A sliding mode speed control method for permanent magnet synchronous motor considering cogging torque disturbance

Abstract

The present invention provides a sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance, which belongs to the field of permanent magnet synchronous motor control. The method comprises the following steps: designing a sliding mode reaching law with predetermined convergence time stability; designing a load torque observer based on the sliding mode reaching law and a mechanical motion model of the permanent magnet synchronous motor and obtaining a disturbance signal containing the cogging torque; multiplying the disturbance signal with the I path and the Q path of an orthogonal reference signal respectively and performing low-pass filtering to obtain two low-frequency terms; obtaining an instantaneous frequency offset of the cogging torque based on the two low-frequency terms, and thus realizing frequency tracking; designing a resonant transfer function; designing a disturbance observer based on the resonant transfer function to estimate the system disturbance; and performing sliding mode speed control based on the estimated value of the system disturbance to obtain a value of the instantaneous frequency offset of the cogging torque. q The present invention can effectively suppress the influence of the cogging torque on the operation of the permanent magnet synchronous motor and improve the operation stability and control accuracy of the permanent magnet synchronous motor.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control, and in particular relates to a sliding mode speed control method for a permanent magnet synchronous motor taking cogging torque disturbance into consideration. Background Art

[0002] Permanent magnet synchronous motors (PMSMs), with their advantages of high efficiency and power density, are widely used in numerous fields, including industrial equipment and new energy vehicles. However, cogging torque, an inherent problem in PMS operation, can cause output torque fluctuations, severely impacting the smoothness and accuracy of PMS operation, reducing system performance, and limiting their application in demanding scenarios. Traditional control methods struggle to effectively suppress cogging torque disturbances, failing to meet the growing demand for high-performance control. Therefore, it is urgent to develop a control strategy that can accurately address cogging torque disturbances and improve the speed control performance of PMSs. Summary of the Invention

[0003] The purpose of the present invention is to propose a sliding mode speed control method for a permanent magnet synchronous motor taking into account the cogging torque disturbance, which can effectively suppress the influence of the cogging torque on the operation of the permanent magnet synchronous motor and improve the operation stability and control accuracy of the permanent magnet synchronous motor.

[0004] The present invention is achieved through the following technical solutions:

[0005] A sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance comprises the following steps:

[0006] Step S1, designing a sliding mode reaching law with a predetermined convergence time stability, designing a load torque observer based on the sliding mode reaching law and a mechanical motion model of the permanent magnet synchronous motor to estimate the load torque, and obtaining a disturbance signal including a cogging torque according to the estimated load torque and a mechanical equation of the permanent magnet synchronous motor, wherein the mechanical equation of the permanent magnet synchronous motor is related to a designed disturbance model of the permanent magnet synchronous motor, and the disturbance model of the permanent magnet synchronous motor includes a low-frequency disturbance related to the load torque and the mechanical angular velocity, and a periodic disturbance related to the cogging torque;

[0007] Step S2: multiplying the disturbance signal by the I path and the Q path of the orthogonal reference signal respectively, and then performing low-pass filtering to obtain two low-frequency terms. Based on the two low-frequency terms, an instantaneous frequency offset of the cogging torque is obtained, and then frequency tracking is performed to estimate the actual disturbance frequency of the cogging torque. The gain involved in the frequency tracking is updated based on the instantaneous frequency offset.

[0008] Step S3: Design a resonant transfer function, estimate the system disturbance using a disturbance observer designed based on the resonant transfer function, and perform sliding mode speed control based on the estimated value of the system disturbance to obtain qThe shaft current is used to control the output torque of the permanent magnet synchronous motor, where the resonant transfer function has a fractional-order calculus operator.

[0009] Furthermore, in step S1, the mechanical motion model of the permanent magnet motor is expressed as , then the load torque observer is expressed as , in, represents the mechanical angular velocity, express The differential of represents the estimated value of the mechanical angular velocity, T e represents the electromagnetic torque, J represents the moment of inertia, B represents the viscous friction coefficient, T L represents the load torque, Indicates load torque T L Seek the derivative, represents the estimated load torque, Express Seek derivation, n t represents the differential of the load torque, represents the gain of the mechanical angular velocity estimation equation, represents the gain of the load torque estimation equation, is the designed sliding mode reaching law, Indicates the scheduled approach time. represents the load torque observer adjustable parameter, represents the sliding surface of the load torque observer, and sgn(.) represents the sign function.

