A Fast Finite-Time Composite Control Method for PMSM Servo Systems Based on Disturbance Compensation

Abstract

This invention relates to the field of high-precision servo control systems, and more particularly to a fast finite-time composite control method for a PMSM servo system based on disturbance compensation. The method first estimates the lumped disturbance of the servo system using a finite-time disturbance observer, and then performs feedforward compensation on the disturbance estimate. Finally, a fast finite-time composite control law based on disturbance compensation is obtained, which is used as a fast finite-time composite speed controller to achieve control of the permanent magnet synchronous motor servo system under disturbance influence. This invention utilizes a finite-time disturbance observer to improve the convergence speed of disturbance observation errors and enhance the disturbance compensation effect. Simultaneously, the composite controller achieves finite-time control of the system and effectively reduces the system's rise time, enabling rapid response of the system under large deviation conditions.

Description

Technical Field

[0001] This invention relates to the field of high-precision servo control systems, and more particularly to a fast finite-time composite control method for a permanent magnet synchronous motor (PMSM) servo system based on disturbance compensation. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) possess advantages such as simple structure, high power factor, high air gap flux density, compact design, low loss, and wide speed range, giving them significant benefits compared to other AC motors. They are widely used in fields with increasingly demanding requirements for motor performance and control precision, including robotics, precision radar, aerospace, and CNC machine tools. However, a PMSM system is a multivariable, nonlinear, and strongly coupled nonlinear system. In practical applications, it always encounters numerous disturbances, including frictional torque, torque ripple, unmodeled dynamics, and load variations. This makes controller design a challenging task. If the controller lacks sufficient capability to eliminate these disturbances, system performance will degrade, hindering high-performance servo control.

[0003] One method to improve the system's disturbance rejection capability is to use a disturbance observer to estimate the disturbance and perform feedforward compensation in the control law. Numerous studies have been conducted by scholars both domestically and internationally regarding the design of disturbance observers. The literature "Xie Chuanlin, Zeng Yuenan, Wang Faliang, et al. Design of PMSM speed loop active disturbance rejection controller based on disturbance compensation [J]. Micromotors, 2017, 45(12):53-56" designed an extended state observer (ESO) to observe and compensate for lumped disturbances present in the PMSM system during operation. However, the ESO can only asymptotically and unbiasedly estimate constant disturbances or disturbances in the form where the first derivative of the disturbance tends to 0. The paper “A.Wu, G.Duan. Design of Generalized PI Observers for Descriptor Linear Systems. IEEE Transactions on Circuits and Systems I: Regular Papers[J], 2006, 53(12): 2828-2837” designed a generalized proportional-integral (GPIO) observer to estimate perturbations. It can accurately estimate not only perturbations whose first derivative tends to 0 with time, but also perturbations whose higher-order derivatives tend to 0 (i.e., perturbations with time series polynomial form). However, its perturbation estimation can only achieve asymptotic convergence, and the convergence speed is slow.

[0004] From the perspective of feedback design, some feedback control methods can also be used to improve the system's disturbance rejection capability. Finite-time control is such an effective nonlinear control method. The literature "Chen Zhe, Wang Yiyan, Liu Chunqiang, et al. Composite finite-time control of permanent magnet synchronous motor servo system [J]. Micro Motor, 2019, 53(3):22-25" designed a finite-time composite control strategy based on the homogeneity method. Compared with the traditional asymptotically stable system, the finite-time stable system can ensure that the system has better convergence performance near the equilibrium point, and also has better disturbance rejection capability. However, this algorithm can only guarantee a large control gain and achieve fast convergence characteristics near the equilibrium point, i.e., within the small deviation operating range. Under the large deviation operating condition, such as the rise phase of the system, the control gain is often very small, which will cause the system rise time to slow down, i.e., it cannot achieve a fast response to large deviations. Summary of the Invention

[0005] The purpose of this invention is to provide a fast finite-time composite control method for a permanent magnet synchronous motor servo system based on disturbance compensation. This method can not only achieve finite-time convergence of the system, but also simultaneously take into account fast response under large deviations and steady-state fluctuations under small deviations, thereby improving the control gain of the system under large deviation conditions and solving the problem of slow rise speed, that is, achieving fast response of the system under large deviation conditions.

[0006] To solve the above technical problems, the technical solution of this invention is as follows: a fast finite-time composite control method for a PMSM servo system based on disturbance compensation. This method first estimates the lumped disturbance of the servo system through a finite-time disturbance observer and then performs feedforward compensation on the disturbance estimate. At the same time, the derivative of the speed reference signal is also fedforward compensated. Finally, a fast finite-time composite control law based on disturbance compensation is obtained. This law is used as a fast finite-time composite speed controller to realize the control of the permanent magnet synchronous motor servo system under the influence of disturbance.

