PMSM improved sliding mode control system and method based on two-stage dynamic boundary layer

Abstract

The invention belongs to the technical field of direct-current synchronous motor control, and particularly relates to a PMSM improved sliding mode control system and method based on a two-section type dynamic boundary layer, in the aspect of rotating speed control, a rotating speed ring terminal sliding mode controller is introduced, related items of load torque and mechanical angular speed are combined into total disturbance, a nonlinear terminal sliding mode surface is selected, and the total disturbance is calculated. The problem that nonlinear disturbance cannot be effectively processed through traditional PI rotating speed control can be solved, finite time convergence of PMSM speed tracking errors is achieved, and meanwhile system buffeting is effectively reduced. In the aspect of current control, an improved sliding-mode observer is obtained according to a two-section quasi sliding-mode surface and an exponential reaching law design based on a terminal saturation function, so that the observation steady-state error of dq-axis back electromotive force is effectively eliminated, high-frequency buffeting in a sliding-mode reaching stage is effectively reduced, and the steady-state and dynamic performance of a system under electrical parameter mismatch is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to an improved sliding mode control system and method for PMSM based on a two-stage dynamic boundary layer. Background Technique

[0002] As one of the most representative types of AC motors, PMSM has many advantages such as simple structure, high torque inertia ratio, small volume, and high efficiency, and has broad application prospects in fields such as precision control and locomotive traction. In terms of control methods, rotor flux-oriented vector control (FOC) based on a PI regulator is extremely widely used. The key lies in the control of the stator current amplitude and spatial position, and double closed-loop control is performed on the speed and the stator direct and quadrature axis currents respectively, and the system has good steady-state performance. However, the parameter selection of the PI regulator depends on the motor mathematical model. Since PMSM is a strongly coupled nonlinear system, the changes in parameters such as the motor resistance R, inductance L, and magnetic flux have a great impact on the system steady-state performance. Therefore, PI control cannot directly meet the requirements of high-performance and high-precision motor control.

[0003] The core idea of PMSM model predictive control is to predict the state at a future moment according to the mathematical models of the inverter and the motor, as well as the state of the motor at the current moment, compare it with the given value, and select the optimal voltage vector to act on the motor. Compared with the PI regulator, model predictive control eliminates complex parameter tuning and has better steady-state performance. The same as the PI regulator, inaccurate motor models or model parameter deviations will lead to inaccurate selection of the control voltage vector, resulting in deviations in the system output current. As time goes by, the cumulative deviation of the system continues to increase, thus deteriorating the control performance of the system.

[0004] Sliding mode control, as a strong robust control that is insensitive to parameters and external disturbances, has been a research hotspot of PMSM in recent years.

[0005] However, there are still the following deficiencies:

[0006] 1. There is a method that uses a high-order sliding mode observer to observe the motor magnetic flux and resistance by using the nth-order differential output of the observer. However, multiple differentiations are very likely to form high-order harmonics, and it is difficult to fully guarantee the accuracy of the observation results;

[0007] 2. There is a method that constructs a parameter identification model by using the current and voltage deviations of the d-axis and q-axis, and designs a suitable control law to ensure the convergence of the observed parameters;

[0008] 3. There is a method that proposes an offline identification method for motor parameters based on the fast Fourier transform, and uses the fundamental waves of the stator voltage and current to identify the stator d-axis and q-axis inductances offline. However, the data obtained by this method cannot adapt to different working conditions of the motor;

[0009] 4. The extended Kalman filter is used to online identify the magnetic flux and inductance L to achieve the optimal estimation of the system in the sense of minimum mean square error. Summary of the Invention

[0010] The object of the present invention is to provide an improved sliding mode control system and method for PMSM based on a two-stage dynamic boundary layer, which uses sliding mode control to predict the future state of the motor and realizes the high-performance and high-precision control requirements of the motor, aiming at the above problems existing in the prior art.

[0011] To achieve the above object, the technical solution of the present invention is as follows:

[0012] In the first aspect, the present invention provides an improved sliding mode control system for PMSM based on a two-stage dynamic boundary layer. The improved sliding mode control system for PMSM includes a speed loop terminal sliding mode control module, a current loop control module, an improved sliding mode observer based on a two-stage dynamic boundary layer, and a permanent magnet synchronous motor control sampling module. The permanent magnet synchronous motor control sampling module is used to collect the mechanical angular velocity ω of the permanent magnet synchronous motor during rotation m , the d-axis current i d and the q-axis current i q . The speed loop terminal sliding mode control module is used to calculate the q-axis current command value i m * according to the mechanical angular velocity command value ω m of the motor and the mechanical angular velocity ω q * of the motor through the speed loop terminal sliding mode controller; the current loop control module is used to control and calculate the set value u d * of the d-axis voltage to be compensated and the set value u q * of the q-axis voltage to be compensated according to the d-axis current command i d , the q-axis current command value i q , the d-axis current i d and the q-axis current i q of the motor through the current loop controller. The improved sliding mode observer based on a two-stage dynamic boundary layer is used to calculate the d-axis back electromotive force e d and the q-axis back electromotive force e q according to the d-axis current i d and the q-axis current i q of the motor through the improved sliding mode observer based on a two-stage dynamic boundary layer, and compensate the d-axis back electromotive force e d and the q-axis back electromotive force e q to the set value u d of the d-axis voltage to be compensated and the set value u q of the q-axis voltage to be compensated to obtain the d-axis voltage u d, q-axis voltage u q , the permanent magnet synchronous motor control sampling module is also used to control the rotation of the permanent magnet synchronous motor based on the d-axis voltage u d , q-axis voltage u q Control the rotation of the permanent magnet synchronous motor.

[0013] The speed loop terminal sliding mode controller is designed based on the bounded lumped disturbance of the differential component and the terminal sliding mode surface, and its mathematical model is shown in Equations (5)-(8):

[0014]

[0015] In the above formula, f ω is the bounded lumped disturbance of the differential component, is the differential component of f ω , l is the known upper bound, f n is the unmodeled term including sampling noise, calculation error, etc.; ω m is the mechanical angular velocity of the motor; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia; ψ f is the rotor magnetic flux; P n is the number of pole pairs; i q is the q-axis current; ω m * is the command value of the mechanical angular velocity of the motor; e ω is the mechanical angular velocity tracking error, e ω = ω m * - ω m ; is the differential component of e ω ; s is the terminal sliding mode surface; β, p, q, η are all control parameters of the speed loop terminal sliding mode controller, is the differential component of i q , differentiating can obtain i q * .

