Adaptive high-order terminal sliding mode observer control method for permanent magnet synchronous motor

Abstract

The present invention relates to the technical field of permanent magnet synchronous motor control. The present invention provides a permanent magnet synchronous motor adaptive high-order terminal sliding mode observer control method. The method comprises: establishing a motor in α‑β Expanded equations in a two-phase stationary coordinate system; design a high-order terminal sliding surface based on the expanded equation; design an adaptive gain; design the current signal control law and back-EMF signal control rate of the high-order terminal sliding surface based on the adaptive gain, expanded equation and high-order terminal sliding surface; obtain the adaptive gain and control gain k The constraint conditions of the adaptive gain are defined; the adaptive high-order terminal sliding mode observer is designed based on the current signal control law and the back electromotive force signal control rate; the electrical angular velocity and the rotor electrical angle are obtained based on the orthogonal component phase-locked loop method; the operation of the motor is controlled based on the field-oriented control and space vector pulse width modulation. The present invention enables the control system to maintain robustness and high-precision output at the same time under high dynamic response requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and in particular to a permanent magnet synchronous motor adaptive high-order terminal sliding mode observer control method. Background Art

[0002] Motor speed control systems are widely used in industrial production and automated control, such as CNC machine tools, automated production lines, robot control systems, and electric vehicle drive systems. In these application scenarios, precise motor speed control is particularly critical, requiring the motor speed control system to have rapid response capabilities under dynamic conditions such as load changes, speed switching, and environmental interference. At the same time, in order to ensure the quality of the final product and the stability of the motor speed control system, the motor speed control system must also provide high-precision speed control during steady-state operation to meet the steady-state performance requirements of zero vibration and low error. These stringent dynamic response and steady-state control performance requirements place extremely high control requirements on the motor speed control system.

[0003] However, the existing sliding mode observer (SMO) and extended sliding mode observer (ESMO) have significant deficiencies in the real-time performance, estimation accuracy and anti-interference ability of the motor control system. Especially in dynamic environments with load and speed changes, traditional observers are prone to severe jitter, which not only affects the stability of the motor control system, but also reduces the control accuracy. In order to solve these problems, the researchers proposed an improved high-order sliding mode observer (High-order Terminal SlidingMode Observer, HOTSMO) to improve the performance of the motor control system. However, the robustness of the HOTSMO method needs to be guaranteed by selecting a large and constant control gain, and a large control gain will produce a large jitter when the system is in sliding surface motion.

[0004] Therefore, these limitations of the existing sliding mode observers prompt us to seek a more effective solution to further improve the performance and reliability of sliding mode observers in real-time dynamic control. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0006] To this end, the purpose of the present invention is to propose an adaptive high-order terminal sliding mode observer control method for a permanent magnet synchronous motor.

[0007] In order to achieve the above-mentioned purpose, the technical solution of the present invention provides a permanent magnet synchronous motor adaptive high-order terminal sliding mode observer control method. The method comprises: step S1: establishing a permanent magnet synchronous motor in α-β The extended equation in the two-phase stationary coordinate system; wherein the expression of the extended equation is:

[0008] (1)

[0009] In formula (1), ; , Expressed as α-β Stator current in two-phase stationary coordinate system; ; , Expressed as α-β Stator voltage in two-phase stationary coordinate system; ; , Expressed as α-β Back EMF in a two-phase stationary coordinate system; ; ; ; It is represented as the electrical angular velocity of the permanent magnet synchronous motor; It is represented as a state matrix related to the stator inductance and stator resistance; It is represented as a state matrix related to the stator inductance; It is represented as a state matrix related to the electrical angular velocity; Represented as a system state matrix; Represented as the input matrix, Indicates stator voltage u How does it affect current? i ; Represented as a 2×2 matrix;

[0010] in, The expression is:

[0011] (2)

[0012] The expression is:

[0013] (3)

[0014] In formula (2) and formula (3), is the stator inductance, is the stator resistance; Represented as a 2×2 matrix;

[0015] The expression is:

[0016] (4)

[0017] The expression is:

[0018] (5)

[0019] Step S2: Based on the extended equation, a high-order terminal sliding surface is designed ; Wherein, the high-order terminal sliding surface The function expression is:

