PMSM control method and system optimized by integral hybrid reaching law and grey wolf algorithm

Abstract

The invention discloses a PMSM control method and system optimized by an integral hybrid reaching law and a grey wolf algorithm. The method comprises the following steps: constructing a mathematical model of a PMSM and collecting an electric signal; constructing a direct-axis and quadrature-axis current prediction equation based on the collected electric signals; constructing a traditional sliding mode observer, and constructing a sliding mode surface according to the current prediction equation; improving the constructed sliding mode surface by using an reaching law; and for an observation signal output by the improved sliding-mode observer, a gray wolf model is used to optimize PLL parameters, and control of the PMSM is completed. According to the method, the constant-speed reaching law of a traditional sliding mode observer is improved, a variable gain function and an integral weighting function are introduced, high-frequency buffeting caused by discontinuous switching is remarkably weakened while the sliding mode control robustness is kept, then PLL parameters are globally optimized through the grey wolf algorithm, the angle convergence speed of the observer is increased, and the precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and specifically relates to a PMSM control method and system optimized by an integral hybrid reaching law and a gray wolf algorithm. Background Art

[0002] Permanent magnet synchronous motors have significant characteristics such as large power density, high efficiency, compact structure, and high reliability. They are widely used in industries such as textiles, spacecraft, and petroleum. At the same time, due to the sensitivity of vector control to parameters, obtaining the rotor position is particularly important.

[0003] Traditional mechanical sensors for direct position detection mainly include resolvers, encoders, Hall sensors, etc. This increases the cost of the motor, increases the volume and weight of the motor, and sensor failure may occur in some relatively harsh scenarios. Therefore, sensorless control technology becomes particularly important.

[0004] Sliding mode observers are favored due to their low sensitivity to system parameter changes and strong robustness to external disturbances. They have a simple algorithm structure and high reliability, and are easy to apply in practical engineering. However, due to the discontinuous characteristics of their control mechanism, sliding mode observers may generate high-frequency jitter due to the non-ideal behavior of the switching switch and the inertia of the system, which will significantly affect the accuracy of rotor position estimation. In addition, as the speed changes, the amplitude of the back electromotive force will also be affected, thereby changing the system bandwidth, weakening the ability to resist speed disturbances under fixed parameter settings, and further affecting the observation accuracy.

[0005] Therefore, developing a sensorless algorithm for sliding mode observers that can effectively suppress high-frequency jitter and enhance the anti-speed disturbance performance has great research value and broad application potential. Such improvements will help improve the stability and accuracy of motor control systems under different operating conditions. Summary of the Invention

[0006] To solve the technical problems in the above background, the present invention provides a PMSM control method optimized by an integral hybrid reaching law and a gray wolf algorithm. The steps include:

[0007] Construct the mathematical model of the PMSM and collect electrical signals;

[0008] Based on the collected electrical signals, construct the direct-axis and quadrature-axis current prediction equations;

[0009] Construct a traditional sliding mode observer and construct a sliding mode surface according to the current prediction equation;

[0010] Improve the constructed sliding mode surface using a reaching law;

[0011] For the observed signal output by the improved sliding mode observer, the gray wolf model is used to optimize the PLL parameters to complete the control of the PMSM.

[0012] Preferably, the constructed mathematical model includes:

[0013]

[0014] Wherein, L d , L q are the inductances of the direct axis and the quadrature axis of the motor respectively; R is the stator resistance; U d , U q are the voltage quantities of the direct axis and the quadrature axis of the motor respectively; i q , i d are the current quantities of the direct axis and the quadrature axis of the motor respectively; w e represents the actual speed of the motor; ψ f represents the magnetic flux.

[0015] Preferably, the collected electrical signals include: i a , i b , i c three-phase currents and voltage U α , U β . The two-phase currents i α , i β in the stationary coordinate system are obtained through the Clark transformation. Then, the currents i α , i β and the electrical angle θ are transformed through the Park transformation to obtain the two-phase currents i d , i q in the synchronous coordinate system;

[0016] The Clark transformation includes the following:

[0017]

[0018] The Park transformation includes the following:

[0019]

[0020] Wherein, θ e represents the electrical angle.

[0021] Preferably, the constructed prediction equations for the direct-axis and quadrature-axis currents include:

[0022]

[0023] Wherein, L d , L q are the inductances of the direct axis and the quadrature axis of the motor respectively; Rs is the stator resistance; i α , i βare the direct-axis and quadrature-axis current quantities in the motor stationary coordinate system; U α and U β are the direct-axis and quadrature-axis voltages in the stationary coordinate system; V α and V β are the back electromotive force components; w e is the actual rotational speed of the motor; is the differential operator.

