A permanent magnet synchronous motor speed control method based on composite sliding mode control

Abstract

This invention discloses a speed control method for a permanent magnet synchronous motor (PMSM) based on composite sliding mode control. The method includes: constructing a mathematical model of the PMSM in a synchronous rotating coordinate system along the d-q axes; designing a layered sliding surface based on the PMSM's mathematical model; designing a hybrid reaching law incorporating a barrier function using the sliding surface; and estimating periodic and aperiodic disturbances in the PMSM's speed using a cascaded extended state observer combined with quasi-resonant control, and then performing feedforward compensation for the sliding mode control. The proposed method effectively improves the speed accuracy of the PMSM, enhances dynamic response, and provides better suppression of periodic and aperiodic disturbances.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and specifically to a method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industries such as robotics, CNC machine tools, and automobiles due to their advantages of simple structure and high reliability. However, the speed quality of PMSMs deteriorates due to various disturbances, resulting in severe periodic and non-periodic speed fluctuations, making it difficult to meet the requirements of high-precision industrial applications.

[0003] In recent years, scholars both domestically and internationally have proposed various advanced control algorithms to suppress disturbances in the speed loop, such as two-degree-of-freedom PI control, fuzzy control, adaptive control, active disturbance rejection control, and sliding mode control (SMC). Among these, sliding mode control, with its strong robustness and anti-disturbance properties, has been widely used in PMSM speed control. However, the robustness and anti-disturbance properties of SMC require a large control gain to ensure performance, which can lead to excessive chattering and severe speed fluctuations. Furthermore, traditional sliding mode control uses a linear sliding surface, and its convergence speed can only be exponential, failing to achieve fixed-time convergence. To address these issues, different improved methods have been proposed, such as observer-based sliding mode control, terminal sliding mode control (TSMC), and observer-based TSMC. Observer-based sliding mode control uses an observer to estimate the lumped disturbance and performs feedforward compensation for SMC, allowing the sliding mode control to select a smaller switching gain to reduce chattering. However, this method still uses a linear sliding surface, resulting in a slower convergence speed. TSMC uses a nonlinear sliding surface, which can guarantee convergence of the sliding state within a finite time. However, the robustness and disturbance rejection of TSMC can only be guaranteed by selecting a large control gain, which can lead to unwanted chattering. Observer-based TSMC can not only reduce chattering by suppressing disturbances using the observer, but also guarantee finite-time convergence using a nonlinear sliding surface. Therefore, this method is widely used in PMSM speed loop control. Although the above studies have achieved certain control effects, further research is needed to effectively suppress speed jitter and periodic disturbances caused by chattering in SMC.

[0004] Therefore, it is necessary to design a speed control method for permanent magnet synchronous motors based on composite sliding mode control to solve the problems existing in the current technology. Summary of the Invention

[0005] In view of this, the present invention proposes a speed control method for permanent magnet synchronous motors based on composite sliding mode control, which aims to solve the problems of speed jitter and periodic and non-periodic disturbances caused by chattering of SMC.

[0006] This invention proposes a speed control method for permanent magnet synchronous motors based on composite sliding mode control, comprising: A mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system along the dq axis is constructed, and a motor speed error model is built based on the mathematical model. The mathematical model includes stator voltage equations, electromagnetic torque equations, and motion equations of the permanent magnet synchronous motor. Based on the mathematical model of the permanent magnet synchronous motor, a layered sliding surface is designed, which includes an inner sliding surface and an outer sliding surface. The coefficients of the inner and outer sliding surfaces are both positive. A non-singular fast terminal sliding surface structure is used to achieve finite-time convergence of the system state. The layered sliding surface design incorporates a hybrid reaching law that includes a barrier function, which consists of a linear decay term, a power decay term, and a barrier function term. The dynamic characteristics of the system are optimized by combining the hybrid reaching law with boundary constraints. A cascaded extended state observer with embedded quasi-resonant control is used to perform hierarchical estimation of periodic and non-periodic disturbances in the speed of a permanent magnet synchronous motor, and to perform feedforward compensation for sliding mode control. The cascaded extended state observer includes a first-stage extended state observer and a second-stage extended state observer. The first-stage extended state observer and the second-stage extended state observer are connected in a cascaded structure. The overall control law is constructed based on the layered sliding surface, the hybrid approach law, and the cascaded expansion state observer. This overall control law is used to generate the reference current for the current loop.

[0007] Furthermore, when constructing the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system of the dq axis, it includes: The stator voltage equation is established, whereby the d-axis stator voltage is related to the d-axis stator current, d-axis inductance, q-axis inductance, q-axis current, mechanical angular velocity, and number of pole pairs, and the q-axis stator voltage is related to the q-axis stator current, q-axis inductance, d-axis inductance, d-axis current, mechanical angular velocity, number of pole pairs, and permanent magnet flux linkage. The electromagnetic torque equation is established, and the electromagnetic torque is related to the number of pole pairs, q-axis current, d-axis current, d-axis inductance, q-axis inductance, and permanent magnet flux linkage. The motion equations of the permanent magnet synchronous motor are established, and the motion equations of the permanent magnet synchronous motor are related to the moment of inertia, friction coefficient, load torque, mechanical angular velocity, torque harmonics caused by current sampling error, number of pole pairs, permanent magnet flux linkage and q-axis current; Under a control strategy where the d-axis current reference value is set to zero, the motion equations of the permanent magnet synchronous motor considering the periodic disturbances caused by current sampling errors are established.