[0007] Preferably, the composite control method specifically comprises:

[0008] Step 1: Set the motor speed reference signal ω * The actual speed feedback signal ω of the permanent magnet synchronous motor servo system is collected;

[0009] Step 2: Calculate the estimated system disturbance z0 using a finite-time disturbance observer (FTDO);

[0010] The method for establishing the finite-time disturbance observer (FTDO) is as follows:

[0011]

[0012] Where ω is the actual speed of the motor, u is the output of the fast finite-time composite controller, and l i r i r represents the gain and exponentiation of the observer. i =1+iδ, J is the total equivalent disturbance inertia of the motor and the load; This is an estimate of ω. sign(·) is the sign function, and z0 is the estimated value of the system disturbance d(t); z j It is an estimate of the j-th derivative of d(t), j = 1,...,n; K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor;

[0013] Step 3: Calculate the output control quantity of the controller using the Fast Finite-Time Composite Controller (FFTC); the calculation method for the control law of the Fast Finite-Time Composite Controller (FFTC) is as follows:

[0014]

[0015] Where u is the output of the fast finite-time composite controller, J represents the total equivalent disturbance inertia of the motor and load, and K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor; This indicates the reference signal ω for the set rotational speed. * The feedforward compensation signal obtained by differentiation, k p1 >0, k p2 >0, 0<α1<1<α2, sig α (ω * -ω)=sign(ω * -ω)|ω * -ω| α , sign(·) is the sign function; z0 represents the system disturbance estimate calculated by FTDO;

[0016] Step 4: Control the permanent magnet synchronous motor servo system based on the output of the Fast Finite Time Composite Controller (FFTC).

[0017] Preferably, the controlled system model of the permanent magnet synchronous motor servo system is as follows:

[0018]

[0019] Where: u d u q For the d-axis and q-axis voltages of the stator windings, i d ,i q Let J be the stator current along the d and q axes, J be the moment of inertia, B be the coefficient of viscous friction, and T be the stator current along the d and q axes. L Where ω is the load torque, L is the mechanical angular velocity of the motor rotor, and R is the stator inductance. s K is the stator resistance. t =3n p ψ f / 2,n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor.

[0020] Preferably, step 4 specifically includes:

[0021] Step 4.1: Convert the control quantity output by the fast finite-time composite controller As the setting signal for the q-axis current controller; setting The collected motor current signal is used as the setting signal for the d-axis current controller; Clarke and Park transforms are performed on the motor current signal to obtain the current value i in the dq coordinate system. d and i q , respectively i d i q As the feedback signal for the d-axis and q-axis current controllers, the output u of the dq-axis current controllers is obtained through their control actions. d and u q ;

[0022] Step 4.2: Adjust the output u of the dq-axis current controller. d and u q Performing the inverse Park transform yields the reference value u of the stator phase voltage in the αβ coordinate system. α and u β ;

[0023] Step 4.3: According to u α and u β PWM control signals are generated using space vector pulse width modulation technology;

[0024] Step 4.4: The controllable switching device IGBT is controlled by the PWM control signal to invert the required three-phase AC power to drive the motor and obtain the actual speed of the motor.

[0025] Preferably, in the permanent magnet synchronous motor servo system, an optical encoder is used to collect the speed signal of the PMSM servo motor, and a Hall current sensor is used to collect the current signal of the motor.

[0026] The present invention has the following beneficial effects:

[0027] I. This invention employs a finite-time disturbance observer (FTDO), which enables finite-time estimation of disturbances. Compared to the traditional generalized proportional-integral observer (GPIO), which can only asymptotically estimate disturbances, FTDO achieves faster convergence of disturbance observation errors and better disturbance compensation.

[0028] II. This invention designs a fast finite-time composite control, which is an improvement on finite-time control based on the homogeneity method, by superimposing a power value α2 greater than 1. This term improves the control gain under large deviation conditions, overcoming the slow rise time of traditional finite-time controllers. The specific principle is: when the system is under large deviation conditions, the power-law term... It plays a major role, providing significant gain and enabling the closed-loop system to have fast response performance. When the system state approaches steady state, the small power term in the control law... It plays a major role, providing significant gain and improving the system's response performance and steady-state accuracy near the equilibrium point. It simultaneously balances rapid response under large deviations and steady-state fluctuations under small deviations, improving the control gain under large deviation conditions and overcoming the drawback of slow rise time. This achieves rapid response under large deviation conditions, and the control algorithm is simple and easy to implement. Attached Figure Description

[0029] Figure 1 This is a flowchart of the fast finite-time composite control method for a permanent magnet synchronous motor servo system based on disturbance compensation according to the present invention.