[0024] Preferably, the constructed traditional sliding mode observer includes:

[0025]

[0026] where e i is the current error, is the derivative of x1; x1 and x2 represent system state variables.

[0027] The defined sliding mode surface function s is:

[0028] s = Cx1 + x2

[0029] where C represents a constant.

[0030] Preferably, the method for improving the constructed sliding mode surface using the reaching law includes:

[0031]

[0032] where s is the sliding mode surface, k(t) is a variable gain function, λ(t) is an adjustable weight factor function, ∫sdt is the current error integral function, sgn(s) is the sign function; t is the current iteration number.

[0033] Preferably, the optimal parameter PLL closed-loop equation optimized by the grey wolf model includes:

[0034]

[0035] where, represents the optimized proportional gain; represents the optimized integral gain; w ref (t) represents the reference angular frequency; w est (t) represents the output angular frequency; t is the current iteration number.

[0036] The present invention also provides a PMSM control system optimized by an integral hybrid reaching law and a grey wolf algorithm, the system is used to implement the above method, and includes: an acquisition module, a prediction module, a construction module, an improvement module, and a control module;

[0037] The acquisition module is used to construct a mathematical model of the PMSM and collect electrical signals;

[0038] The prediction module is used to construct the direct-axis and quadrature-axis current prediction equations based on the collected electrical signals.

[0039] The construction module is used to construct a traditional sliding mode observer and construct a sliding mode surface according to the current prediction equations.

[0040] The improvement module is used to improve the constructed sliding mode surface by using a reaching law.

[0041] The control module is used to optimize the PLL parameters using a gray wolf model for the observation signals output by the improved sliding mode observer, and complete the control of the PMSM.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] By improving the constant speed reaching law of the traditional sliding mode observer, introducing the variable gain function k(t) and the integral weight function λ(t), the present invention significantly weakens the high-frequency chattering caused by discontinuous switching while maintaining the robustness of the sliding mode control. The integral link compensates for the steady-state deviation through the cumulative error, further reducing the influence of high-frequency oscillation on the system. Then, the PLL parameters are globally optimized by the gray wolf algorithm, improving the convergence speed and accuracy of the observer angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0045] Figure 1 It is a schematic flowchart of the method according to an embodiment of the present invention;

[0046] Figure 2 It is a flowchart of the gray wolf algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0049] Embodiment 1

[0050] As Figure 1 、 Figure 2 shown, the following are the schematic diagrams of the method flow of this embodiment, and the steps include:

[0051] S1. Construct a mathematical model of the PMSM and collect electrical signals.

[0052] In this embodiment, the established mathematical model of the PMSM (permanent magnet synchronous motor) is as follows:

[0053]

[0054] Among them, L d 、L q are the inductance values of the direct axis and the quadrature axis of the motor respectively; R is the stator resistance; U d 、U q are the voltage values of the direct axis and the quadrature axis of the motor respectively; i q 、i d are the current values of the direct axis and the quadrature axis of the motor respectively; w e represents the actual speed of the motor; ψ f represents the magnetic flux.

[0055] Collect the three-phase currents of i a 、i b 、i c and the voltage U α 、U β through the voltage sensor. Obtain the two-phase currents i α 、i β in the stationary coordinate system through the Clark transformation. Then, transform the currents i α 、i β and the electrical angle θ through the Park transformation to obtain the two-phase currents i d 、i q in the synchronous coordinate system.

[0056] The above Clark transformation is as follows:

[0057]

[0058] The above Park transformation is as follows:

[0059]

[0060] Among them, θ e represents the electrical angle.

[0061] Compare the U α 、U β collected by the voltage sensor with the bus voltage U dcThree-phase voltages are obtained through a vector pulse width modulation module.

[0062] S2. Based on the collected electrical signals, construct direct-axis and quadrature-axis current prediction equations.

[0063] Transform the formula into a form symmetric with respect to the direct-axis and quadrature-axis inductances L d 、L q :

[0064]

[0065] The constructed current equations are as follows:

[0066]

[0067] Among them, L d 、L q are the inductances of the direct axis and quadrature axis of the motor respectively; Rs is the stator resistance; i α 、i β are the direct-axis and quadrature-axis current values in the stationary coordinate system of the motor respectively; U α 、U β are the direct-axis and quadrature-axis voltages in the stationary coordinate system; V α 、V β are the back electromotive force components; w e is the actual rotational speed of the motor; is the differential operator.

