Pmsm sliding mode control method based on pl-leso and improved reaching law

Abstract

The application discloses a PMSM sliding mode control method based on PL-LESO and improved approaching law, belongs to the field of electronic control technology, and specifically comprises the following steps: constructing a mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system; introducing an error correlation variable gain and a smooth switching function to construct a new type of exponential approaching law based on a speed error state and a sliding mode principle, so as to obtain a low-chatter sliding mode speed controller; connecting a lead correction network in series in a disturbance output channel of a traditional second-order linear extended state observer, so as to obtain a phase-lead linear extended state observer PL-LESO; and feeding a disturbance estimation value to a speed controller for dynamic compensation, so as to form a composite anti-disturbance sliding mode control system. The method can effectively suppress the chattering of the sliding mode control, improve the phase lag problem of disturbance estimation, and improve the dynamic quality, steady-state accuracy and anti-disturbance performance of the system.

Description

Technical Field

[0001] This invention relates to the field of electronic control technology, and in particular to a PMSM sliding mode control method based on PL-LESO and an improved reaching law. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs), with their high efficiency, high power density, and excellent dynamic performance, have become one of the mainstream motors in modern electric drive fields, widely used in industrial drives, new energy vehicles, home appliances, and precision servo systems. Addressing the high-precision and robust control requirements of PMSMs, sliding mode control, as a typical nonlinear variable structure control method, constructs a sliding surface and switches control laws to drive the system state to converge and slide along the sliding surface. It possesses inherent robustness to system parameter perturbations and external disturbances, making it a core technology direction for improving PMSM control performance. Simultaneously, disturbance estimation and compensation technology based on extended state observers, by uniformly expanding system model uncertainties, parameter changes, and external disturbances into new state variables, achieves real-time estimation and dynamic compensation without relying on a precise mathematical model of the controlled object. This is a general technical path for handling nonlinear uncertain system control problems.

[0003] However, in practical applications, sliding mode control is limited by the discontinuous nature of the switching function, which can cause high-frequency oscillations in the control signal. This can lead to torque pulsation and mechanical vibration in the motor, which can weaken the control accuracy and operational stability of the system, as well as adversely affect the service life and user experience of the equipment. Furthermore, traditional second-order linear extended state observers have an inherent phase lag characteristic in the disturbance estimation process. The dynamic response of their disturbance estimates lags behind the actual disturbance, which reduces the system's tracking accuracy for fast time-varying disturbances and its ability to suppress high-frequency disturbances. This prevents the system from fully utilizing the disturbance feedforward compensation to resist disturbances. Summary of the Invention

[0004] The purpose of this invention is to provide a PMSM sliding mode control method based on PL-LESO and an improved reaching law, thereby solving the aforementioned technical problems.

[0005] To achieve the above objectives, this invention provides a PMSM sliding mode control method based on PL-LESO and an improved reaching law, comprising the following steps: S1. Based on the three-phase electromagnetic characteristics and rigid body motion law of permanent magnet synchronous motor, the mathematical model of the motor in synchronous rotating coordinate system is obtained through coordinate transformation and equation derivation. S2. Based on the speed error state and sliding mode control principle, a new exponential reaching law is constructed by introducing error-correlated variable gain and smooth switching function to obtain a low-chattering sliding mode speed controller. S3. Based on the perturbation estimation framework of the traditional second-order linear extended state observer, phase compensation is performed by connecting a lead compensation network in series in the perturbation output channel to obtain the phase-leading linear extended state observer PL-LESO. S4. Based on the sliding mode speed controller and PL-LESO, a composite anti-disturbance sliding mode control system for permanent magnet synchronous motors is obtained by feeding the disturbance estimate forward to the speed controller for dynamic compensation.

[0006] Preferably, the specific steps of S1 include: S11. Based on the voltage and flux constraint relationship of the stator winding of the permanent magnet synchronous motor, the physical equations of the three-phase circuit are given, and the three-phase voltage equations and stator flux equations of the PMSM are obtained. S12. Based on the mapping relationship between the three-phase stationary coordinate system and the synchronous rotating coordinate system, the stator voltage equation and flux linkage equation under the dq synchronous rotating coordinate system are derived through coordinate transformation calculation. S13. Based on the electromechanical energy conversion mechanism and the rigid body rotation law, the electromagnetic torque equation and mechanical motion equation in the dq coordinate system are derived by substituting the magnetic flux expression in the coordinate system.