[0020] (6)

[0021] In formula (6), Expressed as α Axial synovial surface function; Expressed as β Axial synovial surface function; Represented as stator current error signal; Expressed as α Shaft stator current error signal; Expressed as β Shaft stator current error signal; sign() represents the sign function; and All are expressed as control gains;

[0022] Wherein, the stator current error signal is obtained The process of differential output value includes:

[0023] Defining the stator current error signal The differential expression of is:

[0024] (7)

[0025] In formula (7), It is represented as the Savitzky-Golay filter i coefficients; Represents the first i The most recent current estimation error samples;

[0026] Combined with the adaptive noise threshold mechanism, the exponentially weighted moving average of the absolute value of the differential is calculated; the expression of the exponentially weighted moving average of the absolute value of the differential is:

[0027] (8)

[0028] In formula (8), Expressed as a smoothing factor; Represents the exponentially weighted moving average calculated at the current moment, Indicated as at the last moment t- 1The exponentially weighted moving average calculated; t Expressed as time;

[0029] If the current differential exceeds the threshold and sensitivity factor defined by EMA The product of the previous stator current error signal is retained. The differential output value of the stator current error signal The expression of the differential output value is:

[0030] (9)

[0031] In formula (9), Expressed as sensitivity factor;

[0032] Step S3: Design an adaptive gain ;

[0033] Step S4: Based on the adaptive gain , the expression of the extended equation, and the high-order terminal sliding surface The function expression of the current signal control law of the high-order terminal sliding surface is designed. Z i and back EMF signal control rate ; Wherein, the current signal control law Z i The function expression is:

[0034] (10)

[0035] In formula (7), Represented as an intermediate variable; g and k All are expressed as control gains;

[0036] The back EMF signal controls the rate The function expression is:

[0037] (11)

[0038] In formula (11), Expressed as α Part of the axis control law; Expressed as β Part of the axis control law; Expressed as α-β Part of the axis control law; is represented as a positive number;a It is expressed as control gain;

[0039] Step S5: Based on Lyapunov's stability theorem, the adaptive gain is obtained and control gain k The constraints of the adaptive gain and control gain k The constraint expression is:

[0040] (12)

[0041] In formula (12), Expressed as α Axis control gain intermediate variable; Expressed as β Axis control variable intermediate gain; Expressed as an estimate; is the estimated error of angular velocity; Expressed as an estimate of the electrical angular velocity; Expressed as the actual value of electrical angular velocity; for t The electrical angular velocity of the permanent magnet synchronous motor observed at any moment; is the estimation error of back EMF; Expressed as β Axis back-EMF estimation error; Expressed as t time β Axis back-EMF estimation error; Expressed as t time α Axis back-EMF estimation error; Expressed as β Axis back EMF estimate; Expressed as t Moment α Axial synovial surface function; Expressed as t Moment β Axial synovial surface function; g is represented as the control gain; D is represented as the upper limit of the current differential error; and D satisfies:

[0042] (13)

[0043] Step S6: Define adaptive gain The expression of the adaptive gain The expression is:

[0044] (14)

[0045] In formula (14), is the adaptive gain exist t 0 The value of the moment;

[0046] Step S7: The current signal control law of the high-order terminal sliding surface Z i and back EMF signal control rate Combined with the above, an adaptive high-order terminal sliding mode observer is designed; the expression of the adaptive high-order terminal sliding mode observer is:

[0047] (15)

[0048] In formula (15), ; Expressed as the estimated electrical angular velocity The relevant state matrix; Expressed as α-β Estimated value of stator current in two-phase stationary coordinate system; Expressed as α-β Estimated value of back EMF in two-phase stationary coordinate system;

[0049] Step S8: Obtain the observed electrical angular velocity based on the orthogonal component phase-locked loop method and the observed rotor electrical angle;

[0050] Step S9: controlling the operation of the permanent magnet synchronous motor based on field oriented control and space vector pulse width modulation.

[0051] Preferably, the permanent magnet synchronous motor is a surface mounted permanent magnet synchronous motor.

[0052] Preferably, The value of is 0.001.