[0068] S3. Construct a traditional sliding mode observer and construct a sliding mode surface according to the current prediction equation.

[0069] Define the system state variables:

[0070]

[0071] In the formula, e i is the current error, is the derivative of x1; x1 and x2 represent the system state variables.

[0072] Define the sliding mode surface function s:

[0073] s = Cx1 + x2

[0074] Among them, C represents a constant and C > 0.

[0075] S4. Improve the constructed sliding mode surface using the reaching law.

[0076]

[0077] In the formula, s is the sliding mode surface, where k(t) is a variable gain function, λ(t) is an adjustable weight factor function, ∫sdt is the current error integral function, and sgn(s) is the sign function.

[0078] Among them, k(t) is a variable gain, which changes according to the magnitude of the error. The specific expression is:

[0079]

[0080] where k0 is the initial gain and α is the variable gain, representing the absolute value of the current observation error.

[0081] λ(t) is an integral weight function, which changes with the time constant. The specific expression is:

[0082] λ(t) = 1 - k1 -βt

[0083] where k1 is the initial gain, t is the system time, and β is the exponential gain.

[0084] The expression of the sign function sgn(s) is:

[0085]

[0086] To prove the stability of the improved reaching law, the Lyapunov function is selected:

[0087]

[0088] Taking the derivative of the formula, we can get:

[0089]

[0090] k(t) > 0 and λ > 0, and the system is globally asymptotically stable.

[0091] S5. For the observed signal output by the improved sliding mode observer, use the grey wolf model to optimize the PLL parameters to complete the control of the PMSM.

[0092] The back electromotive force obtained by observation is passed through a first-order low-pass filter and then through a PLL to obtain the electrical angle value. Through the sliding mode observer, the two-phase back electromotive force signals e α 、e β These signals can be directly obtained from the output of the sliding mode observer. The observed back electromotive force signals e α and e β are filtered through a first-order low-pass filter to filter out high-frequency noise and chattering signals. The transfer function of the low-pass filter is:

[0093]

[0094] Among them, τ is the time constant of the filter, which determines the cutoff frequency.

[0095] The filtered back EMF signal is:

[0096]

[0097] Among them, e αβ Indicates the back electromotive force signal.

[0098] PLL is used to extract the rotor electrical angle θ from the filtered back EMF signal. The core of PLL is to estimate the rotor position by tracking the phase of the back EMF signal. The back EMF signal is as follows:

[0099]

[0100] e β =Ecos(θ)

[0101] Where E is the magnitude of the back EMF and θ is the electrical angle of the rotor.

[0102] The traditional PLL output angular frequency is estimated as:

[0103]

[0104] Where, e(t) is the phase error; K p , K i are the proportional gain and integral gain of the PI controller; t is the current iteration number.

[0105] Combining the mathematical model of the three-phase permanent magnet synchronous motor and the PI controller, the phase error differential equation can be obtained:

[0106]

[0107] Substituting e(t) = δ, we get the simplified form:

[0108]

[0109] Among them, w ref (t) represents the reference angular frequency.

[0110] The objective function is defined as a comprehensive indicator of phase error:

[0111] J(K p ,K i )=w1|e ss |+w2max|e(t)|+w3τ rise

[0112] Among them, w1, w2, w3 all represent weight coefficients; τ riseIndicates the rise time.

[0113] Solve the steady-state error e through Laplace transform ss :

[0114]

[0115] where E(s) is the error transfer function.

[0116] Use the grey wolf model to optimize the PLL parameters. The steps include:

[0117] S501. Initialize the wolf pack and generate the Tent mapping chaotic sequence:

[0118]

[0119] where x n represents the nth step value in the chaotic sequence; r ∈ [0, 1] is a random number

[0120] S502. Sort the grey wolves in descending order of fitness value and select Alpha(X α ), Beta(X β ), Delta(X δ ). Among them, Alpha(X α ), Beta(X β ), Delta(X δ ) correspond to the optimal solution, sub-optimal solution, and third-optimal solution in the optimization process respectively.