[0030] Figure 2 This is a block diagram of a permanent magnet synchronous motor servo system based on vector control according to an embodiment of the present invention;

[0031] Figure 3 This is a block diagram of the fast finite-time composite controller structure of the permanent magnet synchronous motor servo system based on disturbance compensation according to an embodiment of the present invention;

[0032] Figure 4 This is a control flowchart of the servo system according to an embodiment of the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] Please refer to Figures 1 to 4This invention discloses a fast finite-time composite control method for a permanent magnet synchronous motor servo system based on disturbance compensation. The method first estimates the lumped disturbance of the servo system using a finite-time disturbance observer and then performs feedforward compensation on the disturbance estimate. Simultaneously, it performs feedforward compensation on the derivative of the speed reference signal. Finally, a fast finite-time composite control law based on disturbance compensation is obtained, which is used as a fast finite-time composite speed controller to achieve control of the permanent magnet synchronous motor servo system under disturbance influence. The specific steps are as follows:

[0035] Step 1: Establish the controlled system model of the permanent magnet synchronous motor servo system; set the motor speed reference signal ω. * The actual speed feedback signal ω of the permanent magnet synchronous motor servo system is collected;

[0036] In this embodiment, the controlled system model of the permanent magnet synchronous motor servo system is as follows:

[0037]

[0038] Where: u d u q For the d-axis and q-axis voltages of the stator windings, i d ,i q Let J be the stator current along the d and q axes, J be the moment of inertia, B be the coefficient of viscous friction, and T be the stator current along the d and q axes. L Where ω is the load torque, L is the mechanical angular velocity of the motor rotor, and R is the stator inductance. s K is the stator resistance. t =3n p ψ f / 2,n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor.

[0039] Step 2: Calculate the estimated system disturbance z0 using a finite-time disturbance observer (FTDO);

[0040] The method for establishing a finite-time disturbance observer (FTDO) is as follows:

[0041]

[0042] Where ω is the actual speed of the motor, u is the output of the fast finite-time composite controller, and l i r i r represents the gain and exponentiation of the observer. i =1+iδ, J is the total equivalent disturbance inertia of the motor and the load. This is an estimate of ω. sign(·) is the sign function, and z0 is the estimated value of the system disturbance d(t); zj It is an estimate of the j-th derivative of d(t), j = 1,...,n; K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor.

[0043] Step 3: Calculate the output control quantity of the controller using the Fast Finite-Time Composite Controller (FFTC); the calculation method for the control law of the Fast Finite-Time Composite Controller (FFTC) is as follows:

[0044]

[0045] Where u is the output of the fast finite-time composite controller, J represents the total equivalent disturbance inertia of the motor and load, and K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor; This indicates the reference signal ω for the set rotational speed. * The feedforward compensation signal obtained by differentiation, k p1 >0, k p2 >0, 0<α1<1<α2, sig α (ω * -ω)=sign(ω * -ω)|ω * -ω| α , sign(·) is the sign function; z0 represents the system disturbance estimate calculated by FTDO;

[0046] See Figure 3 , Figure 3 This paper illustrates a fast finite-time composite controller (FFTC) based on a finite-time observer and a fast finite-time controller. The specific calculation method is as follows: the reference signal ω for the given system rotational speed... * After differentiation, the feedforward compensation signal of the controller is obtained. Using the controller's output signal The feedback signal ω of the actual rotational speed is used, and the estimated value of the disturbance z0 is obtained through a finite-time observer (FTDO). Then ω... * The speed error is obtained by subtracting the actual speed ω collected by the encoder, i.e., e = ω. * -ω. Speed ​​error e in fast finite time control Under the influence of the feedforward compensation signal Subtract the disturbance estimate z0, and finally multiply by the proportion. That is, the control output of the entire composite controller is obtained.

[0047] Step 4: Control the permanent magnet synchronous motor servo system based on the output of the Fast Finite-Time Controller (FFTC), combined with... Figure 2 and Figure 4 Step 4 specifically involves:

[0048] Step 4.1: Convert the control quantity output by the fast finite-time composite controller As the setting signal for the q-axis current controller; setting The collected motor current signal is used as the setting signal for the d-axis current controller; Clarke and Park transforms are performed on the motor current signal to obtain the current value i in the dq coordinate system. d and i q , respectively i d i q As the feedback signal for the d-axis and q-axis current controllers, the output u of the dq-axis current controllers is obtained through their control actions. d and u q ;

[0049] Step 4.2: Adjust the output u of the dq-axis current controller. d and u q Performing the inverse Park transform yields the reference value u of the stator phase voltage in the αβ coordinate system. α and u β ;

[0050] Step 4.3: According to u α and u β PWM control signals are generated using space vector pulse width modulation technology;

[0051] Step 4.4: The controllable switching device IGBT is controlled by the PWM control signal to invert the required three-phase AC power to drive the motor and obtain the actual speed of the motor.