[0007] Preferably, the specific steps of S2 include: S21. Based on the difference between the reference speed and the actual speed, the speed loop state equation is obtained by defining the speed error state variable and differentiating it. The formula for the speed error state variable is: ; In the formula, The rotational speed error is the state variable. The reference mechanical angular velocity for PMSM; This refers to the actual mechanical angular velocity of the PMSM. The velocity loop state equation is: ; in, ; ; S22. Based on the convergence performance requirements of the sliding mode, a linear sliding function is constructed by selecting the sliding surface coefficients to obtain the linear sliding surface; The formula for a linear sliding surface is: ; In the formula, For sliding surface functions; Let be the sliding surface coefficient, satisfying ; S23. Based on the requirements of speed and smoothness in the reaching process, a new exponential reaching law is obtained by constructing an error-related variable gain term and replacing the discontinuous switching function with a hyperbolic tangent function. The expression for the error-related variable gain term is: ; in, A variable gain function is associated with the sliding mode control error; Based on the steady-state gain constant, satisfying ; Let be the gain adjustment coefficient, satisfying ; The coefficients are power coefficients, satisfying ; Let be the transition rate coefficient, satisfying ; For power-approaching gain, satisfying ; The expression for the new exponential reaching law is: ; in, The first derivative of the sliding surface function; The gain constant is exponentially approaching the linear gain constant, and satisfies... ; It is a hyperbolic tangent smoothing function; S24. Based on the matching relationship between the sliding surface derivative and the novel approaching law, the control law of the sliding speed controller is obtained by substituting the control input into the velocity loop state equation to complete the design of the sliding controller.

[0008] Preferably, S2 also includes convergence characteristic analysis and system stability analysis, specifically: Based on the convergence characteristic evaluation index of sliding mode variable, the rapid convergence and chattering suppression characteristics of the new convergence law are obtained by comparing the error convergence process with that of the traditional convergence law. Based on Lyapunov stability theory, by selecting a positive definite Lyapunov function and substituting it into a novel reaching law for differentiation verification, we obtain the stability conclusion that the sliding mode variable is globally asymptotically convergent.

[0009] Preferably, based on the positive definiteness constraint of the sliding mode variable, by selecting a quadratic Lyapunov function and substituting it into the reaching law to derive the derivative sign, a strict criterion for asymptotic stability of the system is obtained. The formula for the Lyapunov function is: ; in, For Lyapunov functions, Let be the sliding surface function; after substituting the novel exponential reaching law and taking the derivative, it satisfies This is to prove that the sliding mode variable converges asymptotically to zero globally in the continuous-time model, and that the system satisfies the asymptotic stability condition.

[0010] Preferably, the PL-LESO structure design process in S3 is as follows: based on the dynamic characteristics of the speed loop of the permanent magnet synchronous motor and the idea of ​​total disturbance expansion, a first-order lead compensation network is connected in series in the disturbance estimation output channel of the traditional second-order linear extended state observer and a time-domain transformation is performed to derive the complete time-domain mathematical model of the phase-leading linear extended state observer, and the total disturbance estimate after phase lead compensation is output.

[0011] Preferably, based on the state equation of the traditional second-order LESO and the differential relationship of the lead compensation network, the third-order time-domain state-space model of PL-LESO is obtained by simultaneously arranging the differential equations of the state variables; the model retains the speed state and original disturbance state estimation channels of the traditional LESO, adds a first-order lead compensation subsystem, and outputs the total disturbance estimate after phase compensation for feedforward compensation.

[0012] Preferably, the PL-LESO performance analysis in S3 specifically involves: using a frequency domain analysis method based on perturbation observation, deriving the transfer relationship between the observer input and the perturbation estimation output to obtain the perturbation observation transfer function of the phase-leading linear extended state observer: ; in, For the perturbation observation transfer function of a traditional second-order linear extended state observer; For the Laplace operator; , Let be the time constant of the first-order lead compensator network, and satisfy . It is used to provide positive phase compensation in the mid-frequency band to reduce the phase lag of disturbance estimation.

[0013] Preferably, the specific steps of S4 include: S41. Based on the architectural relationship between the permanent magnet synchronous motor body, sliding mode speed controller and phase-leading linear extended state observer, a composite disturbance rejection control system model is obtained by building the signal transmission links of each link. S42. Based on the total disturbance estimate output by the phase-leading linear extended state observer, the disturbance estimate is superimposed onto the control output of the sliding mode speed controller through a feedforward channel to obtain the q-axis reference current control signal after disturbance compensation, thereby realizing real-time dynamic compensation for the total disturbance of the system.