[0053] Beneficial effects of the present invention:

[0054] (1) The adaptive high-order terminal sliding mode observer control method of the permanent magnet synchronous motor of the present invention provides a motor speed control system control scheme that combines an adaptive gain adjustment mechanism (referred to as GA-HOTSMO) and a robust current error differential estimation method. Specifically, the adaptive gain adjustment mechanism significantly improves the anti-disturbance capability of the motor speed control system under dynamic conditions by introducing an adaptive gain adjustment mechanism. When the system load or speed undergoes a transient change, the gain coefficient can be adaptively adjusted according to the system state, so that the system can quickly adapt to external disturbances and quickly restore steady-state output, reduce the impact of jitter, and achieve finite time convergence. Compared with the traditional sliding mode controller method, the present invention significantly reduces the jitter problem caused by sudden changes and achieves finite time convergence, so that the control system can maintain robustness and high-precision output under high dynamic response requirements.

[0055] Specifically, the robust current error differential estimation method combines Savitzky-Golay filtering with adaptive noise thresholding, which can accurately estimate the current error differential and smooth the error signal. Through this filtering strategy, the present invention avoids the problem of amplifying high-frequency noise in traditional differential methods, thereby achieving high-precision control output under steady-state conditions. This method not only improves the smoothing performance of the system in steady-state operation, but also effectively suppresses sudden noise interference while maintaining signal characteristics, thereby improving the accuracy and stability of differential estimation.

[0056] (2) The design of the present invention has significant advantages in enhancing the steady-state performance of sliding mode control. Specifically, the adaptive gain adjustment mechanism automatically reduces the gain when the system state is close to the sliding mode surface, thereby effectively suppressing chattering, and at the same time increases the gain in time when the system state deviates from the steady state to enhance the stability of the system. Through reasonable parameter selection, the present invention achieves a balance between the dynamic response speed and steady-state accuracy of the system, ensuring that the system can converge quickly and maintain smooth control in a stable state, thereby improving the overall reliability and control accuracy of the system.

[0057] Additional aspects and advantages of the invention will become apparent from the following description, or may be learned by practice of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic flow chart showing a method for controlling a permanent magnet synchronous motor using an adaptive high-order terminal sliding mode observer according to an embodiment of the present invention is shown;

[0059] Figure 2 An overall control schematic block diagram of sensorless control according to an embodiment of the present invention is shown;

[0060] Figure 3A Savitzky-Golay filtering and adaptive noise threshold flow chart of current error differentiation according to an embodiment of the present invention is shown;

[0061] Figure 4 A schematic design block diagram of an orthogonal component phase-locked loop according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0062] In order to more clearly understand the above-mentioned objectives, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0063] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0064] Figure 1 FIG. 1 is a schematic flow chart showing a method for implementing an adaptive high-order terminal sliding mode observer for permanent magnet synchronous motor control according to an embodiment of the present invention. Figure 1 As shown, the implementation method includes:

[0065] Step S1: Establish a permanent magnet synchronous motor α-β The extended equation in the two-phase stationary coordinate system; wherein the expression of the extended equation is:

[0066] (1)

[0067] In formula (1), ; , Expressed as α-β Stator current in two-phase stationary coordinate system; ; , Expressed as α-β Stator voltage in two-phase stationary coordinate system; ; , Expressed as α-β Back EMF in a two-phase stationary coordinate system; ; ; ; It is represented as the electrical angular velocity of the permanent magnet synchronous motor; It is represented as a state matrix related to the stator inductance and stator resistance; It is represented as a state matrix related to the stator inductance; It is represented as a state matrix related to the electrical angular velocity; Represented as a system state matrix; Represented as the input matrix, Indicates stator voltage u How does it affect current? i ; Represented as a 2×2 matrix;

[0068] in, The expression is:

[0069] (2)

[0070] The expression is:

[0071] (3)

[0072] In formula (2) and formula (3), is the stator inductance, is the stator resistance; Represented as a 2×2 matrix;

[0073] The expression is:

[0074] (4)

[0075] The expression is:

[0076] (5)

[0077] Step S2: Based on the extended equation, design a high-order terminal sliding surface ; Wherein, the high-order terminal sliding surface The function expression is:

[0078] (6)

[0079] In formula (6), Expressed as α Axial synovial surface function; Expressed as β Axial synovial surface function; Represented as stator current error signal; Expressed as α Shaft stator current error signal; Expressed as β Shaft stator current error signal; sign() represents the sign function; and All are expressed as control gains;

[0080] Among them, Figure 3 As shown in the figure, the specific process of Savitzky-Golay filtering and adaptive noise threshold using current error differential is introduced. First, determine whether the 5-point window data of the Savitzky-Golay filter and the coefficients of the Savitzky-Golay filter have been initialized; when the judgment result is yes, obtain the stator current error signal ; When the judgment result is no, continue to initialize the 5-point window data of the Savitzky-Golay filter and the coefficients of the Savitzky-Golay filter. After the 5-point window data of the Savitzky-Golay filter and the coefficients of the Savitzky-Golay filter are initialized, the stator current error signal is obtained. ; Update the buffer again, the purpose is to make the buffer store the latest stator current error signal data; then use the Savitzky-Golay filter (SG filter for short) to filter the stator current error signal stored in the buffer, the purpose is to effectively smooth the current error signal and reduce the amplification of high-frequency noise in the derivation process; then calculate the absolute value of the stator current error signal data difference; then combine the adaptive noise threshold mechanism to update the exponentially weighted moving average of the absolute value of the differential; then determine whether the current differential exceeds the noise threshold (the noise threshold is the threshold defined by EMA and the sensitivity factor product of EMA); if the current differential exceeds the threshold and sensitivity factor defined by EMA The product of the previous stator current error signal is retained. The differential output value; if the current differential does not exceed the threshold and sensitivity factor defined by EMA The stator current error signal is then used The current value of the differential; then update the previous value of the stator current error signal; finally output the stator current error signal The differential output value of the stator current error signal is obtained The algorithm for the differential output value of the current estimation error is executed. The algorithm uses a 5-point sliding window to approximate the first-order derivative of the current estimation error, and uses the pre-calculated Savitzky-Golay coefficient to weighted sum the latest 5 error samples in the buffer. To further suppress sudden noise interference, the algorithm introduces an adaptive noise threshold mechanism based on exponentially weighted moving average: the noise threshold is dynamically adjusted by tracking the average absolute value of the current error derivative, and the current derivative estimate is compared with the threshold, thereby effectively suppressing the amplification effect of high-frequency noise on the derivative calculation, while detecting and suppressing sudden noise interference, improving the accuracy and stability of current derivative estimation.

[0081] That is, obtain the stator current error signal The process of differential output value includes:

[0082] Defining the stator current error signal The differential expression of is:

[0083] (7)

[0084] In formula (7), It is represented as the Savitzky-Golay filter i coefficients; Represents the first i The most recent current estimation error samples;

[0085] Combined with the adaptive noise threshold mechanism, the exponentially weighted moving average (EMA) of the absolute value of the differential is calculated to estimate the average rate of change of the current error; the expression of the exponentially weighted moving average of the absolute value of the differential is:

[0086] (8)

[0087] In formula (8), Expressed as a smoothing factor; Represents the exponentially weighted moving average calculated at the current moment, Indicated as at the last moment t-1 The calculated exponentially weighted moving average; t Expressed as time;

[0088] If the current differential exceeds the threshold and sensitivity factor defined by EMA The product of the previous stator current error signal is retained. The differential output value of the stator current error signal The expression of the differential output value is:

[0089] (9)

[0090] In formula (9), Expressed as sensitivity factor;

[0091] Step S3: Design an adaptive gain ;

[0092] Step S4: Based on adaptive gain , the expression of the extended equation, and the high-order terminal sliding surface Function expression of the current signal control law of the high-order terminal sliding surface is designedZ i and back EMF signal control rate ; Wherein, the current signal control law Z i The function expression is:

[0093] (10)

[0094] In formula (7), Represented as an intermediate variable; g and k All are expressed as control gains;

[0095] The back EMF signal controls the rate The function expression is:

[0096] (11)