[0008] Furthermore, when constructing the motor speed error model based on the mathematical model of the permanent magnet synchronous motor, it includes: The difference between the reference mechanical angular velocity and the actual mechanical angular velocity is defined as the speed tracking error; Calculate the first and second derivatives of the speed tracking error; The torque harmonics, load torque, friction torque, and parameter perturbations caused by current sampling errors are uniformly represented as a lumped disturbance term; The lumped disturbance term is expressed as the sum of a periodic disturbance term and an aperiodic disturbance term, wherein the periodic disturbance term is the torque harmonic caused by the current sampling error, and the aperiodic disturbance term includes the first derivative of the reference mechanical angular velocity, parameter perturbation, load torque, and friction torque.

[0009] Furthermore, when designing the layered sliding surface based on the mathematical model of the permanent magnet synchronous motor, the following steps are included: The inner sliding surface is defined based on the rotational speed error and its first coefficient, the first derivative of the rotational speed error and its second coefficient, and the integral of the rotational speed error and its third coefficient. The outer sliding surface is defined based on the integral of the power transformation of the inner sliding surface and its fourth coefficient; The coefficients of both the inner and outer sliding surfaces are positive, and the exponent of the power transformation of the outer sliding surface satisfies the constraint that it is greater than zero and less than 1.

[0010] Furthermore, the parameter settings for the layered sliding surface include: Set the first coefficient of the inner sliding surface c 1 is a real number greater than zero; Set the second coefficient of the inner sliding surface c 2 is a real number greater than zero; Set the third coefficient of the inner sliding surface. c 3 is a real number greater than zero; Set the fourth coefficient of the outer sliding surface. c 4 is a real number greater than zero; Set the exponent r of the power transformation of the outer sliding surface to a real number that is greater than zero and less than 1; The parameter settings satisfy the mathematical constraints of system nonsingularity and finite-time convergence.

[0011] Furthermore, when incorporating the hybrid reaching law of the barrier function into the layered sliding surface design, the following is included: The linear decay term is obtained based on the negative value of the sliding surface and its first positive coefficient; The power attenuation term is obtained by power of the absolute value of the sliding surface and its second positive coefficient, power of the absolute value of the rotational speed error and the sign function of the sliding surface, wherein both powers are positive numbers less than 1 and their sum is less than 1; The barrier function term is obtained from the barrier function and its third positive coefficient and the sliding surface sign function, wherein the barrier function is obtained by calculating the prior boundary, the barrier function gain and the absolute value of the sliding surface.

[0012] Furthermore, the parameter settings for the hybrid reaching law include: Set the first positive coefficient k1 of the linear decay term to a real number greater than zero; Set the second positive coefficient k2 of the power decay term to a real number greater than zero; Set the third positive coefficient k3 of the barrier function term to a real number greater than zero; Set the power α of the absolute value of the sliding surface to a real number that is greater than zero and less than 1; Set the power β of the rotational speed error to a real number that is greater than zero and less than 1; The sum of α and β is set to a positive number less than 1 to ensure that the system converges faster than the traditional convergence law.

[0013] Furthermore, the structural design for constructing the cascaded extended state observer includes: Construct a first-level extended state observer. The input of the first-level extended state observer is the speed tracking error, and the output is the estimated value of the speed tracking error and the estimated value of the total disturbance. Construct a second-level extended state observer. The inputs of the second-level extended state observer are the speed tracking error and the output of the first-level extended state observer. The output is the estimated value of the residual disturbance. The second-stage extended state observer incorporates a quasi-resonant controller, which accurately tracks periodic disturbances at specific frequencies caused by current sampling errors.

[0014] Furthermore, the parameter settings of the cascaded extended state observer include: Set the gain coefficient of the first-stage extended state observer; set the gain coefficient of the second-stage extended state observer; set the resonant frequency of the quasi-resonant controller to match the frequency of the periodic disturbance caused by the current sampling error; The total disturbance estimate is calculated based on the output of the cascaded extended state observer. The total disturbance estimate is the sum of the total disturbance estimate output by the first-stage extended state observer and the residual disturbance estimate output by the second-stage extended state observer.

[0015] Furthermore, when constructing the overall control law based on the layered sliding surface, the hybrid reaching law, and the cascaded extended state observer, it includes: Based on the layered sliding surface and the hybrid approach law, the sliding control law is derived, and the equivalent control term and switching control term are obtained. The equivalent control term includes the first derivative of the rotational speed error and its first coefficient, the rotational speed error and its third coefficient, and the power transformation of the inner sliding mode surface integral and its fourth coefficient. The switching control term includes a linear decay term, a power decay term, and a barrier function term; The total disturbance estimate output by the equivalent control term, the switching control term, and the cascaded extended state observer is combined to form the total control law, which is used to generate the reference current of the current loop.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. In this invention, a layered sliding surface is designed. The inner sliding surface uses an integral sliding surface to enhance robustness, while the outer sliding surface uses a non-singular terminal sliding surface to ensure that the system state variables converge in a finite time.