[0016] The improved sliding mode observer based on the two-segment dynamic boundary layer includes an improved q-axis sliding mode observer and an improved d-axis sliding mode observer. The structures of the improved d-axis sliding mode observer and the improved q-axis sliding mode observer are the same. The improved d-axis sliding mode observer is designed according to the two-segment quasi-sliding mode surface and the exponential reaching law based on the terminal saturation function. The mathematical expression of the improved d-axis sliding mode observer is shown in Equation (28):

[0017]

[0018] In the above formula, f3(σ d)To improve the d-axis sliding mode observer, the d-axis sliding mode surface function of the d-axis sliding mode observer is σ d = 0 indicates that the system enters the sliding mode surface. Let the first quasi-sliding mode surface be The second quasi-sliding mode surface Based on the first quasi-sliding mode surface and the second quasi-sliding mode surface, σ d of state space is divided into 3 regions. The region satisfying (-Δ ≤ σ d < -λ) ∪ (λ < σ d ≤ Δ) is region Ⅰ. The region satisfying (σ d > Δ) ∪ (σ d < -Δ) is region Ⅱ. The region satisfying -λ ≤ σ d ≤ λ is region Ⅲ. And an exponential reaching law based on the terminal saturation function is introduced in region Ⅲ L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; e dc is a positive real number related to the bound of e d ; λ = |e SS |, e dmax is the upper bound of e d ; is the differential component of σ d ; k and p are the control parameters of the improved d-axis sliding mode observer; k d is the switching gain of the improved q-axis sliding mode observer.

[0019] The mathematical model of the permanent magnet synchronous motor control sampling module is shown in Equations (1)-(4):

[0020]

[0021] In the above formula, u d , u q are the d-axis and q-axis voltages respectively; i d , i q are the d-axis and q-axis currents respectively; ψ d , ψ q are the d-axis and q-axis magnetic fluxes respectively; L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; ψ f is the rotor magnetic flux; R s is the stator resistance; P is the differential operator; P n is the number of pole pairs; ω e , ω m are the measured electrical angular velocity and mechanical angular velocity of the motor respectively; T e , T L are the electromagnetic torque and load torque respectively; J is the moment of inertia; B is the viscous friction coefficient.

[0022] In a second aspect, the present invention provides an improved sliding mode control method for a PMSM based on a two-stage dynamic boundary layer. The improved sliding mode control method for the PMSM includes:

[0023] Collect the mechanical angular velocity ω of the permanent magnet synchronous motor during rotation m of the d-axis current i d and the q-axis current i q ;

[0024] Calculate the q-axis current command value i m * through the speed loop terminal sliding mode controller according to the mechanical angular velocity command value ω of the motor m of the motor and the mechanical angular velocity ω q * ;

[0025] Calculate the set value u d * ' of the d-axis voltage to be compensated and the set value u q * ' of the q-axis voltage to be compensated by the current loop controller according to the d-axis current command i d = 0, the q-axis current command value i q , the d-axis current i d , the q-axis current i q through PID regulation control;

[0026] Calculate the d-axis back electromotive force e d and the q-axis back electromotive force e q through the improved sliding mode observer based on the two-stage dynamic boundary layer according to the d-axis current i d and the q-axis current i q , and compensate the d-axis back electromotive force e d and the q-axis back electromotive force e q to the set value u' of the d-axis voltage to be compensated d and the set value u' of the q-axis voltage to be compensated q to obtain the d-axis voltage u d and the q-axis voltage u q ;

[0027] Control the rotation of the permanent magnet synchronous motor based on the d-axis voltage u d and the q-axis voltage u q .

[0028] The construction steps of the speed loop terminal sliding mode controller include:

[0029] 1.1 Define the bounded lumped disturbance f of the differential component ω as shown in Equation (5)

[0030]

[0031] In the above formula, is the differential of f ω , l is the known upper bound, ω m is the mechanical angular velocity of the motor; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia; f n is the unmodeled term including sampling noise, calculation error, etc.;

[0032] 1.2 Based on Equation (5), a first-order system shown in Equation (6) is obtained. By taking an appropriate i q , ω m is made to track ω m * within a finite time:

[0033]

[0034] In the above formula, P n is the number of pole pairs; ψ f is the rotor magnetic flux; i q is the q-axis current;

[0035] 1.3 Take the mechanical angular velocity tracking error and the speed tracking error as e ω = ω m * - ω m , ω m * is the command value of the motor mechanical angular velocity, and the terminal sliding mode surface s shown in Equation (7) is introduced. The mathematical model of the speed loop terminal sliding mode controller designed is shown in Equations (5)-(8):

[0036]

[0037] In the above formula, β, p, q, and η are all control parameters of the speed loop terminal sliding mode controller, is the differential of i q , and differentiating can obtain i q * .

[0038] The improved sliding mode observer based on the two-segment dynamic boundary layer includes an improved q-axis sliding mode observer and an improved d-axis sliding mode observer. The structures of the improved d-axis sliding mode observer and the improved q-axis sliding mode observer are the same. The improved d-axis sliding mode observer is designed according to the two-segment quasi-sliding mode surface and the exponential reaching law based on the terminal saturation function. The construction steps of the improved d-axis sliding mode observer include:

[0039] 2.1 Let the d - axis sliding mode surface function of the d - axis sliding mode observer be σ d =0 indicates that the system enters the sliding mode surface. Let the first quasi - sliding mode surface The second quasi - sliding mode surface Based on the first quasi - sliding mode surface and the second quasi - sliding mode surface, divide the state space of σ d of into 3 regions. The region satisfying (-Δ ≤ σ d < - λ) ∪ (λ < σ a ≤ Δ) is region Ⅰ. The region satisfying (σ d > Δ) ∪ (σ d < - Δ) is region Ⅱ. The region satisfying - λ ≤ σ d ≤ λ is region Ⅲ. In region Ⅲ, introduce an exponential reaching law based on the terminal saturation function where is the differential component of σ d ; k and p are both control parameters of the improved d - axis sliding mode observer;

[0040] 2.2 The mathematical model of the designed improved d - axis sliding mode observer is shown in Equation (28):

[0041]

[0042] In the above formula, e dc is a positive real number related to the bound of e d ; e dmax is the upper bound of e d ; k d is the switching gain of the improved q - axis sliding mode observer, L s is the dq - axis inductance, and the d - axis and q - axis inductances are equal.