[0097] In formula (11), Expressed as α Part of the axis control law; Expressed as β Part of the axis control law; Expressed as α-β Part of the axis control law; The value of is 0.001; a It is expressed as control gain;

[0098] Step S5: Based on Lyapunov's stability theorem, the adaptive gain is obtained and control gain k The constraints of the adaptive gain and control gain k The constraint expression is:

[0099] (12)

[0100] In formula (12), Expressed as α Axis control gain intermediate variable; Expressed as β Axis control variable intermediate gain; Expressed as an estimate; is the estimated error of angular velocity; Expressed as an estimate of the electrical angular velocity; Expressed as the actual value of electrical angular velocity; for t The electrical angular velocity of the permanent magnet synchronous motor observed at any moment; is the estimation error of back EMF; Expressed as βAxis back-EMF estimation error; Expressed as t time β Axis back-EMF estimation error; Expressed as t time α Axis back-EMF estimation error; Expressed as β Axis back EMF estimate; Expressed as t Moment α Axial synovial surface function; Expressed as t Moment β Axial synovial surface function; g is represented as the control gain; D is represented as the upper limit of the current differential error; and D satisfies:

[0101] (13)

[0102] Step S6: Define adaptive gain The expression of the adaptive gain The expression is:

[0103] (14)

[0104] In formula (14), is the adaptive gain exist t 0 The value of the moment;

[0105] Step S7: The current signal control law of the high-order terminal sliding surface Z i and back EMF signal control rate Combined with the above, an adaptive high-order terminal sliding mode observer is designed; the expression of the adaptive high-order terminal sliding mode observer is:

[0106] (15)

[0107] In formula (15), ; Expressed as the estimated electrical angular velocity The relevant state matrix; Expressed as α-β Estimated value of stator current in two-phase stationary coordinate system; Expressed as α-β Estimated value of back EMF in two-phase stationary coordinate system;

[0108] Step S8: Obtain the observed electrical angular velocity based on the orthogonal component phase-locked loop method and the observed rotor electrical angle;

[0109] Step S9: Control the operation of the permanent magnet synchronous motor based on field oriented control and space vector pulse width modulation.

[0110] In this embodiment, a permanent magnet synchronous motor (PMSM) uses a permanent magnet material as a rotor to excite and establish a main magnetic field, and the rotor rotation speed is the same as the speed of the rotating magnetic field generated by the stator winding. In a specific embodiment, the permanent magnet synchronous motor is a surface mounted permanent magnet synchronous motor.

[0111] In this embodiment, in step S8, Figure 4 As shown, the extraction of rotor position and speed is achieved by using quadrature component phase-locked loop (Q-PLL) technology. The back electromotive force observed by the observer is used as the input of the phase-locked loop, and the observed motor rotor position and speed are output.

[0112] The structure of the phase-locked loop based on the improved orthogonal component is as follows Figure 4 As shown, K p and K i Represent the proportional and integral gains of the PI controller respectively. and is the quadrature input signal. 1 / s represents the differential link. represents the estimated rotor position. represents the error function input to the PI controller; x In the figure it is shown ;

[0113] Compared with the traditional Q-PLL method, the speed signal estimated by the improved Q-PLL method contains the estimated back-EMF signal and , so the speed information can be obtained through Figure 4 The process is estimated naturally.

[0114] In this embodiment, in step S9, the operation of the permanent magnet synchronous motor is controlled based on field oriented control (FOC) and space vector pulse width modulation (SVPWM). Figure 2 As shown, the entire control strategy adopts a vector control strategy. Both the speed outer loop and the current inner loop use PI controllers for tracking control. The adaptive high-order terminal sliding mode observer and phase-locked loop technology are used to replace the use of sensors in traditional vector control. At this time, the rotor position and speed are obtained by the designed algorithm.

[0115] Figure 2 middle , Expressed as α-β Stator current in two-phase stationary coordinate system; , Expressed as α-β Stator voltage in two-phase stationary coordinate system; ; , Expressed as α-β Back EMF in a two-phase stationary coordinate system; Expressed as α Axial synovial surface function; Expressed as β Axial synovial surface function; Expressed as α Shaft stator current error signal; Expressed as β Shaft stator current error signal; sign() represents the sign function; and All are expressed as control gains; Z i The current signal control law representing the high-order terminal sliding surface; Indicates the back-EMF signal control rate.