[0121] S503. Update the positions of the wolf pack:

[0122] D α = |C1X α -X i |, D β = |C2X β -X i |, D δ = |C3X δ -X i |

[0123]

[0124] where C1, C2, C3 ∈ [0, 1] are random numbers; A = 2ar - a, is the linear attenuation factor; r ∈ [0, 1] is a random number; T is the maximum number of iterations; X i，new represents the position of the grey wolf individual after update; D α represents the distance between the current grey wolf individual and the Alpha wolf; D β represents the distance between the current grey wolf individual and the Beta wolf; D δRepresents the distance between the current grey wolf individual and the Delta wolf; Represents the adjusted proportional gain coefficient; Represents the adjusted integral gain coefficient; X i Represents the distance between the current grey wolf individual and Alpha(X α ), Beta(X β ), Delta(X δ ) wolves, due to calculating the position update weight.

[0125] S504. Boundary constraint:

[0126]

[0127] Among them, K p，max Represents the maximum boundary of the proportional gain; K p，min Represents the minimum boundary of the proportional gain; K i，max Represents the maximum boundary of the integral gain; K i，min Represents the minimum boundary of the integral gain.

[0128] S505. Optimal parameter PLL closed-loop equation:

[0129]

[0130] Among them, Represents the optimized proportional gain; Represents the optimized integral gain; w est (t) represents the output angular frequency.

[0131] Embodiment 2

[0132] This embodiment also provides a PMSM control system optimized by an integral hybrid reaching law and a grey wolf algorithm, including: an acquisition module, a prediction module, a construction module, an improvement module, and a control module; the acquisition module is used to construct a mathematical model of the PMSM and collect electrical signals; the prediction module is used to construct direct-axis and quadrature-axis current prediction equations based on the collected electrical signals; the construction module is used to construct a traditional sliding mode observer and construct a sliding mode surface according to the current prediction equation; the improvement module is used to improve the constructed sliding mode surface by using a reaching law; the control module is used to optimize the PLL parameters using a grey wolf model for the observation signal output by the improved sliding mode observer to complete the control of the PMSM.

[0133] Next, in combination with this embodiment, it will be detailed how the present invention solves technical problems in real life.

[0134] First, use the acquisition module to construct a mathematical model of the PMSM and collect electrical signals.

[0135] In this embodiment, the established mathematical model of the PMSM (permanent magnet synchronous motor) is as follows:

[0136]

[0137] Among them, L d and L q are the inductances of the direct axis and the quadrature axis of the motor respectively; R is the stator resistance; U d and U q are the voltage quantities of the direct axis and the quadrature axis of the motor respectively; i q and i d are the current quantities of the direct axis and the quadrature axis of the motor respectively; w e represents the actual speed of the motor; ψ f represents the magnetic flux.

[0138] Collect the three-phase currents of i a , i b , i c and collect the voltage U α , U β through the voltage sensor. Obtain the two-phase currents i α , i β in the stationary coordinate system through the Clark transformation, and then transform the currents i α , i β and the electrical angle θ into the two-phase currents i d , i q in the synchronous coordinate system through the Park transformation.

[0139] The above Clark transformation includes the following:

[0140]

[0141] The above Park transformation includes the following:

[0142]

[0143] Among them, θ e represents the electrical angle.

[0144] Use the voltage sensor to collect U α , U β and the bus voltage U dc to obtain the three-phase voltage through the vector pulse width modulation module.

[0145] The prediction module constructs the prediction equations of the direct-axis and quadrature-axis currents based on the collected electrical signals.

[0146] Transform the formula into the symmetric form of the direct-axis and quadrature-axis inductances L d , L q :

[0147]

[0148] The constructed current equation is as follows:

[0149]

[0150] Where L d and L q are the inductances of the direct axis and quadrature axis of the motor respectively; Rs is the stator resistance; i α and i β are the current values of the direct axis and quadrature axis in the stationary coordinate system of the motor respectively; U α and U β are the voltages of the direct axis and quadrature axis in the stationary coordinate system; V α and V β are the back electromotive force components; w e is the actual rotational speed of the motor; is the differential operator.

[0151] Use the building block to construct a traditional sliding mode observer, and construct a sliding mode surface according to the current prediction equation.

[0152] Define the system state variables:

[0153]

[0154] In the formula, e i is the current error, is the derivative of x1; x 1、 x2 represents the system state variables.

[0155] Define the sliding mode surface function s:

[0156] s = Cx1 + x2

[0157] Where C represents a constant and C > 0.

[0158] The improvement module improves the constructed sliding mode surface using the reaching law.