[0043] The control process of the permanent - magnet synchronous motor based on the d - axis voltage u d and the q - axis voltage u q can be simplified to the mathematical model shown in Equations (1) - (4):

[0044]

[0045] In the above formula, u d and u q are the d - axis and q - axis voltages respectively; i d and i q are the d - axis and q - axis currents respectively; ψ d and ψ q are the d - axis and q - axis magnetic fluxes respectively; L s is the dq - axis inductance, and the d - axis and q - axis inductances are equal; ψ f is the rotor magnetic flux; R s is the stator resistance; P is the differential operator; Pn is the number of pole pairs; ω e , ω m are the measured electrical angular velocity and mechanical angular velocity of the motor respectively; T e , T L are the electromagnetic torque and load torque respectively; J is the moment of inertia; B is the viscous friction coefficient.

[0046] In a third aspect, the present invention provides a PMSM improved sliding mode control device based on a two-stage dynamic boundary layer. The PMSM improved sliding mode control device includes a memory and a processor; the memory is used to store computer program codes and transmit the computer program codes to the processor; the processor is used to execute the foregoing PMSM improved sliding mode control method according to the instructions in the computer program codes.

[0047] In a fourth aspect, the present invention provides a computer-readable storage medium with a computer program stored thereon. When the computer program is executed by a processor, the foregoing PMSM improved sliding mode control method is implemented.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] 1. For the PMSM improved sliding mode control system based on a two-stage dynamic boundary layer of the present invention, in terms of speed control, a speed loop terminal sliding mode controller is introduced. The relevant terms of the load torque and mechanical angular velocity are combined into a total disturbance, and a non-linear terminal sliding mode surface is selected, which can overcome the problem that traditional PI speed control cannot effectively handle non-linear disturbances, realize the finite-time convergence of the PMSM speed tracking error, and effectively reduce the system chattering at the same time; compared with traditional PI speed control, through the terminal sliding mode controller, the overshoot in the no-load starting stage of the PMSM can be reduced by 18%, the speed drop under the sudden increase of non-linear load conditions can be reduced by 4%, the overshoot in the starting stage when the electrical parameters are mismatched can be reduced by 30%, and the adjustment time can be reduced by 0.1 s, effectively improving the dynamic and steady-state performance of the speed response.

[0050] 2. For the PMSM improved sliding mode control system based on a two-stage dynamic boundary layer of the present invention, in terms of current control, an improved sliding mode observer is designed according to the two-stage quasi-sliding mode surface and the exponential reaching law based on the terminal saturation function, which not only effectively eliminates the observation steady-state error of the dq-axis back electromotive force, but also effectively reduces the high-frequency chattering in the sliding mode reaching stage, improving the steady-state and dynamic performance of the system under electrical parameter mismatch; after decoupling compensation, the PI parameters are tuned and optimized. Compared with traditional PI current control, there is no overshoot in the current tracking process in the no-load stage, the dynamic response speed in the load stage is accelerated, and the dynamic tracking performance of the dq-axis current command is improved. Description of the Drawings

[0051] Figure 1 Schematic diagram of the improved sliding mode control system of PMSM based on two - stage dynamic boundary layer according to the present invention.

[0052] Figure 2 For e ω Simulation convergence curve graph.

[0053] Figure 3 For Figure 1 Schematic diagram of the current loop controller in

[0054] Figure 4 Quasi - sliding mode state trajectory graph before improvement.

[0055] Figure 5 For Figure 4 Structural diagram of the current closed - loop system in region Ⅰ of

[0056] Figure 6 Improved quasi - sliding mode state trajectory graph of the present invention.

[0057] Figure 7 Simulation results of the output speed under no load by applying PI control and the control method described in the present invention.

[0058] Figure 8 Simulation results of the output torque under no load by applying PI control and the control method described in the present invention.

[0059] Figure 9 Simulation results of the d - axis current of the motor under no load by applying PI control and the control method described in the present invention.

[0060] Figure 10 Simulation results of the output speed when a 1 Nm step load is suddenly applied at 0.1 s by applying PI control and the control method described in the present invention.

[0061] Figure 11 Simulation results of the output torque when a 1 Nm step load is suddenly applied at 0.1 s by applying PI control and the control method described in the present invention.

[0062] Figure 12 Simulation results of the d - axis current of the motor when a 1 Nm step load is suddenly applied at 0.1 s by applying PI control and the control method described in the present invention.

[0063] Figure 13 Sampling values of the motor output speed and output torque of the control method described in the present invention under step load.

[0064] Figure 14 Sampling values of the stator d - axis and q - axis currents of the control method described in the present invention under step load.

[0065] Figure 15This is the structural schematic diagram of the improved sliding mode control device for PMSM based on the two-stage dynamic boundary layer according to the present invention. Specific embodiments

[0066] The present invention will be further described in detail below in conjunction with specific embodiments and the accompanying drawings.