[0017] 2. In this invention, a hybrid reaching law is designed, in which an error is introduced to improve the convergence speed, and a barrier function is introduced into the reaching law. The closer to the prior boundary, the greater the switching gain, so that the speed fluctuation is always constrained within the predetermined boundary.

[0018] 3. In this invention, a cascaded extended state observer with embedded quasi-resonant control is used, which can improve the estimation accuracy while taking a smaller bandwidth, and at the same time improve the estimation accuracy under periodic disturbances.

[0019] 4. In this invention, a layered sliding surface, a hybrid reaching law, and a cascaded extended state observer with embedded quasi-resonant control are combined to construct a composite control law. Through mutual cooperation, better dynamic response, steady-state accuracy, and anti-interference performance are achieved. Attached Figure Description

[0020] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a flowchart illustrating the speed control method for a permanent magnet synchronous motor based on composite sliding mode control according to one embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the implementation principle of the sliding mode control method for a permanent magnet synchronous motor according to one embodiment of the present invention; Figure 3 This is a startup response diagram of a traditional terminal sliding mode control combined with an interference observer according to one embodiment of the present invention; Figure 4 This is a startup response diagram of a conventional two-stage extended state observer according to one embodiment of the present invention; Figure 5 This is a startup response diagram of the permanent magnet synchronous motor speed control method based on composite sliding mode control according to one embodiment of the present invention; Figure 6 This is a simulation diagram of the rotational speed under a sudden load applied by a traditional terminal sliding mode control combined with an interference observer according to one embodiment of the present invention; Figure 7 This is a simulation diagram of the sudden load rotation speed of a conventional two-stage extended state observer according to one embodiment of the present invention; Figure 8 This is a simulation diagram of the sudden load speed of the permanent magnet synchronous motor speed control method based on composite sliding mode control according to one embodiment of the present invention; Figure 9 This is a steady-state FFT analysis diagram of a traditional terminal sliding mode control combined with an interference observer according to one embodiment of the present invention; Figure 10 This is a steady-state FFT analysis diagram of a conventional two-stage extended state observer according to one embodiment of the present invention; Figure 11 The steady-state FFT analysis diagram of the permanent magnet synchronous motor speed control method based on composite sliding mode control according to one embodiment of the present invention is shown. Figure 12 This is a disturbance observation diagram of the permanent magnet synchronous motor speed control method based on composite sliding mode control according to one embodiment of the present invention. Detailed Implementation

[0021] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] For this, please refer to Figure 1 As shown, this application proposes a speed control method for a permanent magnet synchronous motor based on composite sliding mode control, including: S1: Construct a mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system of the dq axis, and build a motor speed error model based on the mathematical model; the mathematical model includes the stator voltage equation, the electromagnetic torque equation, and the motion equation of the permanent magnet synchronous motor; S2: Based on the mathematical model of the permanent magnet synchronous motor, a layered sliding surface is designed. The layered sliding surface includes an inner sliding surface and an outer sliding surface. A non-singular fast terminal sliding surface structure is used to achieve finite-time convergence of the system state. S3: Combine the layered sliding surface design with a hybrid reaching law that includes a barrier function. The hybrid reaching law includes a linear decay term, a power decay term, and a barrier function term. The dynamic characteristics of the system are optimized by combining the hybrid reaching law with boundary constraints. S4: A cascaded extended state observer with embedded quasi-resonant control is used to perform hierarchical estimation of periodic and non-periodic disturbances in the speed of the permanent magnet synchronous motor, and feedforward compensation is performed for sliding mode control. S5: Construct the overall control law based on the layered sliding surface, the hybrid approach law, and the cascaded expansion state observer. The overall control law is used to generate the reference current of the current loop.

[0023] Specifically, a precise mathematical model of the permanent magnet synchronous motor (PMSM) in the dq-axis synchronous rotating coordinate system is constructed. This model includes stator voltage equations, electromagnetic torque equations, and the PSM's motion equations. A complete state description is established through the coupling relationships between voltage, current, inductance, permanent magnet flux linkage, and mechanical angular velocity along the d and q axes. Based on this, the difference between the reference and actual mechanical angular velocities is defined as the speed tracking error. A speed error model is further constructed by calculating its first and second derivatives. Torque harmonics, load disturbances, friction torque, and parameter uncertainties caused by current sampling errors are uniformly represented as lumped disturbance terms, which are then divided into periodic and non-periodic disturbances for targeted compensation by the subsequent controller. A layered sliding surface is designed based on the mathematical model. The inner sliding surface is composed of a proportional combination of the speed error, its first derivative, and integral terms, used to adjust the basic dynamics of the tracking error. The outer sliding surface introduces a power transformation structure based on the inner sliding surface to achieve rapid convergence of the state variables within a finite time. By reasonably constraining the sliding surface coefficients and power exponents, the system is guaranteed to be free of singularities in the entire state space, while also improving the limited convergence speed of traditional sliding mode methods. A hybrid reaching law incorporating a barrier function is constructed by combining layered sliding surfaces. This reaching law consists of a linear decay term, a power decay term, and a barrier function term. The power decay term is used to achieve fast convergence, while the barrier function term enhances the constraint capability when the state approaches the boundary region, thereby improving the dynamic consistency of the system in different operating stages such as large errors, small errors, and boundary regions. Through the combined effect of multiple reaching terms, the system exhibits less chattering, faster reaching speed, and higher steady-state accuracy. A cascaded extended state observer (ESO) with an embedded quasi-resonant controller is introduced. The first-stage ESO is used to estimate the rotational speed error and lumped disturbance in real time, while the second-stage ESO further extracts residual disturbance information and uses the quasi-resonant controller to accurately track periodic disturbances of specific frequencies (such as torque harmonics caused by current sampling errors). The cascaded structure enables hierarchical estimation of disturbances in different frequency domains, thereby improving the accuracy of disturbance observation and providing more effective feedforward compensation for sliding mode control. The overall control law is constructed based on the hierarchical sliding surface, the hybrid reaching law, and the output of the cascaded extended state observer. The control law includes an equivalent control term, a switching control term, and a disturbance compensation term. The equivalent control term reflects the ideal dynamic behavior of the system, the switching control term realizes multimodal sliding mode reaching characteristics through linear, power, and barrier functions, and the disturbance compensation term is provided by the disturbance estimate output by the cascaded ESO. The three types of terms are superimposed to generate the reference current input for the current loop, enabling fast, accurate, and robust speed control of the permanent magnet synchronous motor under various disturbance environments.

