An adaptive control method for permanent magnet synchronous motor

Abstract

The present invention discloses an adaptive control method for a permanent magnet synchronous motor, comprising a second-order super-distorted linear sliding mode (SOSML) speed observer and a speed controller based on a compensated continuous adaptive terminal sliding mode algorithm. The SOSML speed observer comprises the following steps: S11, obtaining the voltage and current of the α-axis and β-axis through voltage and current sensors and Park transformation, and completing speed estimation in a stationary coordinate system; S12, establishing a model to be estimated through a system model of the PMSM; S13, applying the SOSML speed observer to a back electromotive force expression in combination with the model to be estimated; and S14, obtaining speed and position estimation expressions through trigonometric function transformation. The present invention incorporates a disturbance compensation input into the PMSM drive system. A Luenberger disturbance observer is used to predict the lumped disturbance, and the prediction result is added as the control input of the compensation control part CAFTSM. To ensure good robustness of the PMSM, the present invention proposes a CAFTSM algorithm with compensation based on the above to design a PMSM speed controller.

Description

Technical Field

[0001] The invention belongs to the field of sensorless driving and control of permanent magnet synchronous motors, and relates to an adaptive control method for permanent magnet synchronous motors. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have advantages such as a high torque-to-inertia ratio and superior power density, making them widely used in high-performance control applications such as new energy electric vehicles, robotic systems, and industrial servo control systems. Field-oriented control (FOC) is a control method that relies on precise rotor position and speed information to achieve high-performance PMSM drive. In specific practical applications, such as turbine permanent magnet synchronous motors, due to their unique air bearing structure, there is no space for installing position sensors. Therefore, accurate estimation of the motor's rotor position and speed is required to achieve FOC control. However, the use of sensors increases the cost of permanent magnet synchronous motors, and external vibration and noise can also affect sensor performance, reducing system reliability.

[0003] Research on PMSM sensorless algorithms can be broadly categorized into two types based on their operating principles: the motor magnetic field saliency model and the back-electromotive force (EMF) fundamental model. When the motor is operating at low speeds, the back-EMF is small, making it difficult to detect effective signals in the presence of a low signal-to-noise ratio. The motor magnetic field saliency model is suitable for rotor position estimation at zero and low speeds. Key methods include high-frequency modulation injection and high-frequency pulse signal injection, but control performance is affected by high-frequency ripple. When the back-EMF is large at medium and high speeds, commonly used rotor position estimation methods include the model reference adaptive (MRAS) algorithm, the extended Kalman filter (EKF), and the sliding mode observer (SMO). MRAS is a speed and position estimation method for motors operating at low and medium speeds. It can identify electrical parameters such as stator resistance and flux during startup, but its performance is poor at medium and high speeds. The EKF algorithm is a nonlinear stochastic observer based on Gaussian noise. It accounts for uncertainties such as observation errors and the system model, and exhibits high robustness. However, its complex structure and high computational complexity make it unsuitable for real-time speed estimation in embedded systems. The sliding mode observer (SMO) is highly resistant to interference, easy to implement, and has a fast response, making it suitable for real-time observation and widely used in sensorless control of PMSMs. Traditional SMOs exhibit chattering, requiring the addition of low-pass filters and phase compensation. To suppress chattering, the superwarp algorithm is a conventional sliding mode algorithm with minimal chattering. When used as an observer, the superwarp algorithm offers advantages such as continuous output control and fixed-time convergence. To further reduce chattering in the superwarp algorithm, this paper proposes an improved second-order superwarp algorithm for use as a speed observer to estimate the speed of a PMSM.

[0004] In terms of PMSM speed control, the proportional integral (PI) controller is a commonly used linear controller with limited control accuracy. If the PI controller is used in the PMSM speed adjustment controller, the PI controller has high requirements on the accuracy of system modeling and is easily affected by external disturbances and the uncertainty of the system internal modeling. PMSM nonlinear speed control methods include robust control, sliding mode control, fuzzy control and H ∞ These nonlinear methods are superior to linear control methods in terms of PMSM control performance. Traditional SMC control methods have problems such as chattering, long convergence time and poor anti-interference ability. Summary of the Invention

[0005] To solve the above problems, the technical solution of the present invention is an adaptive control method for a permanent magnet synchronous motor, comprising a second-order super-distorted sliding mode (SOSML) speed observer part and a speed controller part based on a compensated continuous adaptive terminal sliding mode algorithm, wherein:

[0006] The SOSML speed observer part includes the following steps:

[0007] S11, obtain the voltage and current of the α-axis and β-axis through voltage and current sensors and Park transformation, and complete the speed estimation in the stationary coordinate system;

[0008] S12, establishing a model to be estimated through a system model of the PMSM;

[0009] S13, using the SOSML speed observer for the back EMF expression in conjunction with the model to be estimated;

[0010] S14, obtain the velocity and position estimation expressions through trigonometric function transformation.