[0052] In this embodiment, a Hall sensor is used to acquire two current signals i a i b The photoelectric encoder is used inside the motor to collect the speed signal of the PMSM servo motor. The experimental platform in this embodiment is based on the Estun EM3A-04ALA211 motor and ED3S servo driver, and the programming language is C.

[0053] All parts not covered in this invention are the same as or implemented using existing technologies.

[0054] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A fast finite-time composite control method for a PMSM servo system based on disturbance compensation, characterized in that: The composite control method first estimates the lumped disturbance of the servo system using a finite-time disturbance observer and then feeds forward the disturbance estimate. Simultaneously, it feeds forward the derivative of the speed reference signal. Finally, it obtains a fast finite-time composite control law based on disturbance compensation, which is used as a fast finite-time composite speed controller to realize the control of the permanent magnet synchronous motor servo system under the influence of disturbance. The composite control method is specifically as follows: Step 1: Set the motor speed reference signal ω * The actual speed feedback signal ω of the permanent magnet synchronous motor servo system is collected; Step 2: Calculate the estimated system disturbance value z0 using a finite-time disturbance observer (FTDO); the method for establishing the FTDO is as follows: Where ω is the actual speed of the motor, u is the output of the fast finite-time composite controller, and l i r i r represents the gain and exponentiation of the observer. i =1+iδ, i = 1, 2, ..., n+2; J is the total equivalent disturbance inertia of the motor and the load. This is an estimate of ω. Let z be the sign function, and z0 be the estimated value of the system disturbance d(t); z j It is an estimate of the j-th derivative of d(t), j = 1,...,n; K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor; Step 3: Calculate the output control quantity of the controller using the Fast Finite-Time Composite Controller (FFTC); the calculation method for the control law of the Fast Finite-Time Composite Controller (FFTC) is as follows: Where u is the output of the fast finite-time composite controller, J represents the total equivalent disturbance inertia of the motor and load, and K t =3n p ψ f / 2, where n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor; This indicates the reference signal ω for the set rotational speed. * The feedforward compensation signal obtained by differentiation, k p1 >0, k p2 >0, 0<α1<1<α2, z0 represents the system disturbance estimate calculated by FTDO, sig α (ω * -ω)=sign(ω * -ω)|ω * -ω| α , It is a symbolic function; Step 4: Use the output of the Fast Finite-Time Composite Controller (FFTC) as the reference signal for the current controller to control the permanent magnet synchronous motor servo system.

2. The fast finite-time composite control method for a PMSM servo system based on disturbance compensation according to claim 1, characterized in that: The controlled system model of the permanent magnet synchronous motor servo system is as follows: Where: u d u q For the d-axis and q-axis voltages of the stator windings, i d ,i q Let J be the stator current along the d and q axes, J be the moment of inertia, B be the coefficient of viscous friction, and T be the stator current along the d and q axes. L Where ω is the load torque, L is the mechanical angular velocity of the motor rotor, and R is the stator inductance. s K is the stator resistance. t =3n p ψ f / 2,n p Let ψ be the extreme logarithm. f The magnetomotive force generated by the permanent magnets on the rotor.

3. The fast finite-time composite control method for a PMSM servo system based on disturbance compensation according to claim 1, characterized in that: Step 4 specifically involves: Step 4.1: Convert the control quantity output by the fast finite-time composite controller As the setting signal for the q-axis current controller; setting The collected motor current signal is used as the setting signal for the d-axis current controller; Clarke transform and Park transform are performed on the acquired motor current signal to obtain the d-axis current controller signal. q Current value i in coordinate system d and i q , respectively i d i q As the feedback signal for the d-axis and q-axis current controllers, the output u of the dq-axis current controllers is obtained through their control actions. d and u q ; Step 4.2: Adjust the output u of the dq-axis current controller. d and u q Performing the inverse Park transform yields the reference value u of the stator phase voltage in the αβ coordinate system. α and u β ; Step 4.3: According to u α and u β PWM control signals are generated using space vector pulse width modulation technology; Step 4.4: The controllable switching device IGBT is controlled by the PWM control signal to invert the required three-phase AC power to drive the motor and obtain the actual speed of the motor.

4. The fast finite-time composite control method for a PMSM servo system based on disturbance compensation according to claim 1, characterized in that: In the permanent magnet synchronous motor servo system, an optical encoder is used to collect the speed signal of the PMSM servo motor, and a Hall current sensor is used to collect the current signal of the motor.

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