[0014] Therefore, the PMSM sliding mode control method based on PL-LESO and improved reaching law adopted in this invention has the following beneficial effects: 1. The novel exponential reaching law achieves a performance balance through a combination of error-related variable gain and hyperbolic tangent smoothing function: the error-related variable gain can adaptively adjust with the sliding mode error amplitude, maintaining a high gain during the large error stage to accelerate the convergence speed of the state to the sliding mode surface, and automatically reducing the gain during the small error stage to avoid overshoot oscillation, thereby improving the dynamic response efficiency of the system; the hyperbolic tangent function is a globally continuous and differentiable smooth function, which eliminates the high-frequency chattering caused by switching actions after replacing the traditional discontinuous sign function, and the reaching law can be rigorously proven by the Lyapunov stability criterion to achieve global asymptotic convergence of the sliding mode variable, ensuring that the speed does not fluctuate continuously during the steady-state operation of the system, and finally achieving a comprehensive improvement in the sliding mode speed controller with fast dynamic response, strong chattering suppression, and high steady-state accuracy.

[0015] 2. The phase-leading linear extended state observer achieves optimized estimation performance by cascading a first-order lead compensation network in the disturbance output channel. This structure retains the state and disturbance estimation framework of the traditional linear extended state observer, providing positive phase compensation in the mid-frequency band only through the additional lead compensation subsystem, without changing the unit tracking characteristics in the low-frequency band. Within the observer's operating frequency band, it reduces the phase lag in disturbance estimation, improving the observation response speed to fast time-varying disturbances. At the same time, the mid-frequency amplitude-frequency characteristics are closer to unity gain, improving the amplitude tracking accuracy of time-varying disturbances, and the high-frequency gain is not significantly increased, avoiding the drawback of the lead compensation circuit easily amplifying high-frequency noise, thus enhancing the real-time performance and estimation accuracy of disturbance observation.

[0016] 3. By combining improved approaching law sliding mode control with disturbance feedforward compensation from a phase-leading linear extended state observer, a composite control system for permanent magnet synchronous motors (PMSMs) with both strong robustness and high disturbance rejection capability was constructed. The sliding mode variable structure itself possesses inherent robustness to system parameter perturbations. Combined with the real-time estimation and feedforward compensation of the total disturbance by the phase-leading linear extended state observer, a dual disturbance rejection mechanism of "passive robustness + active compensation" is formed. Under no-load starting conditions, it can balance rapid start-up and stable operation. Under sudden load changes, it can effectively reduce the instantaneous speed fluctuation amplitude and shorten the speed recovery time, comprehensively improving the dynamic quality, steady-state control accuracy, and load disturbance rejection capability of the PMSM speed control system.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 A flowchart of the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by the present invention; Figure 2 The algorithm block diagram of the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention is shown.

[0019] Figure 3 A comparison diagram of chattering in the novel reaching law of the PMSM sliding mode control method based on PL-LESO and the improved reaching law provided by this invention.

[0020] Figure 4 The disturbance observation Bode plot is provided in the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention.

[0021] Figure 5 The no-load starting speed diagram of the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention.

[0022] Figure 6 The sudden load speed waveform diagram of the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by the present invention.

[0023] Figure 7 The sudden load unloading speed waveform diagram of the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by the present invention.

[0024] Figure 8 The flowchart illustrates the construction of a mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system in the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention.

[0025] Figure 9 The flowchart shows the design of a speed controller based on a novel reaching law in the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention.

[0026] Figure 10 The flowchart illustrates the construction of a phase-leading linear extended state observer in the PMSM sliding mode control method based on PL-LESO and improved reaching law provided by this invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0028] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0029] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0030] Existing sliding mode control schemes are constrained by the discontinuous characteristics of the switching function, and generally suffer from chattering problems caused by high-frequency oscillations in the control signal. This can easily lead to motor torque pulsation and mechanical vibration, weakening the system's control accuracy and operational stability, and limiting the equipment's service life and user experience. At the same time, traditional second-order linear extended state observers have inherent phase lag characteristics in the disturbance estimation process. The dynamic response of the disturbance estimate lags behind the actual disturbance, reducing the system's tracking accuracy for fast time-varying disturbances and its ability to suppress high-frequency disturbances, making it difficult to fully utilize the disturbance feedforward compensation's anti-disturbance effect.