[0011] Preferably, the model to be estimated in the PMSM stationary coordinate system in S12 is:

[0012]

[0013] in, and are the estimated current values of the α-axis and β-axis, and is the estimated value of the back electromotive force of the α-axis and the β-axis, U α and U β is the voltage value between the α-axis and the β-axis, R is the stator resistance, and L is the stator inductance.

[0014] Preferably, the back electromotive force expression based on the SOSML observer in S13 is:

[0015]

[0016] Among them, i α and i β are the actual values of the current in the α-axis and β-axis, and the parameters k1, k2, k3 and k4 are ≥ 0.

[0017] Preferably, the speed estimation value calculated by the transformation of the trigonometric function in S14 is obtained based on the back electromotive force, and the speed estimation expression is:

[0018]

[0019] where ψ f is the magnetic link;

[0020] The position estimate calculated by the transformation of the trigonometric function is obtained by combining the velocity estimation integral and the inverse tangent function, where the convergence time of the SOSML velocity observer is T r , when the speed observer has not converged, it is used; when the speed observer has converged, it is calculated using the inverse tangent function. The position estimation expression is:

[0021]

[0022] Preferably, the CAFTSM controller with compensation in S20 is a PMSM that implements a FOC control strategy in a synchronous coordinate system, sets the d-axis reference current to 0, and implements speed control by adjusting the q-axis reference current. The CAFTSM control output expression is:

[0023]

[0024] Where J is the damping coefficient, P n is the number of magnetic pole pairs, Kt is the torque constant, is the derivative of the target velocity, Indicates the difference between the target speed and the current speed. Represents the sliding surface, where parameters λ1, λ2, and λ3 are all positive numbers greater than 0, and parameter Both p1 and q1 are odd numbers, and the parameters p2 and q2 are both odd numbers and satisfy 0<α1<α2<2, and the parameters g1, g2 and η are all positive numbers greater than 0. is the disturbance compensation part of the Luenberger observer;

[0025] Among them, the equivalent control is:

[0026]

[0027] Among them, the adaptive switching items are:

[0028]

[0029] Preferably, the disturbance compensation part of the Luenberger observer is obtained by the state equation under the PMSM synchronous coordinate to obtain the Luenberger observer equation, and the lumped disturbance One of the state variables is an estimate of the lumped disturbance of the system.

[0030] Preferably, the state equation of the PMSM in synchronous coordinates is expressed as:

[0031]

[0032] Among them, x is the state variable, The second variable D(t) is the lumped disturbance, y is the output variable of the state equation, which is used as part of the input of the Luenberger observer equation, and u is the input variable. C =

[10] .

[0033] Preferably, the Luenberger observer equation is expressed as:

[0034]

[0035] Among them, the H matrix is the observer gain matrix. To ensure the convergence of the observer error system, H is designed to be [2l g l g 2 ] T , is the estimated value of x, is the estimated value of y.

[0036] The present invention has at least the following beneficial effects: In order to overcome the problems existing in the prior art, the PMSM speed adjustment control strategy can be designed as terminal sliding mode control (TSM). In order to enable the PMSM drive system to achieve good control performance, continuous non-singular fast terminal sliding mode control (CFTSM) is proposed and used in the control system. The CFTSM method has the characteristics of finite time convergence and chatter suppression, and also avoids the singularity problem in TSM. In order to further improve the response performance and anti-interference ability of CFTSM, the present invention proposes a continuous adaptive non-singular fast terminal sliding mode (CAFTSM) speed control method, which adds an adaptive rate to the conventional exponential approach rate to improve the response performance. In addition, in order to improve the dynamic response performance of the PMSM drive system and reduce the tracking error, the present invention adds a disturbance compensation input to the PMSM drive system, uses the Luenberger disturbance observer to predict the lumped disturbance, and adds the prediction result as the compensation control part to the control input of the CAFTSM; in order to make the PMSM have good robustness, based on the above, the present invention proposes a CAFTSM algorithm with compensation to design a PMSM speed controller. The present invention further reduces speed estimation errors, compensates for system internal and external disturbances to the maximum extent, and improves the speed regulation dynamic response capability and anti-interference capability of the sensorless controlled PMSM. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flowchart of the steps of the adaptive control method of a permanent magnet synchronous motor according to an embodiment of the present invention;