[0010] Furthermore, in step S1, the disturbance signal including the tooth groove rotation Expressed as , in, k is a discrete time step, T For the control period, the permanent magnet synchronous motor disturbance model d Expressed as , the low-frequency perturbation is expressed as , the periodic perturbation is expressed as .

[0011] Furthermore, in step S2, according to the formula Online estimation of actual disturbance frequency of cogging torque ,in, represents the gain involved in frequency tracking, which is based on Update, tanh(.) represents the hyperbolic tangent function, To set the parameter, its value should not be greater than the reference angular frequency of the cogging torque One tenth of represents the instantaneous frequency offset of the cogging torque, and They are the low-frequency items corresponding to the I and Q paths respectively.

[0012] Furthermore, in step S2, the disturbance signal including the cogging rotation is multiplied by the I path and the Q path of the orthogonal reference signal to obtain the disturbance signal including the cogging rotation. I Road Component and the disturbance signal containing the cogging rotation Q Road Component , Respectively and Perform low-pass filtering to remove high-frequency components ,get and ,in, is the instantaneous disturbance signal containing the tooth rotation, A represents the amplitude of the cogging torque disturbance, represents the initial phase of the disturbance signal, t Indicates time.

[0013] Furthermore, in step S3, the resonant transfer function Expressed as ,in, is a fractional calculus operator, and is an adaptive parameter that satisfies , s Represents the complex frequency.

[0014] Furthermore, in step S3, the disturbance observer is expressed as , represents the estimated value of system disturbance in the frequency domain, is the filter, Indicates the inverse of the filter cutoff frequency, in the low frequency band Approaching 0, Becomes a low-pass filter at the resonant frequency tends to infinity, When it is set to 1, the effect of simultaneously estimating low-frequency disturbance and cogging torque disturbance is achieved.

[0015] Furthermore, in step S3, the q Shaft current Expressed as , in, represents the sliding surface, then , Represents a given mechanical angular velocity, p represents the number of pole pairs of the permanent magnet synchronous motor, represents the permanent magnet flux, Express Seek derivation, represents the estimation of the permanent magnet synchronous motor disturbance model, is the upper bound of the system state convergence time, μ Indicates adjustable parameters, 0< μ <1.

[0016] The present invention has the following beneficial effects:

[0017] The present invention first designs a torque observer based on the designed sliding mode convergence law and the mechanical motion model of the permanent magnet synchronous motor, obtains a disturbance signal containing the cogging torque according to the estimated load torque and the mechanical equation of the permanent magnet synchronous motor, and the designed sliding mode convergence law has a predetermined convergence time stability. Regardless of the initial state, the system state can converge to the origin within the predetermined convergence time, and the upper limit of the convergence time is the predetermined convergence time. Then, the disturbance signal containing the cogging rotation is multiplied by the I path and the Q path of the orthogonal reference signal respectively, and then low-pass filtered to obtain two low-frequency terms. The instantaneous frequency offset of the cogging torque is obtained based on the two low-frequency terms, and frequency tracking is implemented to estimate the actual disturbance frequency of the cogging torque. Finally, a disturbance observer is designed based on the designed resonant transfer function to estimate the system disturbance, and sliding mode speed control is performed based on the estimated value of the system disturbance to obtain q The shaft current is used to control the output torque of the permanent magnet synchronous motor. The designed resonant transfer function incorporates fractional-order calculus operators, enabling dynamic reshaping of the response frequency, real-time adjustment of the resonant parameters based on frequency deviation, and elimination of phase lag at the resonant peak through fractional-order phase shaping. These steps optimize the permanent magnet synchronous motor model, control algorithm, and disturbance estimation and compensation mechanism, effectively suppressing the effects of cogging torque and other disturbances on the permanent magnet synchronous motor's operation, improving its operational smoothness and control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be described in further detail below with reference to the accompanying drawings.

[0019] Figure 1Flowchart of the present invention.