[0031] Based on the above analysis, this invention is designed. (See appendix.) Figures 1-10 The PMSM sliding mode control method based on PL-LESO and improved reaching law includes the following steps: S1. Based on the three-phase electromagnetic characteristics and rigid body motion law of permanent magnet synchronous motor, the mathematical model of the motor in synchronous rotating coordinate system is obtained through coordinate transformation and equation derivation. The specific steps of S1 include: S11. Based on the voltage and flux constraint relationship of the stator winding of the permanent magnet synchronous motor, the physical equations of the three-phase circuit are given, and the three-phase voltage equations and stator flux equations of the PMSM are obtained. The three-phase stator voltage equations are: ; in, , , This refers to the three-phase phase voltage of the stator. , , This refers to the three-phase current of the stator; Stator phase resistance; , , For the full flux linkage of the three-phase stator windings; The stator flux linkage equation is: ; In the formula, , , The self-inductance of the three-phase stator windings; , , , , , For the mutual inductance between the three-phase stator windings; For permanent magnet flux linkage; The rotor electrical angle is given.

[0032] S12. Based on the mapping relationship between the three-phase stationary coordinate system and the synchronous rotating coordinate system, the stator voltage equation and flux linkage equation under the dq synchronous rotating coordinate system are derived through coordinate transformation calculation. The stator voltage equation in the dq synchronous rotating coordinate system is: ; in, , These are the d-axis and q-axis stator voltages, respectively. , These are the d-axis and q-axis stator currents, respectively. , These are the stator flux linkages along the d and q axes, respectively. For the rotor's electric angular velocity, and for the coupling term introduced by the rotating coordinate transformation; The stator flux linkage equation in the dq coordinate system is: ; in, , These are the d-axis and q-axis stator inductances, respectively.

[0033] S13. Based on the electromechanical energy conversion mechanism and the rigid body rotation law, the electromagnetic torque equation and mechanical motion equation in the dq coordinate system are derived by substituting the magnetic flux expression in the coordinate system.

[0034] The electromagnetic torque equation in the dq coordinate system is: ; in, Electromagnetic torque; This represents the number of pole pairs of the motor. The mechanical motion equation of the rotor is: ; in, This is the moment of inertia of the motor shaft; This refers to the rotor's mechanical angular velocity; This is the load torque; is the coefficient of viscous friction.

[0035] S2. Based on the speed error state and sliding mode control principle, a new exponential reaching law is constructed by introducing error-correlated variable gain and smooth switching function to obtain a low-chattering sliding mode speed controller. The specific steps of S2 include: S21. Based on the difference between the reference speed and the actual speed, the speed loop state equation is obtained by defining the speed error state variable and differentiating it. Specifically, the system's state variables are taken as: ; in, The rotational speed error is the state variable. Assuming the PMSM reference mechanical angular velocity is a piecewise constant signal, and considering that the speed command is within each constant value interval, there are... ; This refers to the actual mechanical angular velocity of the PMSM. right Differentiating and rearranging the equations of motion of the rotor, we obtain the velocity loop state equations: ; in, ; .

[0036] S22. Based on the convergence performance requirements of the sliding mode, a linear sliding function is constructed by selecting the sliding surface coefficients to obtain the linear sliding surface; The formula for a linear sliding surface is: ; in, For sliding surface functions; Let be the sliding surface coefficient, satisfying Its value determines the convergence speed of the sliding mode.

[0037] S23. Based on the requirements of speed and smoothness in the reaching process, a new exponential reaching law is obtained by constructing an error-related variable gain term and replacing the discontinuous switching function with a hyperbolic tangent function. The expression for the error-related variable gain term is: ; in, A variable gain function is associated with the sliding mode control error; Based on the steady-state gain constant, satisfying ; Let be the gain adjustment coefficient, satisfying ; The coefficients are power coefficients, satisfying ; Let be the transition rate coefficient, satisfying ; For power-approaching gain, satisfying ; The expression for the new exponential reaching law is: ; in, The first derivative of the sliding surface function; The gain constant is exponentially approaching the linear gain constant, and satisfies... ; The hyperbolic tangent smoothing function is defined by its standard definition. The function output range is ,exist It is continuously differentiable at any point and has no abrupt transitions.