[0038] Figure 2 A system structure diagram corresponding to the adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

[0039] Figure 3 A block diagram of back electromotive force estimation using an SOSML observer in an adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

[0040] Figure 4 A block diagram of a permanent magnet synchronous motor position and speed estimation method based on back electromotive force according to an embodiment of the present invention;

[0041] Figure 5 A block diagram of a CAFTSM controller for an adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

[0042] Figure 6 A block diagram of a compensated CAFTSM speed controller of a permanent magnet synchronous motor adaptive control method according to an embodiment of the present invention;

[0043] Figure 7Figure 1 is a diagram of PMSM speed and position estimation based on the SOSML observer during the experiment of the adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention. (a) is a speed estimation diagram, and (b) is a position estimation block diagram.

[0044] Figure 8 Error comparison diagrams based on the SOSML observer and the conventional super-distortion observer (STSMO) during the experiment of the adaptive control method for the permanent magnet synchronous motor according to an embodiment of the present invention, (a) is a speed error comparison diagram, and (b) is a position error comparison diagram;

[0045] Figure 9 This is a comparison diagram of startup responses between a compensated CAFTSM speed controller and a conventional CFTSM speed controller during an experiment of an adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

[0046] Figure 10 Graph comparing speed regulation between a compensated CAFTSM speed controller and a conventional CFTSM speed controller during an experiment of an adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention. (a) is an overall graph, and (b) is a partial magnified graph of load variation.

[0047] Figure 11 Graphs of disturbances predicted by the Luenberger observer and actual disturbances during experiments of the adaptive control method for a permanent magnet synchronous motor according to an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0049] On the contrary, the present invention covers any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention as defined by the claims. Furthermore, to facilitate a better understanding of the present invention, certain specific details are described in detail below in the detailed description of the present invention. Those skilled in the art will be able to fully understand the present invention without these details.

[0050] See also Figure 1 , is a flowchart of the steps of the sensorless control method of the permanent magnet synchronous motor based on the SOSML observer compensation adaptive sliding mode embodiment of the present invention, including S10, the SOSML speed observer part and S20, the speed controller part based on the compensation continuous adaptive terminal sliding mode algorithm, wherein,

[0051] S10, the SOSML speed observer part includes the following steps:

[0052] S11, obtain the voltage and current of the α-axis and β-axis through voltage and current sensors and Park transformation, and complete the speed estimation in the stationary coordinate system;

[0053] S12, establishing a model to be estimated through a system model of the PMSM;

[0054] S13, using the SOSML speed observer for the back EMF expression in conjunction with the model to be estimated;

[0055] S14, obtain the velocity and position estimation expressions through trigonometric function transformation.

[0056] Figure 2 The figure shows the overall control block diagram of the PMSM sensorless drive, which includes a compensation speed controller, PI controllers for the q-axis and d-axis, a space vector pulse width modulation module (SVPWM), an inverter module, a PMSM, a voltage and current sensor (Sensor), a SOSML observer module, and a coordinate transformation module. The three-phase voltage and three-phase current of the PMSM are measured by voltage and current sensors, and then transformed into stationary coordinates by the Clack transformation module and sent to the SOSML observer module for speed and position estimation. After the Clack transformation, the three-phase current is used in the SOSML observer module on one path and in the Park transformation module on the other path to convert the current in the stationary coordinate system into the current in the synchronous coordinate system. The transformation result is used for the PI controllers of the q-axis and d-axis. Speed control adopts the FOC control strategy, setting the reference current i of the d-axis. d ref is 0, the reference current i of the q axis q ref To compensate for the output of the speed controller, two PI controllers are used to adjust the voltages of the d-axis and q-axis so that the SVPWM module outputs corresponding multi-channel modulated pulse signals. The multi-channel pulse signals are converted by the inverter to output three-phase AC power to control the torque of the PMSM.

[0057] Figure 3 The block diagram of the estimated back electromotive force in the SOSML observer is shown in Figure 1. The input is the voltage and current of the α-axis and β-axis, and the output is the back electromotive force of the α-axis and β-axis. The model to be estimated is obtained from the model in the PMSM synchronous coordinate system. Represents the integral operation, which is used to calculate the estimated current values of the α-axis and β-axis. The estimated value of the back electromotive force can be obtained by subtracting the estimated value from the actual value and combining it with the SOSML algorithm. The estimated value of the back electromotive force is as follows:

[0058]

[0059] where i α and i β is the actual value of the current on the α-axis and β-axis, and are the estimated current values of the α-axis and β-axis, and is the estimated back EMF value of the α-axis and the β-axis, and the parameters k1, k2, k3 and k4 are ≥ 0. The result of the EMF estimation is used to feed back into the differential equation of the model to be estimated and as the output of this module.