[0024] Understandably, replacing the traditional single-layer sliding mode structure with a layered sliding mode surface enhances the robustness of the controller and achieves rapid global convergence of the system state variables. Introducing a hybrid reaching law incorporating a barrier function, and utilizing the synergistic effect of linear decay, power decay, and barrier constraints, gives the sliding mode surface superior convergence characteristics across different error ranges, reducing chattering caused by switching terms and improving rotational speed quality. Constructing a cascaded extended state observer embedded with quasi-resonant control allows for layered and accurate estimation of periodic and aperiodic disturbances, enabling targeted suppression of periodic disturbances such as torque harmonics caused by current sampling errors, thereby improving disturbance compensation. The resulting overall control law combines strong robustness with low chattering characteristics, making the generation of the current loop reference current more accurate.

[0025] This application further proposes the following when constructing a mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system along the dq axis: The stator voltage equation is established. The d-axis stator voltage is related to the d-axis stator current, d-axis inductance, q-axis inductance, q-axis current, mechanical angular velocity, and number of pole pairs. The q-axis stator voltage is related to the q-axis stator current, q-axis inductance, d-axis inductance, d-axis current, mechanical angular velocity, number of pole pairs, and permanent magnet flux linkage. An electromagnetic torque equation is established, which is related to the number of pole pairs, q-axis current, d-axis current, d-axis inductance, q-axis inductance, and permanent magnet flux linkage. The motion equations of the permanent magnet synchronous motor are established. The motion equations of the permanent magnet synchronous motor are related to the moment of inertia, friction coefficient, load torque, mechanical angular velocity, torque harmonics caused by current sampling error, number of pole pairs, permanent magnet flux linkage and q-axis current. Under the control strategy of setting the d-axis current reference value to zero, the motion equation of the permanent magnet synchronous motor considering the periodic disturbance caused by the current sampling error is established.

[0026] Specifically, a mathematical model of the dq permanent magnet synchronous motor in a synchronous rotating coordinate system is established, and its stator voltage equation is as follows: ; in, u d , u q These represent the stator voltages in the d-axis and q-axis coordinates, respectively. i d , i q These represent the stator currents in the d-axis and q-axis coordinates, respectively. L d , L q Let be the inductance in the d-axis and q-axis coordinates, respectively. ψ f It is a permanent magnet flux linkage. RFor stator resistance, ω m The mechanical angular velocity is the rotational angle. p n is the number of magnetic pole pairs.

[0027] The electromagnetic torque equation is: ; The equation of motion for a permanent magnet synchronous motor is: ; When using i d =0, and due to periodic disturbances in the rotational speed caused by inverter nonlinearity, flux harmonics, and current sampling errors, and considering that the effects of inverter nonlinearity and flux harmonics are relatively small and can be ignored, the periodic disturbances caused by current sampling errors are the primary consideration. Therefore, the motion equation of the permanent magnet synchronous motor can be written as: ; in, J For rotational inertia, B The coefficient of friction, T L For load torque, T i This refers to torque harmonics caused by current sampling errors.

[0028] use f To represent the lumped disturbance present in the PMSM, the motion equation of the permanent magnet synchronous motor can be further rewritten as:

[0029] ; in, b 0=3 p n ψ f / 2 J Δ b = b - b 0, b 0 is a parameter b The nominal value, f =Δ bi q +(- T L - Bω m + T i ) / J .

[0030] This application further proposes, when constructing a motor speed error model based on a mathematical model of a permanent magnet synchronous motor, including: The difference between the reference mechanical angular velocity and the actual mechanical angular velocity is defined as the speed tracking error; Calculate the first and second derivatives of the speed tracking error; The torque harmonics, load torque, friction torque, and parameter perturbations caused by current sampling errors are uniformly represented as a lumped disturbance term; The lumped disturbance term is represented as the sum of periodic and non-periodic disturbance terms. The periodic disturbance term is the torque harmonic caused by the current sampling error, and the non-periodic disturbance term includes the first derivative of the reference mechanical angular velocity, parameter perturbation, load torque, and friction torque.