[0038] See Figure 3 As shown, this novel approach law has the characteristic of adaptive error adjustment: when the sliding mode error amplitude is large, the variable gain is maintained at a high level, driving the system state to quickly approach the sliding mode surface; when the sliding mode error amplitude is small, the variable gain decays smoothly, and with the globally continuous and differentiable hyperbolic tangent function, it eliminates the discontinuous jumps caused by the traditional sign function, suppresses high-frequency chattering from the root, and makes the system state stabilize near zero after convergence, without continuous steady-state fluctuations.

[0039] S24. Based on the matching relationship between the sliding surface derivative and the novel approaching law, the control law of the sliding speed controller is obtained by substituting the control input into the velocity loop state equation to complete the design of the sliding controller.

[0040] S2 also includes convergence characteristic analysis and system stability analysis, specifically: Based on the convergence characteristic evaluation index of sliding mode variable, the rapid convergence and chattering suppression characteristics of the new convergence law are obtained by comparing the error convergence process with that of the traditional convergence law. Based on Lyapunov stability theory, by selecting a positive definite Lyapunov function and substituting it into a novel reaching law for differentiation verification, we obtain the stability conclusion that the sliding mode variable is globally asymptotically convergent.

[0041] Based on the positive definiteness constraint of sliding mode variables, by selecting a quadratic Lyapunov function and substituting it into the reaching law to derive the derivative sign, a strict criterion for asymptotic stability of the system is obtained. The formula for the Lyapunov function is: ; in, For Lyapunov functions, Let be the sliding surface function; after substituting the novel exponential reaching law and taking the derivative, it satisfies This is to prove that the sliding mode variable converges asymptotically to zero globally in the continuous-time model, and that the system satisfies the asymptotic stability condition.

[0042] The stability derivation process is as follows: Obviously, when From time to time , and when hour ,therefore For sliding mode variables A positive definite function.

[0043] Differentiating with respect to V, we get: ; Substituting the new approach law into the above equation, we have: according to The definition, when the parameters satisfy , , , , Time, always ; Therefore, we can conclude that: ; when hour, This is true. This indicates that the Lyapunov function is monotonically non-increasing along the system trajectory. Therefore, the constructed reaching law can guarantee that the sliding mode variable converges asymptotically to zero globally under the continuous-time ideal model, thereby making the system state asymptotically approach the designed sliding surface.

[0044] To further obtain an engineering-feasible sliding mode control law, system parameters and control inputs are defined based on the dynamic characteristics of the velocity loop: ; in, To control the gain coefficient, This is the system control input. Therefore, the state equation of the velocity loop system is: ; To improve the convergence speed of the system state and ensure smoothness near the sliding surface, a linear sliding surface is selected as: ; Differentiating the above equation and substituting the velocity loop state equation, we get: ; To ensure the system satisfies the novel reaching law, the sliding surface derivative must be equal to the reaching law expression: ; By refining and solving for the control input, the sliding mode control law can be obtained: ; Since the control input is defined as Therefore, the final q-axis reference current output by the speed loop is: .

[0045] S3. Based on the perturbation estimation framework of the traditional second-order linear extended state observer, phase compensation is performed by connecting a lead compensation network in series in the perturbation output channel to obtain the phase-leading linear extended state observer PL-LESO. The PL-LESO structure design process in S3 is as follows: Based on the dynamic characteristics of the speed loop of the permanent magnet synchronous motor and the idea of ​​total disturbance expansion, a first-order lead compensation network is connected in series in the disturbance estimation output channel of the traditional second-order linear extended state observer and a time-domain transformation is performed to derive the complete time-domain mathematical model of the phase-leading linear extended state observer, and the total disturbance estimate after phase lead compensation is output.

[0046] Based on the state equation of the traditional second-order LESO and the differential relationship of the lead compensation network, the third-order time-domain state-space model of PL-LESO is obtained by simultaneously rearranging the differential equations of the state variables. The model retains the speed state and original disturbance state estimation channels of the traditional LESO, and adds a first-order lead compensation subsystem to output the total disturbance estimate after phase compensation for feedforward compensation.

[0047] The traditional second-order LESO based on the PMSM velocity loop is: ; in, These are the observed values ​​for the rotational speed error status; The original total disturbance observations output by the traditional second-order LESO include all system uncertainties such as motor parameter perturbations, external load disturbances, and unmodeled dynamics. The speed loop system control gain constant; The actual output observations of the velocity loop system; , These are the two sets of observation gain coefficients for a second-order linear extended state observer.