[0060] Figure 4 The block diagram for estimating the position and velocity of the PMSM is shown in Figure 1. The position estimation expression is based on the observer convergence time T r Perform segmented calculations, and the expression is

[0061]

[0062] In the synchronous coordinate system, PMSM can be modeled as follows to facilitate FOC strategy to control speed

[0063]

[0064] Where J is the damping coefficient, P n is the number of magnetic pole pairs, Kt is the torque constant, ω e is the rotor angle, B is the moment of inertia, J is the damping coefficient, ψ f is the magnetic flux, T L is the torque load. i d ,i q ,U d ,U q They represent the d-axis current, q-axis current, d-axis voltage, and q-axis voltage respectively. R is the stator resistance and L is the inductance.

[0065] Based on the above modeling and combined with the observer's speed estimation, it is rewritten into the following formula and used for the design of the equivalent controller

[0066]

[0067] i q ref is the reference current of the q axis, where the disturbance is measured using the Luenberger observer. The actual calculation expression of the disturbance is as follows

[0068]

[0069] The error state variables are defined according to the PMSM modeling equation as follows:

[0070]

[0071] is the derivative of the target velocity, Indicates the difference between the target speed and the current speed. is the derivative of the difference, which can be substituted into the PMSM system model as

[0072] Figure 5 The block diagram of the CAFTSM controller is mainly designed based on the equations of the PMSM system in the synchronous coordinate system and the continuous non-singular adaptive sliding mode control algorithm. The input of the CAFTSM controller is the target speed ω e ref and estimated speed The output is the uncompensated q-axis reference current The equivalent control u eq Designed for

[0073]

[0074] Adaptive switching item u b Designed for

[0075]

[0076] The continuous non-singular fast terminal sliding surface s is designed as

[0077]

[0078] Among them, λ1>0, λ2>0, 0<α1<α2<2, and p1, p2, q1 and q2 are all positive odd numbers. In the adaptive exponential reaching law, the parameters λ3, g1, g2 and η are all constants greater than 0. is the disturbance estimate of the Luenberger disturbance observer.

[0079] According to the PMSM synchronous coordinate modeling, the design state equation is expressed as follows:

[0080]

[0081] Where x is the state variable, The second variable D(t) is the lumped disturbance. y is the output variable of the state equation, which is used as part of the input of the Luenberger observer equation, and u is the input variable. C =

[10] .

[0082] The Luenberger observer equation can be expressed as:

[0083]

[0084] in is the estimated value of x, is the estimated value of y. Its derivative can be written as

[0085]

[0086] The H matrix is the observer gain matrix. To ensure the convergence of the observer error system, H is designed as [2l g l g 2 ] T , satisfying the condition Re{λ i (A-HC)}<0(i=1,2).

[0087] Figure 6 The block diagram of the compensated CAFTSM speed controller includes the CAFTSM controller, the Luenberger observer and a constant gain block. The output of the CAFTSM controller is the uncompensated q-axis reference current. One is used as the input of Luenberger disturbance observer, and the other is used as the subsequent output. The input of Luenberger disturbance observer is the uncompensated q-axis reference current and estimated speed, and the output is the disturbance estimate, which is adjusted by constant After the gain is compensated to Get the output reference q-axis current

[0088] In order to prove the closed-loop stability of the designed controller, the Lyapunov equation is designed:

[0089]

[0090] s in the formula u =-u b , define the lumped disturbance estimation error Substituting the expressions of equivalent control and sliding surface into the Lyapunov equation, we can obtain Re{λ i The condition (A-HC)}<0(i=1,2) is easy to prove That is, the closed-loop stability of the controller involved in the present invention is explained.

[0091] Figure 7 Figure 1 shows the PMSM speed and position estimation diagrams based on the SOSML observer during the experiment. (a) is the speed estimation diagram, and (b) is the position estimation block diagram. It can be seen that the speed and position estimation of the present invention is very effective, and the predicted value and the actual value change almost simultaneously. Figure 8The following plots compare the errors of the SOSML-based observer and the conventional super-distortion observer (STSMO) during the experiment. (a) shows the velocity error comparison, and (b) shows the position error comparison. Regarding velocity error, the SOSML-based observer of the present invention exhibits smaller steady-state error and better dynamic response than the STSMO, and responds more quickly to speed changes. Regarding position error, the present invention performs similarly to the conventional observer, with slightly less latency.