[0116] in, ;

[0117] ;

[0118] represents adaptive gain; g and k All are expressed as control gains; , Represented as an intermediate variable; is the estimated error of angular velocity; for t The electrical angular velocity of the permanent magnet synchronous motor observed at any moment; represents the estimated rotor position; is the estimation error of back EMF; , Respectively expressed as α-β Estimated value of electron current in two-phase stationary coordinate system; , Respectively expressed as α-β Estimated value of back EMF in the two-phase stationary reference frame.

[0119] In this embodiment, the adaptive high-order terminal sliding mode observer control method of a permanent magnet synchronous motor of the present invention provides a motor speed control system control scheme that combines an adaptive gain adjustment mechanism (GA-HOTSMO for short) and a robust current error differential estimation method. Specifically, the adaptive gain adjustment mechanism significantly improves the anti-disturbance capability of the motor speed control system under dynamic conditions by introducing an adaptive gain adjustment mechanism. When the system load or speed undergoes a transient change, the gain coefficient can be adaptively adjusted according to the system state, so that the system can quickly adapt to external disturbances, quickly restore steady-state output, reduce the impact of jitter, and achieve finite time convergence. Compared with the traditional sliding mode controller method, the present invention significantly reduces the jitter problem caused by sudden changes, and achieves finite time convergence, so that the control system can maintain robustness and high-precision output under high dynamic response requirements.

[0120] Specifically, the robust current error differential estimation method combines Savitzky-Golay filtering with adaptive noise thresholding, which can accurately estimate the current error differential and smooth the error signal. Through this filtering strategy, the present invention avoids the problem of amplifying high-frequency noise in traditional differential methods, thereby achieving high-precision control output under steady-state conditions. This method not only improves the smoothing performance of the system in steady-state operation, but also effectively suppresses sudden noise interference while maintaining signal characteristics, thereby improving the accuracy and stability of differential estimation.

[0121] The design of the present invention has significant advantages in enhancing the steady-state performance of sliding mode control. Specifically, the adaptive gain adjustment mechanism automatically reduces the gain when the system state is close to the sliding mode surface, thereby effectively suppressing chattering, and at the same time increases the gain in time when the system state deviates from the steady state to enhance the stability of the system. Through reasonable parameter selection, the present invention achieves a balance between the dynamic response speed and the steady-state accuracy of the system, ensuring that the system can converge quickly and maintain smooth control in a stable state, thereby improving the overall reliability and control accuracy of the system.

[0122] In summary, the present invention proposes an adaptive high-order terminal sliding mode observer control method for a permanent magnet synchronous motor. The core of this implementation method is to design an adaptive gain control law that can adjust the control gain in real time according to the system state, thereby effectively reducing the impact of jitter and achieving finite time convergence during system operation. Furthermore, the implementation method can automatically adjust the gain parameters under different working conditions, suppressing control jitter while ensuring system stability. In addition, the designed robust current estimation method can accurately estimate the current error differential and suppress sudden noise interference, thereby improving the accuracy and stability of differential estimation.