[0048] Based on this, the lead compensation network is connected in series with the disturbance estimation output channel to obtain the corrected disturbance estimate. The formula is: ; in, Let be the lead time constant of the first-order lead compensator network; For the Laplace operator; The attenuation coefficient of the lead compensation network satisfies ; Transforming the above equation to the time domain, we get: ; Traditional LESO equations include: ; Therefore, it can be further written as: ; After sorting, we can obtain: ; Therefore, the complete mathematical model of PL-LESO can be expressed as: ; As can be seen from this model, PL-LESO does not change the estimation structure of the state and the original perturbation in traditional LESO, but rather... Based on this, a first-order lead correction subsystem is added, thus forming a tandem observation structure of traditional LESO and phase lead network.

[0049] The PL-LESO performance analysis in S3 specifically involves: using a frequency domain analysis method based on perturbation observations, and deriving the transfer relationship between the observer input and the perturbation estimation output, to obtain the perturbation observation transfer function of the phase-leading linear extended state observer. ; in, For the perturbation observation transfer function of a traditional second-order linear extended state observer; For the Laplace operator; , Let be the time constant of the first-order lead compensator network, and satisfy . It is used to provide positive phase compensation in the mid-frequency band to reduce the phase lag of disturbance estimation.

[0050] The derivation of the transfer function is as follows: The observation error is defined as: ; According to the second form of traditional LESO, we have: ; Substituting, we get: ; On the other hand, the difference between the extended system state equation and the observer equation yields: ; Summarized as follows: ; Substituting the previous expression into the previous one, eliminate... We can obtain: ; After further processing, the perturbation observation transfer function of the traditional second-order LESO is obtained as follows: ; Combining the lead compensation relation, the perturbation observation transfer function of PL-LESO can be obtained as follows: ; As can be seen from the above equation, the essential difference between PL-LESO and traditional LESO lies in the addition of a phase lead network to its disturbance estimation channel. This network does not change the basic characteristics of unit tracking in the low-frequency band, but it can provide positive phase compensation in the mid-frequency band, thereby effectively improving the dynamic lag of disturbance estimation.

[0051] The observer bandwidth and lead compensation parameter are set. Specifically, the observer bandwidth is 100 rad / s and the lead compensation parameter is 0.66. Bode plots for the two sets of observers are drawn as follows. Figure 4 As shown. Within the observer's operating frequency band, the phase lag of PL-LESO is smaller than that of traditional LESO. At 250 rad / s, the phase lag of traditional LESO is about 90°, while that of PL-LESO is only about 35°, with a phase compensation of 55°. The phase compensation effect is significant, improving the observation response speed to fast time-varying disturbances. The amplitude-frequency characteristics of PL-LESO are closer to 0 dB in the mid-frequency band, resulting in higher amplitude tracking accuracy for disturbances. This effectively reduces the steady-state error of observations under time-varying disturbances and optimizes the amplitude tracking characteristics. In the high-frequency band, the amplitude-frequency characteristics of PL-LESO and traditional LESO show a similar attenuation trend, without significant high-frequency gain amplification. Through reasonable parameter tuning, the inherent defects of the lead compensation stage are effectively suppressed.

[0052] S4. Based on the sliding mode speed controller and PL-LESO, a composite anti-disturbance sliding mode control system for permanent magnet synchronous motors is obtained by feeding the disturbance estimate forward to the speed controller for dynamic compensation.

[0053] The specific steps of S4 include: S41. Based on the architectural relationship between the permanent magnet synchronous motor body, sliding mode speed controller and phase-leading linear extended state observer, a composite disturbance rejection control system model is obtained by building the signal transmission links of each link. See the overall block diagram of the ESMC system based on PL-LESO and a novel reaching law. Figure 2 As shown in Table 1, typical parameters of a permanent magnet synchronous motor are as follows: Table 1 PMSM Parameter Table

[0054] S42. Based on the total disturbance estimate output by the phase-leading linear extended state observer, the disturbance estimate is superimposed onto the control output of the sliding mode speed controller through a feedforward channel to obtain the q-axis reference current control signal after disturbance compensation, thereby realizing real-time dynamic compensation for the total disturbance of the system.

[0055] In the embodiments of the present invention, the system control performance is verified through three typical operating conditions: 1. No-load start condition: The motor is started under no-load conditions, with a given speed of 1500 r / min. The starting dynamic response performance, control speed, and overshoot suppression capability of the new control method are verified. The no-load start speed waveforms of the three control methods are shown below. Figure 5 As shown in the simulation results, under the no-load starting condition of the motor, the ESMC+PL-LESO control strategy further improves the speed tracking accuracy and running stability while maintaining the rapid starting capability; all three methods can complete the no-load start in a short time, and ESMC+PL-LESO still maintains a fast dynamic response.