[0067] Example 1:

[0068] See Figure 1 , an improved sliding mode control system for PMSM based on a two-stage dynamic boundary layer, including a speed loop terminal sliding mode control module, a current loop control module, an improved sliding mode observer based on a two-stage dynamic boundary layer, and a permanent magnet synchronous motor control sampling module. The permanent magnet synchronous motor control sampling module is used to collect the motor mechanical angular velocity ω m of the permanent magnet synchronous motor during rotation, the d-axis current i d , the q-axis current i q , and the rotor angle θ r . The speed loop terminal sliding mode control module is used to calculate the q-axis current command value i m * through the speed loop terminal sliding mode controller according to the motor mechanical angular velocity command value ω m and the motor mechanical angular velocity ω q * ; the current loop control module is used to calculate the d-axis voltage set value u d * to be compensated = 0, the q-axis current command value i q * , the d-axis current i d , and the q-axis current i q through the current loop controller, and the improved sliding mode observer based on the two-stage dynamic boundary layer is used to calculate the d-axis back electromotive force e d ′ and the q-axis back electromotive force e q ′ to be compensated according to the d-axis current i d and the q-axis current i q , and compensate the d-axis back electromotive force e d and the q-axis back electromotive force e q to the d-axis voltage set value u d ′ and the q-axis voltage set value u q ′ to be compensated to obtain the d-axis voltage u d and the q-axis voltage u q . The permanent magnet synchronous motor control sampling module is also used to collect the rotor angle θ d collected q and the d-axis current i rThe d-axis voltage u obtained from the third-step calculation d and the q-axis voltage u q are subjected to an inverse Park transformation to obtain the α-axis voltage setpoint u α and the β-axis voltage setpoint u β . Then, combined with the given DC-side voltage U of the inverter dc , a two-level inverter is used to control the rotation of the PMSM motor;

[0069] Specifically, the speed-loop terminal sliding mode controller is designed based on the bounded lumped perturbation of the differential component and the terminal sliding mode surface, and its mathematical model is shown in Equations (5)-(8):

[0070]

[0071] In the above formula, f ω is the bounded lumped perturbation of the differential component, is the differential component of f ω , l is the known upper bound, and f n is the unmodeled term including sampling noise, calculation error, etc.; ω m is the mechanical angular velocity of the motor; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia; ψ f is the rotor magnetic flux; P n is the number of pole pairs; i q is the q-axis current; ω m * is the mechanical angular velocity command value of the motor; e ω is the mechanical angular velocity tracking error, and e ω =ω m * -ω m ; is the differential component of e ω ; s is the terminal sliding mode surface; β, p, q, and η are the control parameters of the speed-loop terminal sliding mode controller; is the differential component of i q , and differentiating can obtain i q * ;

[0072] Specifically, the improved sliding mode observer based on the two-segment dynamic boundary layer includes an improved q-axis sliding mode observer and an improved d-axis sliding mode observer. The improved d-axis sliding mode observer and the improved d-axis sliding mode observer are both designed based on the two-segment quasi-sliding mode surface and the exponential reaching law based on the terminal saturation function. The mathematical expression of the improved d-axis sliding mode observer is shown in Equation (28):

[0073]

[0074] In the above formula, f3(σ d ) is the improved d-axis sliding mode observer, and the d-axis sliding mode surface function of the d-axis sliding mode observer is σ d = 0 indicates that the system enters the sliding mode surface. Let the first quasi-sliding mode surface The second quasi-sliding mode surface Based on the first quasi-sliding mode surface and the second quasi-sliding mode surface, the d state space of σ is divided into three regions. The region satisfying (-α ≤ σ d < -λ) ∪ (λ < σ d ≤ Δ) is region I, the region satisfying (σ d > Δ) ∪ (σ d < -Δ) is region II, and the region satisfying -λ ≤ σ d ≤ λ is region III. And an exponential reaching law based on the terminal saturation function is introduced in region III L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; e dc is a positive real number related to the bound of e d ; λ = |e SS |, e d max is the upper bound of e d ; is the differential of σ d ; k and p are the control parameters of the improved d-axis sliding mode observer; k d is the switching gain of the improved q-axis sliding mode observer;

[0075] Specifically, the mathematical model of the permanent magnet synchronous motor control sampling module is shown in formulas (1) - (4):

[0076]

[0077] In the above formula, u d , u q are the d-axis and q-axis voltages respectively; i d , i q are the d-axis and q-axis currents respectively; ψ d , ψ q are the d-axis and q-axis magnetic fluxes respectively; L S is the dq-axis inductance; ψ f is the rotor magnetic flux; R S is the stator resistance; P is the differential operator; P n is the number of pole pairs; ω e , ω m are the measured electrical angular velocity and mechanical angular velocity of the motor respectively; T e , T Lare the electromagnetic torque and the load torque respectively; J is the moment of inertia; B is the viscous friction coefficient; L d and L q are the stator d-axis and q-axis inductances respectively.

[0078] Embodiment 2:

[0079] An improved sliding mode control method for PMSM based on a two-stage dynamic boundary layer is carried out in the following steps in sequence:

[0080] First step: Based on the permanent magnet synchronous motor control model, according to the d-axis voltage u d and the q-axis voltage u q control the rotation of the permanent magnet synchronous motor. Specifically, the calculated d-axis voltage u d and the q-axis voltage u q and the collected rotor angle θ r are subjected to an inverse Park transformation to obtain the α-axis voltage set value u α and the β-axis voltage set value u β . Then, combined with the given voltage U dc of the DC side of the inverter, the three-phase currents i a , i b , and i c are obtained through a two-level inverter to control the rotation of the PMSM motor; the permanent magnet synchronous motor control model is built based on the following premises: Premise 1: The stator windings are sinusoidally distributed in the stator slots; Premise 2: The flux distortion caused by switching harmonics is ignored; Premise 3: The magnetic saturation of the iron core and the iron loss caused by hysteresis and eddy currents are ignored.

[0081] The permanent magnet synchronous motor control model can be simplified to the mathematical model shown in Equations (1)-(4):

[0082]

[0083] In the above formula, u d and u q are the d-axis and q-axis voltages respectively; i d and i q are the d-axis and q-axis currents respectively; ψ d and ψ q are the d-axis and q-axis magnetic fluxes respectively; L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; ψ f is the rotor magnetic flux; R s is the stator resistance; P is the differential operator; P n is the number of pole pairs; ω e and ω m are the measured electrical angular velocity and mechanical angular velocity of the rotor respectively; T e and T Lare the electromagnetic torque and the load torque (Nm), respectively; J is the moment of inertia (kgm 2 2); B is the viscous friction coefficient.