[0020] Figure 2 This is a principle block diagram of the present invention. DETAILED DESCRIPTION

[0021] like Figure 1 and Figure 2 As shown in FIG, the sliding mode speed control method of a permanent magnet synchronous motor considering the cogging torque disturbance includes the following steps:

[0022] Step S1, designing a sliding mode reaching law with a predetermined convergence time stability, designing a load torque observer based on the sliding mode reaching law and a mechanical motion model of the permanent magnet synchronous motor to estimate the load torque, and obtaining a disturbance signal including cogging rotation according to the estimated load torque and a mechanical equation of the permanent magnet synchronous motor, wherein the mechanical equation of the permanent magnet synchronous motor is related to a designed disturbance model of the permanent magnet synchronous motor, and the disturbance model of the permanent magnet synchronous motor includes a low-frequency disturbance related to the load torque and the mechanical angular velocity, and a periodic disturbance related to the cogging torque;

[0023] The sliding mode reaching law is expressed as ,in, represents the differential of the synovial surface, T c is the scheduled convergence time, μ is an adjustable parameter, 0< μ <1, sgn( x ) is the sign function, x Returns 0 if it is 0. x If it is greater than 0, it returns 1. x If the value is less than 0, it returns -1.

[0024] The predetermined time stability of the sliding mode reaching law is proved by Lyapunov method:

[0025] Select the Lyapunov function as , the function obviously satisfies: 1. Positive definiteness: 2. Radial Unboundedness: When | s |→∞, then | V ( s )|→∞;

[0026] Compute the differential of a Lyapunov function: , substituting it into the sliding mode reaching law, we get the differential expression: ;

[0027] By separating the variables and integrating them, we can find the upper limit of convergence time: rewrite the above differential expression as follows: ,

[0028] Separate the variables and integrate: ,

[0029] The left-hand side integral is obtained by variable substitution Simplify and get , substitute the upper and lower limits 𝑉0 and 0 (corresponding to and ),get , after sorting, we get the convergence time: ;

[0030] when , ,therefore ,when , , so , so no matter what the initial state 𝑉0 is, the system state 𝑠( t ) at time 𝑇 𝑐 It converges to the origin, and the upper bound of the convergence time is 𝑇 𝑐 , which is independent of the initial conditions.

[0031] The mechanical motion model of the permanent magnet motor is expressed as , then the load torque observer is expressed as , in, represents the mechanical angular velocity, express The differential of represents an estimated value of the mechanical angular velocity (in this embodiment, a dot above a symbol represents a differential, and a chamfer above a symbol represents an estimated value); T e Represents electromagnetic torque, its unit is , is the torque generated by the interaction between the current in the stator winding of the permanent magnet synchronous motor and the magnetic field of the rotor permanent magnet. It is the power source that drives the permanent magnet synchronous motor rotor to rotate. Its size is related to the permanent magnet flux, the number of pole pairs, and the 𝑞-axis current. The expression is , p represents the number of pole pairs of the permanent magnet synchronous motor, which is a dimensionless integer. It determines the magnetic field structure of the permanent magnet synchronous motor and the relationship between the electrical angle and the mechanical angle. It plays an important role in the expressions of electromagnetic torque and cogging torque. It represents the permanent magnet flux linkage, and its unit is Wb (Weber). It is the magnetic flux generated by the rotor permanent magnet. It is an important parameter of the permanent magnet synchronous motor and directly affects the magnitude of the electromagnetic torque. q is the q-axis current, whose unit is A. In the vector control of permanent magnet synchronous motor, the 𝑞-axis current is the key variable for controlling electromagnetic torque. By controlling 𝑖 𝑞It can adjust the output torque of the motor; J represents the moment of inertia, and its unit is , which reflects the resistance of the motor rotor and connected load to changes in rotational state. The greater the moment of inertia, the more difficult it is to change the motor speed; B represents the viscous friction coefficient, and its unit is , which is used to measure the magnitude of the viscous friction force experienced by the motor during rotation. The viscous friction force is proportional to the rotation speed of the rotor, that is, 𝐵𝜔 𝑚 Represents the resistance torque due to viscous friction; T L Indicates load torque, its unit is , is the torque applied to the motor shaft by the external load driven by the motor, its direction is opposite to the direction of motor rotation, hindering the rotation of the motor; Indicates the load torque T L Derivative; represents the estimated load torque; Express Derivative; n t express; represents the gain of the mechanical angular velocity estimation equation, represents the gain of the load torque estimation equation, Indicates the scheduled approach time. It represents the adjustable parameter of the load torque observer, and its value range is between (0,1). represents the sliding surface of the load torque observer; sgn(.) represents the sign function.