[0056] 2. Sudden Load Condition: The motor operates in steady-state no-load mode at 1500 r / min, and a rated load of 0.64 N·m is suddenly applied in 0.3 s to verify the load disturbance rejection performance of the new control method and the disturbance suppression effect of feedforward compensation. The speed waveforms of the three control methods under the sudden load are shown below. Figure 6 As shown in the simulation results, after a sudden load application, all three methods exhibit an instantaneous speed drop. However, ESMC+PL-LESO recovers to 1500 r / min faster than ESMC and ESMC+LESO, with almost no overshoot. The simulation results of the sudden load application demonstrate that phase lead correction effectively reduces the estimation lag of traditional LESO, improving the timeliness of feedforward compensation and load disturbance rejection performance.

[0057] 3. Sudden Load Removal Condition: The rated load is suddenly removed in 0.8 seconds. The speed waveforms under the three control methods during this condition are as follows: Figure 7 As shown in the simulation results, after a sudden load unloading, the speed of all three control strategies experiences a momentary surge. However, the ESMC+PL-LESO control strategy performs best in terms of overshoot suppression and recovery speed. The overshoot is significantly reduced compared to ESMC and ESMC+LESO, and the recovery to the given speed is faster. The simulation results of sudden load unloading show that PL-LESO effectively reduces the compensation lag of traditional LESO, improving the system's disturbance rejection recovery capability and dynamic stability.

[0058] In summary, this invention designs a sliding mode speed controller by constructing a novel exponential reaching law containing an error-correlated variable gain and a hyperbolic tangent smoothing function. This ensures the system state rapidly approaches the sliding surface while eliminating high-frequency chattering caused by discontinuous switching at its source, thus improving the system's steady-state control accuracy and operational stability. Simultaneously, by connecting a first-order lead compensation network in series with the disturbance output channel of a traditional second-order linear extended state observer, a phase-leading linear extended state observer is constructed. This effectively compensates for the phase lag in disturbance estimation without altering the low-frequency unit tracking characteristics or amplifying high-frequency noise, improving the tracking accuracy and response speed to time-varying disturbances. The combined architecture forms a composite disturbance rejection control system that combines the inherent robustness of sliding mode control to parameter perturbations with the active compensation capability of disturbance observation feedforward. This comprehensively improves the dynamic response quality, steady-state operational stability, and load disturbance suppression capability of the motor speed control system, better adapting to the control requirements of high-precision servo and industrial drive scenarios.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A PMSM sliding mode control method based on PL-LESO and improved reaching law, characterized in that, Includes the following steps: S1. Based on the three-phase electromagnetic characteristics and rigid body motion law of permanent magnet synchronous motor, the mathematical model of the motor in synchronous rotating coordinate system is obtained through coordinate transformation and equation derivation. S2. Based on the speed error state and sliding mode control principle, a new exponential reaching law is constructed by introducing error-correlated variable gain and smooth switching function to obtain a low-chattering sliding mode speed controller. S3. Based on the perturbation estimation framework of the traditional second-order linear extended state observer, phase compensation is performed by connecting a lead compensation network in series in the perturbation output channel to obtain the phase-leading linear extended state observer PL-LESO. S4. Based on the sliding mode speed controller and PL-LESO, a composite anti-disturbance sliding mode control system for permanent magnet synchronous motors is obtained by feeding the disturbance estimate forward to the speed controller for dynamic compensation.

2. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 1, characterized in that: The specific steps of S1 include: S11. Based on the voltage and flux constraint relationship of the stator winding of the permanent magnet synchronous motor, the physical equations of the three-phase circuit are given, and the three-phase voltage equations and stator flux equations of the PMSM are obtained. S12. Based on the mapping relationship between the three-phase stationary coordinate system and the synchronous rotating coordinate system, the stator voltage equation and flux linkage equation under the dq synchronous rotating coordinate system are derived through coordinate transformation calculation. S13. Based on the electromechanical energy conversion mechanism and the rigid body rotation law, the electromagnetic torque equation and mechanical motion equation in the dq coordinate system are derived by substituting the magnetic flux expression in the coordinate system.

3. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 1, characterized in that: The specific steps of S2 include: S21. Based on the difference between the reference speed and the actual speed, the speed loop state equation is obtained by defining the speed error state variable and differentiating it. The formula for the speed error state variable is: ； In the formula, The speed error state variable; The reference mechanical angular velocity for PMSM; This refers to the actual mechanical angular velocity of the PMSM. The velocity loop state equation is: ； in, ; ; S22. Based on the convergence performance requirements of the sliding mode, a linear sliding function is constructed by selecting the sliding surface coefficients to obtain the linear sliding surface; The formula for a linear sliding surface is: ； In the formula, For sliding surface functions; Let be the sliding surface coefficient, satisfying ; S23. Based on the requirements of speed and smoothness in the reaching process, a new exponential reaching law is obtained by constructing an error-related variable gain term and replacing the discontinuous switching function with a hyperbolic tangent function. The expression for the error-related variable gain term is: ； in, A variable gain function is associated with the sliding mode control error; Based on the steady-state gain constant, satisfying ; Let be the gain adjustment coefficient, satisfying ; The coefficients are power coefficients, satisfying ; For the transition rate coefficient, satisfying ; For power-approaching gain, satisfying ; The expression for the new exponential reaching law is: ； in, The first derivative of the sliding surface function; For an exponentially approaching linear gain constant, and satisfying ; It is a hyperbolic tangent smoothing function; S24. Based on the matching relationship between the sliding surface derivative and the novel approaching law, the control law of the sliding speed controller is obtained by substituting the control input into the velocity loop state equation to complete the design of the sliding controller.

4. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 3, characterized in that: S2 also includes convergence characteristic analysis and system stability analysis, specifically: Based on the convergence characteristic evaluation index of sliding mode variable, the rapid convergence and chattering suppression characteristics of the new convergence law are obtained by comparing the error convergence process with that of the traditional convergence law. Based on Lyapunov stability theory, by selecting a positive definite Lyapunov function and substituting it into a novel reaching law for differentiation verification, we obtain the stability conclusion that the sliding mode variable is globally asymptotically convergent.

5. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 4, characterized in that: Based on the positive definiteness constraint of sliding mode variables, by selecting a quadratic Lyapunov function and substituting it into the reaching law to derive the derivative sign, a strict criterion for asymptotic stability of the system is obtained. The formula for the Lyapunov function is: ； in, For Lyapunov functions, Let be the sliding surface function; after substituting the novel exponential reaching law and taking the derivative, it satisfies This is to prove that the sliding mode variable converges asymptotically to zero globally in the continuous-time model, and that the system satisfies the asymptotic stability condition.

6. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 1, characterized in that: The PL-LESO structure design process in S3 is as follows: Based on the dynamic characteristics of the speed loop of the permanent magnet synchronous motor and the idea of ​​total disturbance expansion, a first-order lead compensation network is connected in series in the disturbance estimation output channel of the traditional second-order linear extended state observer and a time-domain transformation is performed to derive the complete time-domain mathematical model of the phase-leading linear extended state observer, and the total disturbance estimate after phase lead compensation is output.

7. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 6, characterized in that: Based on the state equation of the traditional second-order LESO and the differential relationship of the lead compensation network, the third-order time-domain state-space model of PL-LESO is obtained by simultaneously rearranging the differential equations of the state variables. The model retains the speed state and original disturbance state estimation channels of the traditional LESO, and adds a first-order lead compensation subsystem to output the total disturbance estimate after phase compensation for feedforward compensation.

8. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 6, characterized in that: The PL-LESO performance analysis in S3 specifically involves: using a frequency domain analysis method based on perturbation observations, and deriving the transfer relationship between the observer input and the perturbation estimation output, to obtain the perturbation observation transfer function of the phase-leading linear extended state observer. ； in, For the perturbation observation transfer function of a traditional second-order linear extended state observer; For the Laplace operator; , Let be the time constant of the first-order lead compensator network, and satisfy . It is used to provide positive phase compensation in the mid-frequency band to reduce the phase lag of disturbance estimation.

9. The PMSM sliding mode control method based on PL-LESO and improved reaching law according to claim 1, characterized in that: The specific steps of S4 include: S41. Based on the architectural relationship between the permanent magnet synchronous motor body, sliding mode speed controller and phase-leading linear extended state observer, a composite disturbance rejection control system model is obtained by building the signal transmission links of each link. S42. Based on the total disturbance estimate output by the phase-leading linear extended state observer, the disturbance estimate is superimposed onto the control output of the sliding mode speed controller through a feedforward channel to obtain the q-axis reference current control signal after disturbance compensation, thereby realizing real-time dynamic compensation for the total disturbance of the system.

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