[0084] Step 2: Establish a speed-loop terminal sliding mode controller and build a Simulink-based model framework; according to the motor mechanical angular velocity command value ω m * and the collected motor mechanical angular velocity ω m , calculate the q-axis current command value i q * ;

[0085] The steps for establishing the terminal sliding mode controller are as follows:

[0086] 1.1 Define the bounded lumped disturbance of the differential component f ω as shown in Equation (5):

[0087]

[0088] In the above formula, f ω is the bounded lumped disturbance of the differential component, is the differential component of f ω , l is the known upper bound, f n is the unmodeled term including sampling noise, calculation error, etc.; ω m is the motor mechanical angular velocity; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia;

[0089] 1.2 Obtain the first-order system shown in Equation (6) based on Equation (5), where i q is the control quantity and ω m is the output quantity; by taking an appropriate i q , make ω m track ω m * in a finite time:

[0090]

[0091] In the above formula, ψ f is the rotor magnetic flux; P n is the number of pole pairs; i q is the q-axis current;

[0092] 1.3 Take the mechanical angular velocity tracking error as e ω = ω m ’ - ω m , ω m * is the motor mechanical angular velocity command value; at ωm * When setting it as a constant, further, there is being e ω the differential component; introducing the terminal sliding mode surface s shown in Equation (7), where β > 0, p and q are positive odd numbers and 1 < p / q < 2, and designing the speed loop terminal sliding mode controller as shown in Equation (8):

[0093]

[0094] In the above formula, β, p, q, and η are the control parameters of the speed loop terminal sliding mode controller; being the differential component of i q of, differentiating to obtain i q * ;

[0095] To prove the system stability of the speed loop terminal sliding mode controller, define the energy function Substituting Equation (7) into it to obtain Equation (9):

[0096]

[0097] According to the Lyapunov criterion, since Therefore holds, which indicates that the control system is stable, and the system state can converge to the equilibrium point in finite time; set the parameters p = 5; q = 3; β = 2; η = 0.05; l = 0.8; tracking the target value ω m * = 1000 rad / s, the initial value ω m (0) = 0 rad / s, the simulation results are as shown in Figure 2 shown, Figure 2 where e ω reaches the equilibrium point at t = 0.08 s, and the reaching process has good rapidity and smoothness.

[0098] Step 3: Construct the current loop controller and build the model framework based on Simulink; specifically, the structural schematic diagram of the current controller is as shown in Figure 3 shown. Through the current loop controller, according to the d-axis current command i d * = 0, the q-axis current command value i q * , the collected d-axis current i d , the q-axis current i q , through PID adjustment control to calculate the d-axis voltage set value u d ′ to be compensated, the q-axis voltage set value u to be compensatedq '.

[0099] Step 4: Establish an improved sliding mode observation module based on a two-stage dynamic boundary layer; use an improved sliding mode observer based on a two-stage dynamic boundary layer to calculate the d-axis back electromotive force e d and q-axis current i q to obtain the d-axis back electromotive force e d and q-axis back electromotive force e q , and compensate the d-axis back electromotive force e d and q-axis back electromotive force e q to the d-axis voltage set value u d ' and the q-axis voltage set value u q ' to obtain the d-axis voltage u d and q-axis voltage u q ;

[0100] Since the i d * = 0 control in the traditional current loop design ignores the dynamic influence of the cross-coupling terms in the back electromotive force and only designs the current loop controller for the dq-axis currents separately, the closed-loop performance of the current control system will be significantly reduced as ω e increases. Therefore, the present invention first constructs an improved sliding mode observation module based on a two-stage dynamic boundary layer to achieve accurate observation and compensation of the back electromotive forces e d and e q , and then tunes and optimizes u d ' and u q ' based on the compensation of the back electromotive forces e d and e q to improve the dynamic and steady-state performance of the current loop; the construction steps of the improved sliding mode observation module based on a two-stage dynamic boundary layer are as follows:

[0101] 2.1 Design an initial sliding mode observer as shown in Equations (9) and (10):

[0102]

[0103] In the above formula, e d = ω e L s i q + f d , e q = -ω e L s i d - ω e ψ f + f q , e d and e q are the back electromotive forces of the d and q axes respectively; f d, f q are the disturbance terms caused by considering the d-axis and q-axis parameters respectively, are the estimated values of the d-axis and q-axis currents respectively, and σ d , σ q are the sliding mode surface functions of the d-axis and q-axis respectively, k d , k q are the switching gains of the d-axis and q-axis observers respectively; f(·) is the equivalent control law;

[0104] Combining Equation (9) and Equation (10) gives Equation (11). When the system enters the sliding mode surface, holds, and e d , e q will be effectively observed, that is, e d =-k d f(σ d ), e q =-k q f(σ q ):

[0105]

[0106] In the above formula, are the differential components of σ d , σ q respectively;

[0107] The observer stability criterion is shown in Equation (12). The equivalent control law of the traditional sliding mode observer is designed as Equation (13). When k q ≥|e q | is satisfied, e d , e q are observed. However, if the upper and lower bounds of e d , e q cannot be accurately estimated, k d , k q need to be selected as very large values to ensure the stability of the observer. Only using the discontinuous sgn(·) function will exacerbate the controller chattering. The present invention uses a saturation function to replace the sgn(·) function and constructs a quasi-sliding mode control function as shown in Equation (14), where Δ is the quasi-sliding mode surface. By using sliding mode control on the switching surface outside the boundary layer and continuous linear control method inside the boundary layer, that is, can effectively weaken the chattering. At this time, the quasi-sliding mode state trajectory is obtained as Figure 4 shown; from Figure 4 it can be seen that after introducing the boundary layer, the state space is divided into 2 regions. -Δ≤σ≤Δ is Region I; σ>Δ or σ<-Δ is Region II. Outside Region II, according to the sliding mode stability criterion, using the sgn(·) function as the equivalent control law, an appropriate k can be selected.d and k q to make σ d and σ q move from the initial state σ d (0) and σ q (0) into the interior of Region I;

[0108]

[0109]

[0110] 2.2 Taking the d-axis as an example, discuss the convergence of σ d in Region I; The current closed-loop system in Region I is as Figure 5 shown. Define G(s) and Φ(s) as the open-loop and closed-loop transfer functions of the system as shown in Eqs. (15) and (16). According to the Hurwitz criterion, the system is stable; Calculate the system error transfer function as shown in Eq. (17). Take e d as a step input. According to the final value theorem, the steady-state error e SS of the system is as shown in Eq. (18). The magnitude of the steady-state error e SS of the system is determined by e d , Δ, and the value of the switching gain k d of the improved d-axis sliding mode observer. If the value of Δ is very small, it will accelerate the convergence rate of e SS , and at the same time, if the value of Δ is very small, it will make the system chatter violently and deteriorate the system performance;

