A control method for a permanent magnet synchronous motor

Abstract

The present invention provides a control method for a permanent magnet synchronous motor. In the speed outer loop, a fractional order sliding mode controller is constructed by designing a fractional order sliding mode surface and a fractional order reaching law; the dung beetle algorithm is used to tune the parameters of the fractional order sliding mode controller to obtain the optimal control parameters of the fractional order sliding mode controller, and the fractional order sliding mode controller generates an optimal q-axis current control command based on the optimal control parameters; in the current inner loop, a fractional order model predictive current controller is constructed by designing a fractional order prediction model and a fractional order cost function, which is used to generate an optimal stator voltage control command; based on the optimal q-axis current control command and the optimal stator voltage control command, the speed and current of the target permanent magnet synchronous motor are controlled respectively, so that the actual speed and current of the target permanent magnet synchronous motor track the given speed and current; the control accuracy of the speed of the permanent magnet synchronous motor is improved by suppressing the speed fluctuation of the permanent magnet synchronous motor.

Description

Technical Field

[0001] The present invention relates to the technical field of synchronous motor control, and particularly relates to a control method for a permanent magnet synchronous motor. Background Art

[0002] In the fields of household appliances such as refrigerators, air conditioners, and fans, it is a gradually developing trend to improve the reliability of the system, improve the power factor, and reduce costs. Permanent magnet synchronous motors are often used in household appliances due to their advantages such as high power density, large torque, small volume, high efficiency, simple control, and high precision. However, due to the different forms of driving loads by permanent magnet synchronous motors, the forms of load signals are also different. When these loads are added to the permanent magnet synchronous motor control system, it will cause fluctuations in the rotational speed, and then cause vibrations in the motor control system, affecting the high-precision control of the rotational speed of the permanent magnet synchronous motor. Summary of the Invention

[0003] The present invention provides a control method for a permanent magnet synchronous motor, and its purpose is to suppress the rotational speed fluctuation to improve the control precision of the rotational speed of the permanent magnet synchronous motor.

[0004] In order to achieve the above purpose, the present invention provides a control method for a permanent magnet synchronous motor, including:

[0005] Step 1, select a target permanent magnet synchronous motor, and the double closed-loop control system of the target permanent magnet synchronous motor includes a speed outer loop and a current inner loop;

[0006] Step 2, design a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop, and construct a fractional-order sliding mode controller based on the fractional-order sliding mode surface and the fractional-order reaching law;

[0007] Step 3, use the dung beetle algorithm to tune the parameters of the fractional-order sliding mode controller to obtain the optimal control parameters of the fractional-order sliding mode controller, and the fractional-order sliding mode controller generates the optimal q-axis current control command for the target permanent magnet synchronous motor based on the optimal control parameters;

[0008] Step 4, design a fractional-order prediction model and a fractional-order cost function in the current inner loop, and construct a fractional-order model predictive current controller based on the fractional-order prediction model and the fractional-order cost function, and the fractional-order model predictive current controller is used to generate the optimal stator voltage control command for the target permanent magnet synchronous motor;

[0009] Step 5, control the rotational speed and current of the target permanent magnet synchronous motor based on the optimal q-axis current control command and the optimal stator voltage control command respectively, so that the actual rotational speed and current of the target permanent magnet synchronous motor track the given rotational speed and current.

[0010] Furthermore, designing a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop includes:

[0011] For a given target signal, define the position tracking error and the velocity tracking error;

[0012] Based on the position tracking error and the velocity tracking error, construct a fast terminal sliding mode surface in the outer speed loop that converges within a preset time;

[0013] Constrain the parameters in the fast terminal sliding mode surface and introduce a fractional-order differential linear term to make the fast terminal sliding mode surface converge, obtaining a fractional-order sliding mode surface;

[0014] Design an approach law introducing a fractional-order operator to obtain a fractional-order approach law for making the double closed-loop control system enter the sliding mode state.

[0015] Furthermore, the expression of the fractional-order sliding mode surface is:

[0016]

[0017] where represents the fractional-order sliding mode surface, represents the position tracking error, represents the velocity tracking error, represents the fractional-order integral operator, represents the differential order, , both represent positive real numbers, , both represent the parameters of the fast terminal sliding mode surface, .

[0018] Furthermore, the expression of the fractional-order approach law is:

[0019]

[0020] where represents the fractional-order approach law, , and both represent undetermined coefficients, represents the fractional-order switching term.

[0021] Furthermore, the expression of the fractional-order sliding mode controller is:

[0022]

[0023] where represents the fractional-order sliding mode controller, represents the inhomogeneous term in the permanent magnet synchronous motor object model, , represents the moment of inertia of the motor, represents the given tracking target signal, Represents the homogeneous term in the object model of the permanent magnet synchronous motor, , represents the damping viscous coefficient.