[0031] Specifically, based on the mathematical model of the permanent magnet synchronous motor, a motor speed error model is constructed, and the speed tracking error is: ; in, ω ref This is the reference trajectory for the mechanical angular velocity.

[0032] The first and second derivatives of the error are: ; Multiple perturbations of error f e It can be defined as follows: ; The error derivative can then be simplified to: ; Based on the impact of these disturbances, they can be divided into periodic disturbances and non-periodic disturbances, and therefore can be represented as: ; Among them, periodic disturbances f p =- T i / J Non-periodic disturbances .

[0033] This application further proposes designing layered sliding surfaces based on the mathematical model of a permanent magnet synchronous motor, including: The inner sliding surface is defined based on the rotational speed error and its first coefficient, the first derivative of the rotational speed error and its second coefficient, and the integral of the rotational speed error and its third coefficient. The outer sliding surface is defined based on the integral of the power transformation of the inner sliding surface and its fourth coefficient; The coefficients of both the inner and outer sliding surfaces are positive, and the exponent of the power transformation of the outer sliding surface satisfies the constraint that it is greater than zero and less than 1.

[0034] The parameter settings for the layered sliding surface include: Set the first coefficient of the inner sliding surface c 1 is a real number greater than zero; Set the second coefficient of the inner sliding surface c 2 is a real number greater than zero; Set the third coefficient of the inner sliding surface. c 3 is a real number greater than zero; Set the fourth coefficient of the outer sliding surface. c 4 is a real number greater than zero; Set the exponent of the power transformation of the outer sliding surface. r It is a real number that is greater than zero and less than 1; The parameter settings satisfy the mathematical constraints of system nonsingularity and finite-time convergence.

[0035] Specifically, a layered sliding surface is designed based on the constructed motor speed error model.

[0036] To achieve global fast convergence of system state variables and enhance the robustness of the controller, a hierarchical nonsingular fast terminal sliding mode controller is adopted, and the sliding surface function is defined as follows: ; In the formula, c 1>0, c 2>0, c 3>0, c 4>0, 0< r <1. Integral sliding surfaces are used for the inner sliding surfaces to enhance robustness, while non-singular terminal sliding surfaces are used for the outer sliding surfaces to ensure that the system state variables converge in finite time.

[0037] This application further proposes a hybrid reaching law incorporating a barrier function when combining layered sliding surface design, including: The linear decay term is obtained based on the negative value of the sliding surface and its first positive coefficient; The power decay term is obtained by powering the absolute value of the sliding surface and its second positive coefficient, powering the absolute value of the rotational speed error and the sign function of the sliding surface, where both powers are positive numbers less than 1 and their sum is less than 1; The barrier function term is obtained from the barrier function, its third positive coefficient, and the sliding surface sign function. The barrier function is obtained by calculating the prior boundary, the barrier function gain, and the absolute value of the sliding surface.

[0038] The parameter settings for the mixed reaching law include: Set the first positive coefficient k1 of the linear decay term to a real number greater than zero; Set the second positive coefficient k2 of the power decay term to a real number greater than zero; Set the third positive coefficient k3 of the barrier function term to a real number greater than zero; Set the power α of the absolute value of the sliding surface to a real number that is greater than zero and less than 1; Set the power β of the rotational speed error to a real number that is greater than zero and less than 1; set up α and β The sum of these numbers is a positive number less than 1, to ensure that the system converges faster than the traditional convergence law.

[0039] Specifically, based on the constructed motor speed error model and combined with the sliding surface design, a hybrid reaching law including a barrier function is proposed.

[0040] To accelerate the convergence speed of system state variables, reduce controller chattering, and limit speed fluctuations, a hybrid reaching law design is proposed as follows: ; in, k 1>0, k 2>0, k 3>0, 0< α <1, 0< β <1, K bf ( s )= εF ( ε -| s |) represents the barrier function. First, an error is introduced into the reaching law. e m To improve the convergence speed. When s and e m As the gain approaches zero, to ensure that the gain decays at a superlinear rate, let 0 < α + β <1: ; As can be seen from the above equation, the convergence speed is significantly better than that of the traditional reaching law. Furthermore, a potential barrier function is introduced into the reaching law. K bf ( s ), F To control the preset value of the gain, the closer it gets to the prior boundary... ε At this time, the greater the switching gain, the more the speed fluctuation is always constrained within the predetermined boundary.

[0041] Convergence time analysis, let: ; Assuming the system is in sliding mode, for any initial state δ (0)≠0, t out converged to δ ( t The time when ) = 0 is: ; When the inner sliding surface reaches 0 within a finite time: ; but: ; In the formula, g (1，2) =(- c 1± O 1 / 2 ) / (2 k 2), O = c 1 2 -4 c 2 c 3>0. Therefore, by selecting appropriately... c 1. c 2. c A value of 3 can achieve convergence of speed tracking error within a finite time.