[0111]

[0112] To solve the contradiction between the convergence rate of the system steady-state error and the system chatter, the present invention adds a second quasi-sliding mode surface Figure 4 in Region I as shown to serve as the first quasi-sliding mode surface, forming a two-stage dynamic boundary layer. Take λ = |e SS |, e d max is the upper bound of e d ; Obtain the improved quasi-sliding mode dynamic trajectory as shown Figure 6 ; Figure 6 In the state space is divided into 3 regions, and the distribution rules of each region are shown in Table 1:

[0113] Table 1 Table of State Space Region Distribution Rules

[0114] Area number Distribution rule I <![CDATA[(-Δ≤σ d <-λ)∪(λ<σ d ≤Δ)]]> II <![CDATA[(σ d >Δ)∪(σ d <-Δ)]]> III <![CDATA[-λ ≤ σ d ≤ λ]]>

[0115] To eliminate the steady-state error and ensure the sliding mode reaching phase, so that the system state can reach the sliding mode surface in finite time, an exponential reaching law based on the terminal saturation function is introduced in region Ⅲ as shown in Equation (20). In Equation (20), both k and p are control parameters for the switching increase of the improved d-axis sliding mode observer, k > 0, 0 < p < 1. Solving Equation (20) gives Equation (21). Taking σ d (t) = 0, the time for the state variable to reach the sliding mode surface is obtained as shown in Equation (22); compared with the traditional constant-speed reaching law, due to the introduction of the |σ d | p term in the exponential reaching law, high-frequency chattering during the reaching phase can be effectively reduced when the system state approaches the sliding mode surface, and finite-time convergence can be achieved at the same time:

[0116]

[0117]

[0118]

[0119] 2.3 Substitute Equation (20) into Equation (11), and the improved quasi-sliding mode control function is obtained as shown in Equation (23). Using the boundedness of e d to further design Equation (23) gives Equation (24). In Equation (24), e dc is a positive real number related to the bound of e d to be designed. Substitute Equation (24) into Equation (11) to get Equation (25). Select an appropriate e dc to satisfy the sliding mode reaching condition. Let e dmax and e dmin be the upper and lower bounds of e d respectively, then Equation (26) holds:

[0120]

[0121]

[0122] In Equation (26), when σ d > 0, to ensure take e dc = e d min ; when σ d < 0, to ensure take e dc = e dmax ; then define to obtain the value of e dc as shown in Equation (27):

[0123] e dc = d2 - d1sgn(σ d) (27);

[0124] The expression of the improved d - axis sliding - mode observer based on the two - stage dynamic boundary layer is finally obtained as shown in Equation (28):

[0125]

[0126] The improved d - axis sliding - mode observer and the improved q - axis sliding - mode observer jointly constitute the improved sliding - mode observer. Considering that the design method of the improved q - axis sliding - mode observer is exactly the same as that of the improved d - axis sliding - mode observer, the specific design process of the improved q - axis sliding - mode observer is not given here.

[0127] Performance verification:

[0128] 1. To verify the correctness of the proposed control method and its robustness under composite disturbances, the traditional PI control method model (hereinafter referred to as PI control) and the control method model proposed in this paper (hereinafter referred to as ISMC control) are respectively built using the Simulink simulation platform for comparative research. The motor body and control parameter settings are shown in Table 1:

[0129] Table 1 Motor body and control parameter settings

[0130]

[0131]

[0132] In Table 1, k ps and k is are the proportional and integral coefficients of the speed - loop regulator under PI control respectively; k pi and k ii are the proportional and integral coefficients of the current - loop regulator under PI control; e qmax and e qmin are the upper and lower bounds of e q respectively. The sampling frequency of the system simulation environment is set to 20 kHz, the simulation duration is set to 0.5 s, and the speed set - point is 1000 r / min.

[0133] The simulated values of the output speed, output torque, and motor d - axis current of PI control and ISMC control under no load are obtained as shown in Figures 7 - 9 respectively. From Figures 7 - 9It can be seen that for the PI speed control, there is no steady-state error, the adjustment time is about 0.1 s, the peak time is about 0.03 s, the overshoot is about 25%, and there is no steady-state error in the torque and d-axis current output, but there is overshoot during the tracking process; for the ISMC speed control, there is no steady-state error, the adjustment time is about 0.15 s, the peak time is about 0.03 s, the overshoot is about 7%, and there is a very small amplitude of chattering in the torque and d-axis current output, and there is no overshoot during the tracking process. This shows that compared with the PI control, the ISMC control has better dynamic control effect. The simulated values of the output speed, output torque, and motor d-axis current of the PI control and the ISMC control under a sudden step load of 1 Nm at 0.1 s are respectively as Figures 10 - 12 shown. From Figures 10 - 12 it can be seen that the effects of the PI control and the ISMC control on the output speed are almost the same, the maximum speed drop is about 40 r / min, and it can quickly return to the steady state after about 0.05 s of dynamic process; in terms of torque output and d-axis current tracking, compared with the PI control, the ISMC control has no overshoot during the tracking process and has a better dynamic response speed. The above results show that the ISMC control has better disturbance rejection ability for sudden load changes.

[0134] 2. To verify the influence of the control method described in the present invention on the performance of the motor system, a motor speed regulation platform is built. The platform consists of a host computer, a power supply, a motor drive board, a DSP control board, a motor back-to-back platform, control software, etc. The development board selects DSPF28379D; the motor drive board uses TEXAS-DRV8305 with a sampling frequency of 20 kHz; the motor uses 42JSF630AS-1000 with an internal speed encoder, and the dq-axis current and torque data are output by the DAC built in the DSP, and a UNI-T UTD2102CEX oscilloscope is used to collect data. The motor starts without load, the rated speed is set to 1000 r / min, and a 1 Nm step load is introduced at t = 0.1 s. The motor output speed and output torque under the step load are as Figure 13 shown, and the sampled values of the stator d and q-axis currents are as Figure 14 shown.

