively, and the outputs of the PI controllers are limited to obtain the reference values ​​of the d-axis and q-axis voltages.

[0046] 7) Employing a space vector pulse-width modulation (SVPWM) strategy, the reference values ​​of the d-axis and q-axis voltages, after being output and limited by the proportional-integral controller, are used in the current cycle. and rotor position angle feedback value θ m The duty cycle of the six PWM pulses driving the voltage source two-level inverter is calculated. Then, the six PWM pulses are output from the drive circuit of the voltage source two-level inverter and sent to the gates of the six power devices of the voltage source two-level inverter, so that the reference values ​​of the d-axis and q-axis output voltages of the voltage source two-level inverter are obtained. Voltage reference value This effect on the motor effectively compensates for the motor's frictional torque.

Claims

1. A friction torque compensation method for surface-mounted permanent magnet synchronous motor based on sliding mode composite control, characterized in that, Includes the following steps: 1) Use the LuGre friction model to represent the frictional torque T present during the operation of the surface-mounted permanent magnet synchronous motor. f ; 2) A novel sliding mode controller is designed based on an improved power-approaching law; 3) Set the rotor position angle reference value θ * and the rotor position angle feedback value θ of the photoelectric encoder m The reference value of the q-axis current is obtained after adjustment by the new sliding mode controller. Based on surface-mounted permanent magnet synchronous motor i d =0 control, obtain d-axis current reference value 4) Construct the observation equations for a dimension-reduced observer used for friction torque compensation; 5) The rotor mechanical angular velocity ω measured by the photoelectric encoder m , and the reference value of rotor mechanical angular velocity ω * and the feedback q-axis current i qm The current compensation amount i corresponding to the friction torque is obtained by adjusting the observation equation of the dimension-reduced observer. Tf The obtained q-axis current reference value i q * With current compensation amount i Tf Subtracting the two values ​​yields the compensated q-axis current reference value. 6) The stator three-phase current i of the motor is detected by the sensor. A i B and i C The feedback motor stator d-axis and q-axis currents i obtained after the Parker transformation dm i qm Use d-axis current reference value and the compensated q-axis current reference value Subtract the feedback motor stator d-axis and q-axis currents i respectively dm i qm The two differences are passed through two proportional-integral (PI) controllers, and the outputs of the PI controllers are limited to obtain the reference values ​​of the d-axis and q-axis voltages, respectively. 7) Employing a voltage space vector modulation strategy, the reference values ​​of the d-axis and q-axis voltages, after being output and limited by the proportional-integral controller, are used in the current cycle. and rotor position angle feedback value θ m The duty cycle of the six PWM pulses driving the voltage source two-level inverter is calculated. Then, the six PWM pulses are output from the drive circuit of the voltage source two-level inverter and sent to the gates of the six power devices of the voltage source two-level inverter, so that the reference values ​​of the d-axis and q-axis output voltages of the voltage source two-level inverter are obtained. Voltage reference value This effect on the motor effectively compensates for the motor's frictional torque.

2. The method for compensating friction torque of a surface-mounted permanent magnet synchronous motor with sliding mode composite control according to claim 1, characterized in that, The equations for the novel sliding mode controller described in step 2) are as follows: In the formula, γ is the control output quantity, and satisfies i q * q is the reference value for the q-axis current; J is the moment of inertia of the motor; K t It is the electromagnetic torque coefficient, and satisfies K t =1.5ψ f p, ψ f θ is the flux linkage constant, p is the number of pole pairs; e is the difference between the rotor position angle reference value and the feedback value, e = θ * -θ m θ * θ is the reference value for the rotor position angle. m Here is the rotor position angle feedback value; here is the friction torque T. f ;T L k1|s| represents the load torque of the motor. α sgn(s) is the power term of the approach law. Here, k1, k2, and α are the variable terms of the reaching law, with values ​​ranging from k1 > 0 to α > 1. sgn() is the sign function, and s is the sliding surface that satisfies the following conditions: c1 is a constant.

3. The friction torque compensation method for a surface-mounted permanent magnet synchronous motor with sliding mode composite control according to claim 1, characterized in that, The process of constructing the observation equation for the dimensionality reduction observer described in step 4) is as follows: Based on the PMSM kinematic equations, the system state equations are obtained as follows: In the formula, x1=ω m Let x be the speed of the motor output, x2 be the total disturbance, and let... ψ f is the flux linkage constant; J is the moment of inertia of the motor; i qm Let e1 and e2 be the feedback stator q-axis current of the motor; define e1 and e2 as observation errors, and satisfy: In the formula, z1 and z2 are the observed values ​​of x1 and x2, respectively; The state equation of the reduced-dimensional observer is obtained as follows: In the formula, p1 and p2 are the observer gains; The observation equation of the dimension-reduced observer is derived from the state equation of the dimension-reduced observer as follows: The current compensation amount for obtaining the frictional torque for: In the formula, K t This is the electromagnetic torque coefficient.

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