[0042] This application further proposes a structural design for constructing a cascaded extended state observer, including: Construct a first-level extended state observer. The input of the first-level extended state observer is the speed tracking error, and the output is the estimated value of the speed tracking error and the estimated value of the total disturbance. Construct a second-level extended state observer. The inputs of the second-level extended state observer are the speed tracking error and the output of the first-level extended state observer. The output is the estimated value of the residual disturbance. The first-stage extended state observer and the second-stage extended state observer are connected in a cascaded structure. The second-stage extended state observer incorporates a quasi-resonant controller, which accurately tracks periodic disturbances at specific frequencies caused by current sampling errors.

[0043] The parameter settings for the cascaded extended state observer include: Set the gain coefficient of the first-stage extended state observer; set the gain coefficient of the second-stage extended state observer; set the resonant frequency of the quasi-resonant controller to match the frequency of the periodic disturbance caused by the current sampling error; The total disturbance estimate is calculated based on the output of the cascaded extended state observer. The total disturbance estimate is the sum of the total disturbance estimate output by the first-stage extended state observer and the residual disturbance estimate output by the second-stage extended state observer.

[0044] Specifically, a cascaded extended state observer with embedded quasi-resonant control is used to estimate the periodic and aperiodic disturbances in the speed of the permanent magnet synchronous motor and to perform feedforward compensation for sliding mode control.

[0045] Traditional extended state observers often use large bandwidths to accurately estimate disturbances. However, large bandwidths introduce additional noise, degrading control performance and resulting in poor suppression of periodic disturbances. To address these issues, a cascaded extended state observer incorporating quasi-resonant control is proposed. The cascaded structure improves estimation accuracy while using a smaller bandwidth, and the embedding of quasi-resonant control enhances estimation accuracy at periodic disturbance frequencies.

[0046] The first-level ESO design is as follows: ; in, x 1 represents the speed tracking error. e m , z 1 represents the estimated value of the speed tracking error. z 2 represents the estimated total disturbance. e α The estimation error of the first-level extended state observer, β 1 and β 2 represents the gain coefficient of the observer, which can be expressed as [ β 1, β 1] T =[2 ω eso1 , ω 2 eso1 ] T , ω eso1 This represents the bandwidth of the first-stage observer.

[0047] The second-level extended state observer is: ; in, e β The estimation error of the second-level extended state observer, z 3 represents the estimated value of the speed tracking error. z 4 represents the estimated value of the residual disturbance, which is mainly composed of periodic harmonics. R ( s () is a quasi-resonant controller. β 3 and β 4 represents the gain coefficient of the observer, which can be expressed as [ β 3, β 4] T =[2 ω eso2 , ω 2 eso2 ] T , ω eso2For the bandwidth of the second-stage observer, in order to simplify parameter tuning, ω eso1 and ω eso2 Selected as the same value, and represented as ω eso .

[0048] The expression for the quasi-resonant controller is: ; in, k r For resonant gain, ω c The cutoff frequency, ω o It is the resonant frequency.

[0049] The total estimated perturbation is calculated based on the estimated perturbations (i.e., z2 and z4) from the two-stage extended state observer: ; in, For total disturbance f e The estimated value.

[0050] This application further proposes that when constructing the overall control law based on layered sliding surfaces, hybrid reaching laws, and cascaded extended state observers, the following should be included: Based on the layered sliding surface and the hybrid approach law, the sliding control law is derived, and the equivalent control term and switching control term are obtained. The equivalent control term includes the first derivative of the speed error and its first coefficient, the speed error and its third coefficient, and the power transformation of the inner sliding mode surface integral and its fourth coefficient. The switching control term includes a linear decay term, a power decay term, and a barrier function term; The total disturbance estimate is formed by combining the equivalent control term, the switching control term, and the output of the cascaded extended state observer. The total control law is used to generate the reference current of the current loop.

[0051] Specifically, based on the designed layered sliding surface and hybrid reaching law, the sliding mode control law is derived. A cascaded extended state observer is used to estimate the lumped disturbance and feedforward compensation is applied to the sliding mode control law, resulting in the overall control law: ; Permanent magnet synchronous motor, input reference current of the current loop i * q for: ; Stability analysis: Define a bounded Lyapunov function: ; When the estimation error reaches a bounded constant At that time, it was: ; V 2≥0, The system is stable if the Lyapunov stability condition is met.

[0052] To verify the superiority of the control method of this invention, simulation analysis was performed using MATLAB / Simulink. The parameters of the permanent magnet synchronous motor are shown in Table 1, and the parameters in the simulation are shown in Table 2.

[0053] Table 1

[0054] Table 2

[0055] In the analysis and comparison of the experimental results, steady-state speed fluctuations and first and second speed harmonics reflect the ability to suppress periodic disturbances, while the speed drop amplitude and recovery time reflect the ability to handle non-periodic disturbances.

[0056] analyze Figure 3 , Figure 4 and Figure 5 The method of this invention has a faster response time. Under steady-state conditions, the rotational speed fluctuation of the traditional terminal sliding mode control combined with the interference observer is 12 r / min; the rotational speed fluctuation of the traditional two-stage extended state observer is 18 r / min; and the rotational speed fluctuation of the method of this invention is 7 r / min. The method of this invention has the smallest rotational speed fluctuation range.