[0123] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A permanent magnet synchronous motor adaptive high-order terminal sliding mode observer control method, characterized in that: include: Step S1: Establish a permanent magnet synchronous motor α-β The extended equation in the two-phase stationary coordinate system; wherein the expression of the extended equation is: （1） In formula (1), ; , Expressed as α-β Stator current in two-phase stationary coordinate system; ; , Expressed as α-β Stator voltage in two-phase stationary coordinate system; ; , Expressed as α-β Back EMF in a two-phase stationary coordinate system; ; ; ; It is represented as the electrical angular velocity of the permanent magnet synchronous motor; It is represented as a state matrix related to the stator inductance and stator resistance; It is represented as a state matrix related to the stator inductance; It is represented as a state matrix related to the electrical angular velocity; Represented as a system state matrix; Represented as the input matrix, Indicates stator voltage u How does it affect current? i ; Represented as a 2×2 matrix; in, The expression is: （2） The expression is: （3） In formula (2) and formula (3), is the stator inductance, is the stator resistance; Represented as a 2×2 matrix; The expression is: （4） The expression is: （5） Step S2: Based on the extended equation, a high-order terminal sliding surface is designed ; Wherein, the high-order terminal sliding surface The function expression is: （6） In formula (6), Expressed as α Axial synovial surface function; Expressed as β Axial synovial surface function; Represented as stator current error signal; Expressed as α Shaft stator current error signal; Expressed as β Shaft stator current error signal; sign() represents the sign function; and All are expressed as control gains; Wherein, the stator current error signal is obtained The process of differential output value includes: Defining the stator current error signal The differential expression of is: （7） In formula (7), It is represented as the Savitzky-Golay filter i coefficients; Represents the first i The most recent current estimation error samples; Combined with the adaptive noise threshold mechanism, the exponentially weighted moving average of the absolute value of the differential is calculated; the expression of the exponentially weighted moving average of the absolute value of the differential is: （8） In formula (8), Expressed as a smoothing factor; Represents the exponentially weighted moving average calculated at the current moment, Indicated as at the last moment t- 1The exponentially weighted moving average calculated; t Expressed as time; If the current differential exceeds the threshold and sensitivity factor defined by EMA The product of the previous stator current error signal is retained. The differential output value of the stator current error signal The expression of the differential output value is: （9） In formula (9), Expressed as sensitivity factor; Step S3: Design an adaptive gain ; Step S4: Based on the adaptive gain , the expression of the extended equation, and the high-order terminal sliding surface The function expression of the current signal control law of the high-order terminal sliding surface is designed. Z i and back EMF signal control rate ; Wherein, the current signal control law Z i The function expression is: （10） In formula (7), Represented as an intermediate variable; g and k All are expressed as control gains; The back EMF signal controls the rate The function expression is: （11） In formula (11), Expressed as α Part of the axis control law; Expressed as β Part of the axis control law; Expressed as α-β Part of the axis control law; is represented as a positive number; a Expressed as control gain; Step S5: Based on Lyapunov's stability theorem, the adaptive gain is obtained and control gain k The constraints of the adaptive gain and control gain k The constraint expression is: （12） In formula (12), Expressed as α Axis control gain intermediate variable; Expressed as β Axis control variable intermediate gain; Expressed as an estimate; is the estimated error of angular velocity; Expressed as an estimate of the electrical angular velocity; Expressed as the actual value of electrical angular velocity; for t The electrical angular velocity of the permanent magnet synchronous motor observed at any moment; is the estimation error of back EMF; Expressed as β Axis back-EMF estimation error; Expressed as t time β Axis back-EMF estimation error; Expressed as t time α Axis back-EMF estimation error; Expressed as β Axis back EMF estimate; Expressed as t Moment α Axial synovial surface function; Expressed as t Moment β Axial synovial surface function; g is represented as the control gain; D is represented as the upper limit of the current differential error; and D satisfies: （13） Step S6: Define adaptive gain The expression of the adaptive gain The expression is: （14） In formula (14), is the adaptive gain exist t 0 The value of the moment; Step S7: The current signal control law of the high-order terminal sliding surface Z i and back EMF signal control rate Combined with the above, an adaptive high-order terminal sliding mode observer is designed; the expression of the adaptive high-order terminal sliding mode observer is: （15） In formula (15), ; Expressed as the estimated electrical angular velocity The relevant state matrix; Expressed as α-β Estimated value of stator current in two-phase stationary coordinate system; Expressed as α-β Estimated value of back EMF in two-phase stationary coordinate system; Step S8: Obtain the observed electrical angular velocity based on the orthogonal component phase-locked loop method and the observed rotor electrical angle; Step S9: controlling the operation of the permanent magnet synchronous motor based on field oriented control and space vector pulse width modulation.

2. The method for controlling a permanent magnet synchronous motor with an adaptive high-order terminal sliding mode observer according to claim 1, characterized in that: The permanent magnet synchronous motor is a surface mounted permanent magnet synchronous motor.

3. The method for controlling a permanent magnet synchronous motor with an adaptive high-order terminal sliding mode observer according to claim 1 or 2, characterized in that: The value of is 0.001.

Images