[0159]

[0160] In the formula, s is the sliding mode surface, where k(t) is a variable gain function, λ(t) is an adjustable weight factor function, ∫sdt is the current error integral function, and sgn(s) is the sign function.

[0161] Among them, k(t) is a variable gain, which changes according to the magnitude of the error, and the specific form is:

[0162]

[0163] Where k0 is the initial gain, α is the variable gain, Represents the absolute value of the current observation error.

[0164] λ(t) is the integral weight function, which changes with the time constant and has the specific form:

[0165] λ(t) = 1 - k1 -βt

[0166] where k1 is the initial gain, t is the system time, and β is the exponential gain.

[0167] The expression of the sign function sgn(s) is:

[0168]

[0169] To prove the stability of the improved reaching law, the Lyapunov function is selected:

[0170]

[0171] Taking the derivative of the formula gives:

[0172]

[0173] k(t) > 0, and λ > 0, the system is globally asymptotically stable.

[0174] The control module uses the grey wolf model to optimize the PLL parameters for the observation signal output by the improved sliding mode observer to complete the control of the PMSM.

[0175] The back electromotive force obtained by observation is passed through a first-order low-pass filter and then through a PLL to obtain the electrical angle value. Through the sliding mode observer, two-phase back electromotive force signals e α 、e β These signals can be directly obtained from the output of the sliding mode observer. The observed back electromotive force signals e α and e β are filtered through a first-order low-pass filter to filter out high-frequency noise and chattering signals. The transfer function of the low-pass filter is:

[0176]

[0177] where τ represents the time constant of the filter, which determines the cut-off frequency.

[0178] The filtered back electromotive force signal is:

[0179]

[0180] where, e αβ represents the back electromotive force signal.

[0181] PLL is used to extract the rotor electrical angle θ from the filtered back EMF signal. The core of PLL is to estimate the rotor position by tracking the phase of the back EMF signal. The back EMF signal is as follows:

[0182] e α =-Esin(θ)

[0183] e β =Ecos(θ)

[0184] Where E is the magnitude of the back EMF and θ is the electrical angle of the rotor.

[0185] The traditional PLL output angular frequency is estimated as:

[0186]

[0187] Where, e(t) is the phase error; K p , K i are the proportional gain and integral gain of the PI controller; t is the current iteration number.

[0188] Combining the mathematical model of the three-phase permanent magnet synchronous motor and the PI controller, the phase error differential equation can be obtained:

[0189]

[0190] Substituting e(t) = δ, we get the simplified form:

[0191]

[0192] Among them, w ref (t) represents the reference angular frequency.

[0193] The objective function is defined as a comprehensive indicator of phase error:

[0194] J(K p ,K i )=w1|e ss |+w2max|e(t)|+w3τ rise

[0195] Among them, w1, w2, w3 all represent weight coefficients; τ rise Indicates the rise time.

[0196] Solving the steady-state error e by Laplace transform ss :

[0197]

[0198] Where E(s) is the error transfer function.

[0199] like Figure 2As shown, the steps of using the Grey Wolf Optimizer to optimize the PLL parameters include:

[0200] S501. Initialization of the wolf pack and generation of Tent mapping chaotic sequence:

[0201]

[0202] where x n represents the nth step value in the chaotic sequence; r ∈ [0, 1] is a random number.

[0203] S502. Sort the grey wolves in descending order of fitness value and select Alpha(X α ), Beta(X β ), and Delta(X δ ).

[0204] S503. Update the positions of the wolf pack:

[0205] D α = |C1X α - X i |, D β = |C2X β - X i |, D δ = |C3X δ - X i |

[0206]

[0207] where C1, C2, C3 ∈ [0, 1] are random numbers; A = 2ar - a, is the linear attenuation factor; r ∈ [0, 1] is a random number; T is the maximum number of iterations; X i，new represents the position of the updated grey wolf individual; D α represents the distance between the current grey wolf individual and the Alpha wolf; D β represents the distance between the current grey wolf individual and the Beta wolf; D δ represents the distance between the current grey wolf individual and the Delta wolf; represents the adjusted proportional gain coefficient; represents the adjusted integral gain coefficient; X i represents the distance between the current grey wolf individual and Alpha(X α ), Beta(X β ), and Delta(X δ ) wolves, which is used to calculate the position update weights.