[0032] The disturbance signal including the cogging rotation is expressed as ,in, k is a discrete time step, T For the control period, the mechanical equation of the permanent magnet synchronous motor is expressed as , the permanent magnet synchronous motor disturbance model is expressed as , the low-frequency perturbation is expressed as , the periodic perturbation is expressed as ; A is the disturbance amplitude, is the reference frequency, is the frequency offset to be estimated, is the initial phase (randomly obtained).

[0033] Step S2: multiplying the disturbance signal by the I path and the Q path of the orthogonal reference signal respectively, and then performing low-pass filtering to obtain two low-frequency terms. Based on the two low-frequency terms, an instantaneous frequency offset of the cogging torque is obtained, and then frequency tracking is performed to estimate the actual disturbance frequency of the cogging torque. The gain involved in the frequency tracking is updated based on the instantaneous frequency offset.

[0034] First generate a reference quadrature signal pair: , and then the disturbance signal containing the tooth groove rotation Multiplying the I-way and Q-way reference signals respectively, the disturbance signals including the cogging rotation are obtained. I Road Component and the disturbance signal containing the cogging rotation Q Road Component , respectively and Perform low-pass filtering to remove high-frequency components ,get and ,in, is the instantaneous disturbance signal containing the tooth rotation, A represents the amplitude of the cogging torque disturbance, represents the initial phase of the disturbance signal, t Indicates time.

[0035] According to the formula Online estimation of actual disturbance frequency , to eliminate the frequency offset caused by the change of permanent magnet synchronous motor parameters, where is the reference angular frequency of the cogging torque, represents the instantaneous frequency offset of the cogging torque, and are the low-frequency terms corresponding to the I and Q paths, represents the frequency offset of the cogging torque to be estimated; represents the gain involved in frequency tracking, which is based on Update, tanh(.) represents the hyperbolic tangent function, To set the parameter, its value should not be greater than the reference angular frequency of the cogging torque one tenth;

[0036] A smooth transition is achieved using the hyperbolic tangent function:

[0037] when : , , converge at full speed;

[0038] when : , , the gain decreases linearly with the error.

[0039] Step S3: Design a resonant transfer function, estimate the system disturbance using a disturbance observer designed based on the resonant transfer function, and perform sliding mode speed control based on the estimated value of the system disturbance to obtain qThe shaft current is used to control the output torque of the permanent magnet synchronous motor, wherein the resonant transfer function has a fractional-order calculus operator;

[0040] Specifically, the resonant transfer function is expressed as ,in, s represents the complex frequency, is a fractional calculus operator. By adjusting this parameter, the resonance peak can present asymmetric characteristics, such as broad peak, narrow peak, and multi-peak superposition. α =0.8, the bandwidth on the right side of the resonance peak increases, and the suppression of frequency fluctuations is more robust; and is an adaptive parameter that satisfies , the gain and bandwidth can be adjusted dynamically. The resonant transfer function designed in this way can achieve frequency adaptation and nonlinear phase compensation. Frequency adaptation means adjusting the resonant parameters in real time according to the frequency deviation to achieve optimal control under all working conditions. Nonlinear phase compensation means eliminating the phase lag at the resonant peak through fractional-order phase shaping to enhance stability.

[0041] The mechanical equation in the frequency domain is expressed as ,but , then the designed disturbance observer is expressed as , is the filter, Represents the inverse of the filter cutoff frequency. , in the low frequency band , , At the resonant frequency Department, , achieving the effect of simultaneously estimating low-frequency disturbances and cogging torque disturbances;

[0042] Let the sliding surface be ,but ,have , Estimating system disturbances to compensate for unknown disturbances ,but q The shaft current is expressed as , input the q-axis current into the current loop to control the permanent magnet synchronous motor, where, represents the sliding surface, Represents a given mechanical angular velocity, p represents the number of pole pairs of the permanent magnet synchronous motor, represents the permanent magnet flux, Express Seek derivation, represents the estimation of the permanent magnet synchronous motor disturbance model, is the upper bound of the system state convergence time, μIndicates adjustable parameters, 0< μ <1.

[0043] The above description is merely a preferred embodiment of the present invention and therefore cannot be used to limit the scope of the present invention. In other words, equivalent changes and modifications made according to the scope of the patent application and the contents of the specification should still fall within the scope of the patent of the present invention.