[0057] analyze Figure 6 , Figure 7 and Figure 8 When a sudden load is applied at 0.2 s, the rotational speed drop amplitude of the traditional terminal sliding mode control combined with the disturbance observer is 32 r / min, with a recovery time of approximately 0.07 s; the rotational speed drop amplitude of the traditional two-stage extended state observer is 50 r / min, with a recovery time of approximately 0.05 s; while the rotational speed drop amplitude of the method of this invention is 14 r / min, with a recovery time of approximately 0.05 s. Therefore, the method of this invention has a superior suppression effect on non-periodic disturbances.

[0058] analyze Figure 9 , Figure 10 and Figure 11According to the Fourier Transform (FFT) analysis of the rotational speed under steady-state conditions, the effects of the first and second harmonics are the most significant. The amplitude of the first harmonic in traditional terminal sliding mode control combined with a disturbance observer is 0.54% of the rotational speed, the amplitude of the second harmonic is 0.10% of the rotational speed, and the THD is 0.66%. The amplitude of the first harmonic in the traditional two-stage extended state observer is 0.21% of the rotational speed, the amplitude of the second harmonic is 0.13% of the rotational speed, and the THD is 0.42%. The amplitude of the first harmonic in the method of this invention is 0.11% of the rotational speed, the amplitude of the second harmonic is 0.04% of the rotational speed, and the THD is 0.28%. Therefore, the method of this invention has a stronger ability to suppress periodic disturbances.

[0059] like Figure 12 As shown, the observer used in this invention can effectively observe periodic and non-periodic disturbances.

[0060] The above analysis shows that the present invention has superior performance and better dynamic performance in suppressing periodic and aperiodic disturbances compared with other methods.

[0061] This invention provides a computer-readable storage medium for storing computer instructions that cause a computer to execute a speed control method for a permanent magnet synchronous motor based on composite sliding mode control. Therefore, it can achieve any effect in the speed control method for a permanent magnet synchronous motor based on composite sliding mode control, which will not be elaborated further here.

[0062] The present invention provides an electronic device comprising: Memory, used to store computer instructions; The processor is used to execute computer instructions to implement a speed control method for permanent magnet synchronous motors based on composite sliding mode control. Therefore, it can achieve any effect found in the speed control method for permanent magnet synchronous motors based on composite sliding mode control, which will not be elaborated upon here.

[0063] In summary, the inner sliding surface uses an integral sliding surface to enhance robustness, while the outer sliding surface uses a non-singular terminal sliding surface to ensure the convergence of the system state variables within a finite time. An error is introduced into the reaching law to improve the convergence speed, and a barrier function is also introduced into the reaching law. The switching gain increases as the system approaches the prior boundary, ensuring that speed fluctuations are always constrained within the predetermined boundary. By employing a cascaded extended state observer and embedding quasi-resonant control, estimation accuracy can be improved while maintaining a smaller bandwidth, and estimation accuracy at periodic disturbance frequencies is also improved. By combining the layered sliding surface, the hybrid reaching law, and the cascaded extended state observer with embedded quasi-resonant control, a composite control law is constructed. Through mutual cooperation, better dynamic response, steady-state accuracy, and anti-interference performance are achieved.

[0064] For any parts not mentioned in this invention, existing technologies can be used or referenced.

[0065] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0066] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control, characterized in that, include: A mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system of the dq axis is constructed, and a motor speed error model is built based on the mathematical model. The mathematical model includes the stator voltage equation, the electromagnetic torque equation, and the motion equation of the permanent magnet synchronous motor. Based on the mathematical model of the permanent magnet synchronous motor, a layered sliding surface is designed, which includes an inner sliding surface and an outer sliding surface. The coefficients of the inner and outer sliding surfaces are both positive. A non-singular fast terminal sliding surface structure is used to achieve finite-time convergence of the system state. The layered sliding surface design incorporates a hybrid reaching law that includes a barrier function, which consists of a linear decay term, a power decay term, and a barrier function term. The dynamic characteristics of the system are optimized by combining the hybrid reaching law with boundary constraints. A cascaded extended state observer with embedded quasi-resonant control is used to perform hierarchical estimation of periodic and non-periodic disturbances in the speed of a permanent magnet synchronous motor, and to perform feedforward compensation for sliding mode control. The cascaded extended state observer includes a first-stage extended state observer and a second-stage extended state observer. The first-stage extended state observer and the second-stage extended state observer are connected in a cascaded structure. The overall control law is constructed based on the layered sliding surface, the hybrid approach law, and the cascaded expansion state observer. The overall control law is used to generate the reference current of the current loop. When incorporating the hybrid reaching law of the barrier function into the layered sliding surface design, the following are included: The linear decay term is obtained based on the negative value of the sliding surface and its first positive coefficient; The power-law attenuation term is obtained by power of the absolute value of the sliding surface and its second positive coefficient, power of the absolute value of the rotational speed error and the sign function of the sliding surface, and the power-law attenuation term is negative, wherein both powers are positive numbers less than 1 and the sum is less than 1; The barrier function term is obtained based on the barrier function and its third positive coefficient and the sliding surface sign function, and the barrier function term is negative. The barrier function is obtained by calculating the prior boundary, the barrier function gain and the absolute value of the sliding surface. The parameter settings for the hybrid reaching law include: Set the first positive coefficient k1 of the linear decay term to a real number greater than zero; Set the second positive coefficient k2 of the power decay term to a real number greater than zero; Set the third positive coefficient k3 of the barrier function term to a real number greater than zero; Set the power α of the absolute value of the sliding surface to a real number that is greater than zero and less than 1; Set the power β of the rotational speed error to a real number that is greater than zero and less than 1; The sum of α and β is set to a positive number less than 1 to ensure that the system converges faster than the traditional convergence law.

2. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 1, characterized in that, When constructing the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system of the dq axis, the following are included: The stator voltage equation is established, whereby the d-axis stator voltage is related to the d-axis stator current, d-axis inductance, q-axis inductance, q-axis current, mechanical angular velocity, and number of pole pairs, and the q-axis stator voltage is related to the q-axis stator current, q-axis inductance, d-axis inductance, d-axis current, mechanical angular velocity, number of pole pairs, and permanent magnet flux linkage. The electromagnetic torque equation is established, and the electromagnetic torque is related to the number of pole pairs, q-axis current, d-axis current, d-axis inductance, q-axis inductance, and permanent magnet flux linkage. The motion equations of the permanent magnet synchronous motor are established, and the motion equations of the permanent magnet synchronous motor are related to the moment of inertia, friction coefficient, load torque, mechanical angular velocity, torque harmonics caused by current sampling error, number of pole pairs, permanent magnet flux linkage and q-axis current; Under a control strategy where the d-axis current reference value is set to zero, the motion equations of the permanent magnet synchronous motor considering the periodic disturbances caused by current sampling errors are established.

3. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 2, characterized in that, When constructing a motor speed error model based on the mathematical model of a permanent magnet synchronous motor, the following should be included: The difference between the reference mechanical angular velocity and the actual mechanical angular velocity is defined as the speed tracking error; Calculate the first and second derivatives of the speed tracking error; The torque harmonics, load torque, friction torque, and parameter perturbations caused by current sampling errors are uniformly represented as a lumped disturbance term; The lumped disturbance term is expressed as the sum of a periodic disturbance term and an aperiodic disturbance term, wherein the periodic disturbance term is the torque harmonic caused by the current sampling error, and the aperiodic disturbance term includes the first derivative of the reference mechanical angular velocity, parameter perturbation, load torque, and friction torque.

4. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 3, characterized in that, When designing layered sliding surfaces based on the mathematical model of a permanent magnet synchronous motor, the following steps are included: The inner sliding surface is defined based on the rotational speed error and its first coefficient, the first derivative of the rotational speed error and its second coefficient, and the integral of the rotational speed error and its third coefficient. The outer sliding surface is defined based on the integral of the power transformation of the inner sliding surface and its fourth coefficient; The coefficients of both the inner and outer sliding surfaces are positive, and the exponent of the power transformation of the outer sliding surface satisfies the constraint that it is greater than zero and less than 1.

5. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 4, characterized in that, The parameter settings for the layered sliding surface include: Set the first coefficient of the inner sliding surface c 1 is a real number greater than zero; Set the second coefficient c2 of the inner sliding surface to a real number greater than zero; Set the third coefficient c3 of the inner sliding surface to a real number greater than zero; Set the fourth coefficient c4 of the outer sliding surface to a real number greater than zero; Set the exponent r of the power transformation of the outer sliding surface to a real number that is greater than zero and less than 1; The parameter settings satisfy the mathematical constraints of system nonsingularity and finite-time convergence.

6. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 5, characterized in that, The structural design for constructing a cascaded extended state observer includes: Construct a first-level extended state observer. The input of the first-level extended state observer is the speed tracking error, and the output is the estimated value of the speed tracking error and the estimated value of the total disturbance. Construct a second-level extended state observer. The inputs of the second-level extended state observer are the speed tracking error and the output of the first-level extended state observer. The output is the estimated value of the residual disturbance. The second-stage extended state observer incorporates a quasi-resonant controller, which accurately tracks periodic disturbances at specific frequencies caused by current sampling errors.

7. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 6, characterized in that, The parameter settings for the cascaded expansion state observer include: Set the gain coefficient of the first-stage extended state observer; set the gain coefficient of the second-stage extended state observer; set the resonant frequency of the quasi-resonant controller to match the frequency of the periodic disturbance caused by the current sampling error; The total disturbance estimate is calculated based on the output of the cascaded extended state observer. The total disturbance estimate is the sum of the total disturbance estimate output by the first-stage extended state observer and the residual disturbance estimate output by the second-stage extended state observer.

8. The method for controlling the speed of a permanent magnet synchronous motor based on composite sliding mode control according to claim 7, characterized in that, When constructing the overall control law based on the layered sliding surface, the hybrid reaching law, and the cascaded extended state observer, the following are included: Based on the layered sliding surface and the hybrid approach law, the sliding control law is derived, and the equivalent control term and switching control term are obtained. The equivalent control term includes the first derivative of the rotational speed error and its first coefficient, the rotational speed error and its third coefficient, and the power transformation of the inner sliding mode surface integral and its fourth coefficient. The switching control term includes a linear decay term, a power decay term, and a barrier function term; The total disturbance estimate output by the equivalent control term, the switching control term, and the cascaded extended state observer is combined to form the total control law, which is used to generate the reference current of the current loop.

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