[0135] From Figure 13 it can be seen that under no-load conditions, the motor speed rises smoothly, the time to reach the rated speed is about 8 ms, the speed overshoot is about 8%, and the fluctuations of the torque and stator dq-axis currents are small; under the condition of sudden step load, the motor dynamic response time is about 4 ms, the motor output speed under steady-state conditions is about 1000 r / min, the output torque is about 1 Nm, the d-axis current is about 0 A, and the q-axis current is about 6 A. The output results can track the set value without static error, which can verify that the system has good disturbance rejection performance.

[0136] Example 3:

[0137] SeeFigure 14 , a PMSM improved sliding mode control device based on a two-stage dynamic boundary layer, comprising a memory and a processor; the memory is used for storing computer program code and transmitting the computer program code to the processor; the processor is used for executing the configuration and operation optimization method described in Embodiment 2 according to the instructions in the computer program code.

[0138] Embodiment 4:

[0139] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the configuration and operation optimization method described in Embodiment 2 is implemented.

[0140] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0141] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure One one process or multiple processes and / or blocks Figure One one block or multiple blocks.

[0142] These computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing devices to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device implements the functions specified in Figure One one process or multiple processes and / or blocks Figure One one block or multiple blocks.

[0143] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable apparatus to generate a computer-implemented process, thereby providing instructions for implementing the functions specified in one process or a plurality of processes and / or blocks Figure One in one block or a plurality of blocks Figure One in the steps of the method.

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific embodiments of the present invention, and any modifications or equivalent replacements made without departing from the spirit and scope of the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. An improved sliding mode control system for PMSM based on a two - stage dynamic boundary layer, characterized in that: The improved sliding mode control system for PMSM includes a speed - loop terminal sliding mode control module, a current - loop control module, an improved sliding mode observer based on a two - stage dynamic boundary layer, and a permanent magnet synchronous motor control sampling module; The permanent magnet synchronous motor control sampling module is used to collect the mechanical angular velocity ω of the permanent magnet synchronous motor during rotation m , the d-axis current i d and the q-axis current i q ; The speed loop terminal sliding mode control module is used to calculate the q-axis current command value i according to the motor mechanical angular velocity command value ω m * and the motor mechanical angular velocity ω m , through the speed loop terminal sliding mode controller q * ; The current loop control module is used to control and calculate the set value u d * = 0 of the d-axis current command i, the set value i q * of the q-axis current, the d-axis current i d and the q-axis current i q , and control the calculation of the set value u d ' of the d-axis voltage to be compensated and the set value u q ' of the q-axis voltage to be compensated; The improved sliding mode observation module based on the two-stage dynamic boundary layer is used to calculate the d-axis back electromotive force e d and q-axis current i q through the improved sliding mode observer based on the two-stage dynamic boundary layer, and calculate the d-axis back electromotive force e d and q-axis back electromotive force e q . Then, the d-axis back electromotive force e d and q-axis back electromotive force e q are compensated to the d-axis voltage set value u d ' to be compensated and the q-axis voltage set value u q ' to be compensated, and the d-axis voltage u d and q-axis voltage u q are obtained; The permanent magnet synchronous motor control sampling module is also used to control the rotation of the permanent magnet synchronous motor based on the d-axis voltage u d and the q-axis voltage u q .

2. The improved sliding mode control system for PMSM based on a two - stage dynamic boundary layer according to claim 1, characterized in that: The speed - loop terminal sliding mode controller is designed based on the bounded lumped disturbance of the differential component and the terminal sliding mode surface, and its mathematical model is shown in formulas (5)-(8): In the above formula, f ω is a bounded lumped disturbance of the differential component, is the differential component of f ω , l is a known upper bound, and f n is an unmodeled term including sampling noise, calculation error, etc.; ω m is the mechanical angular velocity of the motor; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia; ψ f is the rotor flux linkage; P n is the number of pole pairs; i q is the q-axis current; ω m * is the command value of the mechanical angular velocity of the motor; e ω is the mechanical angular velocity tracking error, and e ω = ω m * - ω m ; is the differential component of e ω ; s is the terminal sliding mode surface; β, p, q, and η are all control parameters of the terminal sliding mode controller of the speed loop, is the differential component of i q , and differentiating can obtain i q * .

3. The improved sliding mode control system for PMSM based on a two - stage dynamic boundary layer according to claim 1, characterized in that: The improved sliding mode observer based on a two - stage dynamic boundary layer includes an improved q - axis sliding mode observer and an improved d - axis sliding mode observer. The structures of the improved d - axis sliding mode observer and the improved q - axis sliding mode observer are the same. The improved d - axis sliding mode observer is designed according to two - stage quasi - sliding mode surfaces and an exponential reaching law based on a terminal saturation function, and the mathematical expression of the improved d - axis sliding mode observer is shown in formula (28): In the above formula, f3(σ d ) is an improved d-axis sliding mode observer, and the d-axis sliding mode surface function of the d-axis sliding mode observer is σ d = 0 indicates that the system enters the sliding mode surface. Let the first quasi-sliding mode surface The second quasi-sliding mode surface Based on the first quasi-sliding mode surface and the second quasi-sliding mode surface, the d state space of σ is divided into three regions, satisfying (-Δ ≤ σ d < -λ) ∪ (λ < σ d ≤ Δ) is region I, satisfying (σ d > Δ) ∪ (σ d < -Δ) is region II, satisfying -λ ≤ σ d ≤ λ is region III, and an exponential reaching law based on the terminal saturation function is introduced in region III L S is the dq-axis inductor, and the d-axis and q-axis inductors are equal; e dc is a positive real number related to the bound of e d ; λ = |e ss |, e d max is the upper bound of e d ; is the differential component of σ d ; k and p are the control parameters of the improved d-axis sliding mode observer; k d is the switching gain of the improved q-axis sliding mode observer.