Claims

1. A sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance, characterized by: The steps include: Step S1, designing a sliding mode reaching law with a predetermined convergence time stability, designing a load torque observer based on the sliding mode reaching law and a mechanical motion model of the permanent magnet synchronous motor to estimate the load torque, and obtaining a disturbance signal including a cogging torque according to the estimated load torque and a mechanical equation of the permanent magnet synchronous motor, wherein the mechanical equation of the permanent magnet synchronous motor is related to a designed disturbance model of the permanent magnet synchronous motor, and the disturbance model of the permanent magnet synchronous motor includes a low-frequency disturbance related to the load torque and the mechanical angular velocity, and a periodic disturbance related to the cogging torque; Step S2: multiplying the disturbance signal by the I path and the Q path of the orthogonal reference signal respectively, and then performing low-pass filtering to obtain two low-frequency terms. Based on the two low-frequency terms, an instantaneous frequency offset of the cogging torque is obtained, and then frequency tracking is performed to estimate the actual disturbance frequency of the cogging torque. The gain involved in the frequency tracking is updated based on the instantaneous frequency offset. Step S3: Design a resonant transfer function, estimate the system disturbance using a disturbance observer designed based on the resonant transfer function, and perform sliding mode speed control based on the estimated value of the system disturbance to obtain q The shaft current is used to control the output torque of the permanent magnet synchronous motor, wherein the resonant transfer function has a fractional-order calculus operator; In step S1, the mechanical motion model of the permanent magnet motor is expressed as , then the load torque observer is expressed as ,in, represents the mechanical angular velocity, express The differential of represents the estimated value of the mechanical angular velocity, T e represents the electromagnetic torque, J represents the moment of inertia, B represents the viscous friction coefficient, T L represents the load torque, Indicates load torque T L Seek derivation, represents the estimated load torque, Express Seek derivation, n t represents the differential of the load torque, represents the gain of the mechanical angular velocity estimation equation, represents the gain of the load torque estimation equation, is the designed sliding mode reaching law, Indicates the scheduled approach time. represents the load torque observer adjustable parameter, represents the sliding surface of the load torque observer, sgn(.) represents the sign function; In step S3, the resonant transfer function Expressed as ,in, is a fractional calculus operator, and is an adaptive parameter that satisfies , s represents the complex frequency; In the step S3, the q Shaft current Expressed as ,in, represents the sliding surface, then , Represents a given mechanical angular velocity, p represents the number of pole pairs of the permanent magnet synchronous motor, represents the permanent magnet flux, Express Seek derivation, represents the estimation of the permanent magnet synchronous motor disturbance model, is the upper bound of the system state convergence time, μ Indicates adjustable parameters, 0< μ <1.

2. The sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance according to claim 1, characterized in that: In step S1, the disturbance signal including the tooth groove rotation Expressed as ,in, k is a discrete time step, T For the control period, the permanent magnet synchronous motor disturbance model d Expressed as , the low-frequency perturbation is expressed as , the periodic perturbation is expressed as .

3. The sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance according to claim 2, characterized in that: In step S2, according to the formula Online estimation of actual disturbance frequency of cogging torque ,in, represents the gain involved in frequency tracking, which is based on Update, tanh(.) represents the hyperbolic tangent function, To set the parameter, its value should not be greater than the reference angular frequency of the cogging torque One tenth of represents the instantaneous frequency offset of the cogging torque, and They are the low-frequency items corresponding to the I and Q paths respectively.

4. The sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance according to claim 3, characterized in that: In step S2, the disturbance signal including the cogging rotation is multiplied by the I path and the Q path of the orthogonal reference signal to obtain the disturbance signal including the cogging rotation. I Road Component and the disturbance signal containing the cogging rotation Q Road Component , respectively and Perform low-pass filtering to remove high-frequency components ,get and ,in, is the instantaneous disturbance signal containing the tooth rotation, A represents the amplitude of the cogging torque disturbance, represents the initial phase of the disturbance signal, t Indicates time.

5. The sliding mode speed control method for a permanent magnet synchronous motor considering cogging torque disturbance according to claim 4, characterized in that: In step S3, the disturbance observer is expressed as , represents the estimated value of system disturbance in the frequency domain, is the filter, Indicates the inverse of the filter cutoff frequency, in the low frequency band Approaching 0, Becomes a low-pass filter at the resonant frequency tends to infinity, When it is set to 1, the effect of simultaneously estimating low-frequency disturbance and cogging torque disturbance is achieved.

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