[0208] S504. Boundary constraint:

[0209]

[0210] Among them, K p，max represents the maximum boundary of the proportional gain; K p，min represents the minimum boundary of the proportional gain; K i，max represents the maximum boundary of the integral gain; K i，min represents the minimum boundary of the integral gain.

[0211] S505. Optimal parameter PLL closed-loop equation:

[0212]

[0213] Among them, represents the optimized proportional gain; represents the optimized integral gain; w est (t) represents the output angular frequency.

[0214] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A control method for PMSM optimized by integral hybrid reaching law and grey wolf algorithm, characterized in that the steps Including: Construct the mathematical model of the PMSM and collect the electrical signals; Based on the collected electrical signals, construct the direct-axis and quadrature-axis current prediction equations; Construct a traditional sliding-mode observer and construct a sliding-mode surface according to the current prediction equations; Improve the constructed sliding-mode surface using the reaching law; For the observation signals output by the improved sliding-mode observer, use the grey wolf model to optimize the PLL parameters to complete the control of the PMSM.

2. The PMSM control method optimized by the integral hybrid reaching law and the grey wolf algorithm according to claim 1, wherein, The constructed mathematical model includes: Among them, L d and L q are the inductance values of the direct axis and quadrature axis of the motor respectively; R is the stator resistance; U d and U q are the voltage values of the direct axis and quadrature axis of the motor respectively; i q and i d are the current values of the direct axis and quadrature axis of the motor respectively; w e represents the actual rotational speed of the motor; ψ f represents the magnetic flux.

3. The PMSM control method optimized by the integral hybrid reaching law and the grey wolf algorithm according to claim 1, wherein, The collected electrical signals include: i a , i b , i c three-phase currents and voltage U α , U β . By performing Clark transformation, two-phase currents i α , i β in the stationary coordinate system are obtained. Then, currents i α , i β and electrical angle θ are transformed through Park transformation to obtain two-phase currents i d , i q in the synchronous coordinate system; The Clark transformation includes the following: The Park transformation includes the following: Among them, θ e represents the electrical angle.

4. The PMSM control method optimized by the integral hybrid reaching law and the grey wolf algorithm according to claim 3, wherein, The constructed direct-axis and quadrature-axis current prediction equations include: Among them, L d and L q are the inductance values of the direct axis and quadrature axis of the motor respectively; Rs is the stator resistance; i α and i β are the current values of the direct axis and quadrature axis in the stationary coordinate system of the motor respectively; U α and U β are the voltages of the direct axis and quadrature axis in the stationary coordinate system; V α and V β are the back electromotive force components; w e is the actual rotational speed of the motor; is the differential operator.

5. The PMSM control method optimized by the integral hybrid reaching law and the gray wolf algorithm according to claim 1, characterized in that The constructed traditional sliding-mode observer includes: where e i is the error of the current, is the derivative of x1; x1 and x2 represent the system state variables; The defined sliding-mode surface function s is: s = Cx1 + x2 where C represents a constant and C > 0.

6. The PMSM control method optimized by the integral hybrid reaching law and the grey wolf algorithm according to claim 5, characterized in that The method for improving the constructed sliding-mode surface using the reaching law includes: In the formula, s is the sliding-mode surface, where k(t) is a variable gain function, λ(t) is an adjustable weighting factor function, ∫sdt is the current error integral function, sgn(s) is the sign function; t is the current iteration number.

7. The PMSM control method optimized by the integral hybrid reaching law and the grey wolf algorithm according to claim 1, characterized in that The optimal parameter PLL closed-loop equation after being optimized by the grey wolf model includes: Among them, represents the optimized proportional gain; represents the optimized integral gain; w ref (t) represents the reference angular frequency; w est (t) represents the output angular frequency; t is the current iteration number.

8. A PMSM control system optimized by an integral hybrid reaching law and a grey wolf algorithm, the system is used to implement the method described in any one of claims 1-7, and is characterized in that, Including: A collection module, a prediction module, a construction module, an improvement module and a control module; The collection module is used to construct the mathematical model of the PMSM and collect the electrical signals; The prediction module is used to construct the direct-axis and quadrature-axis current prediction equations based on the collected electrical signals; The construction module is used to construct a traditional sliding-mode observer and construct a sliding-mode surface according to the current prediction equations; The improvement module is used to improve the constructed sliding-mode surface using the reaching law; The control module is used to, for the observation signals output by the improved sliding-mode observer, use the grey wolf model to optimize the PLL parameters to complete the control of the PMSM.

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