4. The improved sliding mode control system for PMSM based on a two - stage dynamic boundary layer according to claim 1, characterized in that: The mathematical model of the permanent magnet synchronous motor control sampling module is shown in formulas (1)-(4): In the above formula, u d and u q are the d-axis and q-axis voltages respectively; i d and i q are the d-axis and q-axis currents respectively; ψ d and ψ q are the d-axis and q-axis magnetic fluxes respectively; L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; ψ f is the rotor magnetic flux; R s is the stator resistance; P is the differential operator; P n is the number of pole pairs; ω e and ω m are the measured electrical angular velocity and mechanical angular velocity of the motor respectively; T e and T L are the electromagnetic torque and load torque respectively; J is the moment of inertia; B is the viscous friction coefficient.

5. An improved sliding mode control method for PMSM based on a two - stage dynamic boundary layer, characterized in that: The improved sliding mode control method for PMSM includes: Collect the mechanical angular velocity ω of the permanent magnet synchronous motor during rotation m , the d-axis current i d and the q-axis current i q ; The speed-loop terminal sliding mode controller calculates the q-axis current command value \(i_q\) according to the motor mechanical angular velocity command value \(\omega_m\) m * and the motor mechanical angular velocity \(\omega_m\) m , and calculates the q-axis current command value \(i_q\) q * ; The current loop controller calculates the d-axis voltage set value u d * = 0, the q-axis current command value i q * , the d-axis current i d , the q-axis current i q , and calculates the d-axis voltage set value u d ' to be compensated and the q-axis voltage set value u q ' to be compensated through PID regulation control; Based on an improved sliding mode observer with a two-stage dynamic boundary layer, the d-axis current i d and the q-axis current i q are used to calculate the d-axis back electromotive force e d and the q-axis back electromotive force e q . Then, the d-axis back electromotive force e d and the q-axis back electromotive force e q are compensated to the d-axis voltage set value u d ' to be compensated and the q-axis voltage set value u q ' to be compensated, resulting in the d-axis voltage u d and the q-axis voltage u q . Based on the d-axis voltage u d and the q-axis voltage u q to control the rotation of a permanent magnet synchronous motor.

6. The improved sliding mode control method for PMSM based on a two - stage dynamic boundary layer according to claim 5, characterized in that: The construction steps of the speed - loop terminal sliding mode controller include: 1.1 Definition of the bounded lumped disturbance \(f\) of the differential quantity ω As shown in Equation (5) In the above formula, is the differential of f ω , l is the known upper bound, ω m is the mechanical angular velocity of the motor; T L is the load torque; B is the viscous friction coefficient; J is the moment of inertia; f n is the unmodeled term including sampling noise, calculation error, etc.; 1.2 Based on Equation (5), a first-order system shown in Equation (6) is obtained. By taking an appropriate i q , the ω m can track ω m * within a finite time: In the above formula, P n is the number of pole pairs; ψ f is the rotor flux linkage; i q is the q-axis current; 1.3 Take the mechanical angular velocity tracking error. The velocity tracking error is e ω = ω m * - ω m , ω m * is the motor mechanical angular velocity command value, and the terminal sliding mode surface s shown in Equation (7) is introduced. The mathematical model of the terminal sliding mode controller for the velocity loop is designed as shown in Equations (5)-(8): In the above formula, β, p, q, and η are all control parameters of the speed loop terminal sliding mode controller. is the differential component of i q . Differentiating can obtain i q * .

7. The improved sliding mode control method for PMSM based on a two - stage dynamic boundary layer according to claim 5, characterized in that: The improved sliding mode observer based on a two - stage dynamic boundary layer includes an improved q - axis sliding mode observer and an improved d - axis sliding mode observer. The structures of the improved d - axis sliding mode observer and the improved q - axis sliding mode observer are the same. The improved d - axis sliding mode observer is designed according to two - stage quasi - sliding mode surfaces and an exponential reaching law based on a terminal saturation function. The construction steps of the improved d - axis sliding mode observer include: 2.1 Let the d - axis sliding mode surface function of the d - axis sliding mode observer be σ d = 0 indicates that the system enters the sliding mode surface. Let the first quasi - sliding mode surface The second quasi - sliding mode surface Based on the first quasi - sliding mode surface and the second quasi - sliding mode surface, divide the state space of σ d into 3 regions, satisfying (-Δ ≤ σ d < -λ) ∪ (λ < σ d ≤ Δ) is region Ⅰ, satisfying (σ d > Δ) ∪ (σ d < -Δ) is region Ⅱ, and satisfying -λ ≤ σ d ≤ λ is region Ⅲ. In region Ⅲ, introduce an exponential reaching law based on the terminal saturation function where is the differential of σ d , and k, p are both control parameters of the improved d - axis sliding mode observer; 2.2 Design the mathematical model of the improved d - axis sliding mode observer as shown in formula (28): In the above formula, e dc is a positive real number related to the bound of e d ; e dmax is the upper bound of e d ; k d is the switching gain for improving the q-axis sliding mode observer, and L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal.

8. The improved sliding mode control method for PMSM based on a two - stage dynamic boundary layer according to claim 5, characterized in that: The control process of controlling the rotation of a permanent magnet synchronous motor based on the d-axis voltage u d and the q-axis voltage u q can be simplified into a mathematical model as shown in Equations (1)-(4): In the above formula, u d and u q are the d-axis and q-axis voltages respectively; i d and i q are the d-axis and q-axis currents respectively; ψ d and ψ q are the d-axis and q-axis magnetic fluxes respectively; L s is the dq-axis inductance, and the d-axis and q-axis inductances are equal; ψ f is the rotor magnetic flux; R s is the stator resistance; P is the differential operator; p n is the number of pole pairs; ω e and ω m are the measured electrical angular velocity and mechanical angular velocity of the motor respectively; T e and T L are the electromagnetic torque and load torque respectively; J is the moment of inertia; B is the viscous friction coefficient.

9. An improved sliding mode control device for PMSM based on a two-stage dynamic boundary layer, characterized in that: The improved sliding mode control device for PMSM includes a memory and a processor; the memory is used to store computer program codes and transmit the computer program codes to the processor; the processor is used to execute the improved sliding mode control method for PMSM according to any one of claims 5 - 8 according to the instructions in the computer program codes.

10. A computer-readable storage medium, characterized in that: A computer program is stored on a computer - readable storage medium, and when the computer program is executed by a processor, it implements the improved sliding mode control method for PMSM according to any one of claims 5 - 8.

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