[0092] Figure 9 This figure compares the startup responses of the compensated CAFTSM speed controller and the conventional CFTSM speed controller during the experiment. The CAFTSM has a faster response speed than the conventional CFTSM, reaching the target speed in a shorter time and achieving better performance. Figure 10 Figure 1 compares the speed regulation of a compensated CAFTSM speed controller and a conventional CFTSM speed controller during an experiment. (a) shows the overall diagram, and (b) shows a zoomed-in view of a specific load change. The compensated CAFTSM controller exhibits the smallest speed drop during a 0.02s load change, followed by the CAFTSM controller, and finally the conventional CFTSM controller. The adaptive reaching law of the present invention enhances the controller's speed regulation capability, improves interference rejection, and enhances robustness. Figure 11 is the estimated disturbance and actual disturbance predicted by the Luenberger observer during the experiment, Figure 11 The load suddenly changes at 0.02s. The prediction result of Luenberger observer is very close to the actual value, and the prediction performance of disturbance is good.

[0093] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for adaptively controlling a permanent magnet synchronous motor, characterized in that: It includes S10, SOSML speed observer part and S20, compensation-based continuous adaptive non-singular fast terminal sliding mode CAFTSM algorithm speed controller part, where: The S10, SOSML speed observer part includes the following steps: S11, obtain the voltage and current of the α-axis and β-axis through voltage and current sensors and Park transformation, and complete the speed estimation in the stationary coordinate system; S12, establishing a model to be estimated through a system model of the PMSM; S13, using the SOSML speed observer for the back EMF expression in conjunction with the model to be estimated; S14, obtain the velocity and position estimation expressions through trigonometric function transformation; The CAFTSM controller with compensation in S20 implements the FOC control strategy of PMSM in the synchronous coordinate system. The d-axis reference current is set to 0, and the speed control is achieved by adjusting the q-axis reference current. The CAFTSM control output expression is: Where J is the damping coefficient, P n is the number of magnetic pole pairs, Kt is the torque constant, is the derivative of the target velocity, Indicates the difference between the target speed and the current speed. Represents the sliding surface, where parameters λ1, λ2, and λ3 are all positive numbers greater than 0, and parameter Both p1 and q1 are odd numbers, and the parameters p2 and q2 are both odd numbers and satisfy 0<α1<α2<2, and the parameters g1, g2 and η are all positive numbers greater than 0. is the disturbance compensation part of the Luenberger observer; Among them, the equivalent control is: Among them, the adaptive switching items are:

2. The method according to claim 1, characterized in that The model to be estimated in the PMSM stationary coordinate system in S12 is: in, and are the estimated current values of the α-axis and β-axis, and is the estimated value of the back electromotive force of the α-axis and the β-axis, U α and U β is the voltage value between the α-axis and the β-axis, R is the stator resistance, and L is the stator inductance.

3. The method according to claim 2, characterized in that The back electromotive force expression based on the SOSML observer in S13 is: Among them, i α and i β are the actual values of the current in the α-axis and β-axis, and the parameters k1, k2, k3 and k4 are ≥ 0.

4. The method according to claim 3, characterized in that The speed estimation value calculated by the transformation of the trigonometric function in S14 is obtained based on the back electromotive force, and its speed estimation expression is: where ψ f is the magnetic link; The position estimate calculated by the transformation of the trigonometric function is obtained by combining the velocity estimation integral and the inverse tangent function, where the convergence time of the SOSML velocity observer is T r , when the speed observer has not converged, it is used; when the speed observer has converged, it is calculated using the inverse tangent function. The position estimation expression is:

5. The method according to claim 1, characterized in that The disturbance compensation part of the Luenberger observer is obtained from the state equation of the PMSM synchronous coordinates to obtain the Luenberger observer equation, and the lumped disturbance One of the state variables is an estimate of the lumped disturbance of the system.

6. The method according to claim 5, characterized in that The state equation of the PMSM in synchronous coordinates is expressed as: Among them, x is the state variable, The second variable D(t) is the lumped disturbance, y is the output variable of the state equation, which is used as part of the input of the Luenberger observer equation, and u is the input variable. C=[1 0].

7. The method according to claim 6, characterized in that The Luenberger observer equation is expressed as: Among them, the H matrix is the observer gain matrix. To ensure the convergence of the observer error system, H is designed to be [2l g l g 2 ] T , l g is the gain parameter of the observer, satisfying l g >0, is the estimated value of x, is the estimated value of y.

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