[0024] Furthermore, a fractional-order prediction model and a fractional-order cost function are designed in the current inner loop, including:

[0025] Based on the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system, a fractional-order differential operator is introduced to construct a fractional-order voltage balance equation in the current inner loop;

[0026] A fractional-order prediction model of the fractional-order voltage balance equation is constructed using the fractional-order predictor-corrector algorithm;

[0027] The d-q axis voltage vectors are selected, and a numerical evaluation index expression of the d-q axis voltage vectors is constructed;

[0028] Based on the numerical evaluation index expression, the fractional-order calculus theory is introduced to design a fractional-order cost function.

[0029] Furthermore, the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system is:

[0030]

[0031] where, represents the differential operator, represents the d-axis voltage in the synchronous coordinate system, represents the q-axis voltage in the synchronous coordinate system, represents the d-axis current in the synchronous coordinate system, represents the q-axis current in the synchronous coordinate system, represents the stator winding phase resistance, represents the d-axis inductance, represents the q-axis inductance, represents the mechanical angular velocity of the permanent magnet synchronous motor, represents the permanent magnet flux linkage.

[0032] Furthermore, the fractional-order voltage balance equation is:

[0033]

[0034] where, represents the stator inductance.

[0035] Furthermore, the fractional-order prediction model is:

[0036] ;

[0037] where, Represents the sampling period of the target permanent magnet synchronous motor control system after discretization. Represents the Gamma function. Represents the correction coefficient.

[0038] Furthermore, the expression of the fractional - order cost function is:

[0039]

[0040] Among them, Represents the fractional - order cost. Represents the termination time set by the fractional - order prediction - correction algorithm. Represents the starting time set by the fractional - order prediction - correction algorithm. Represents the fractional - order order when converting the summation relationship in the numerical evaluation index into a fractional - order integral operation. Represents the q - axis current control command output by the speed outer - loop control. Represents the d - axis control command output by the speed outer - loop control. Represents the weight factor. Represents the sampling time.

[0041] The above - mentioned solution of the present invention has the following beneficial effects:

[0042] In the speed outer - loop of the target permanent magnet synchronous motor, the present invention designs a fractional - order sliding surface and a fractional - order reaching law, and constructs a fractional - order sliding - mode controller based on the fractional - order sliding surface and the fractional - order reaching law; uses the dung beetle algorithm to tune the parameters of the fractional - order sliding - mode controller to obtain the optimal control parameters of the fractional - order sliding - mode controller, and the fractional - order sliding - mode controller generates the optimal q - axis current control command based on the optimal control parameters; designs a fractional - order prediction model and a fractional - order cost function in the current inner - loop of the target permanent magnet synchronous motor, and constructs a fractional - order model - predictive current controller based on the fractional - order prediction model and the fractional - order cost function, and the fractional - order model - predictive current controller is used to generate the optimal stator voltage control command; controls the speed and current of the target permanent magnet synchronous motor based on the optimal q - axis current control command and the optimal stator voltage control command respectively, so that the actual speed and current of the target permanent magnet synchronous motor track the given speed and current; compared with the prior art, the present invention introduces the fractional - order operator into the traditional sliding - mode controller and model - predictive current controller, improves the control accuracy of the speed of the permanent magnet synchronous motor by suppressing the speed fluctuation of the permanent magnet synchronous motor, and provides a sufficient basis and reliability guarantee for the fault - tolerant control mechanism of high - performance permanent magnet synchronous motors.

[0043] Other beneficial effects of the present invention will be described in detail in the subsequent specific implementation part. Brief Description of the Drawings

[0044] Figure 1Schematic flowchart of an embodiment of the present invention;

[0045] Figure 2 Schematic flowchart of the dung beetle algorithm in an embodiment of the present invention;

[0046] Figure 3 is the mechanical angular velocity and the q-axis current in the synchronous coordinate system response waveform diagram. Detailed implementation manners

[0047] To make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are 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] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0049] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a locking connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0050] In addition, the technical features involved in different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] The present invention provides a control method for a permanent magnet synchronous motor aiming at the existing problems.

[0052] As Figure 1 shown, an embodiment of the present invention provides a control method for a permanent magnet synchronous motor, including:

[0053] Step 1: Select a target permanent magnet synchronous motor. The double closed-loop control system of the target permanent magnet synchronous motor includes a speed outer loop and a current inner loop;

[0054] Step 2: Design a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop, and construct a fractional-order sliding mode controller based on the fractional-order sliding mode surface and the fractional-order reaching law;

[0055] Step 3: Use the dung beetle algorithm to tune the parameters of the fractional-order sliding mode controller to obtain the optimal control parameters of the fractional-order sliding mode controller. The fractional-order sliding mode controller generates the optimal q-axis current control command for the target permanent magnet synchronous motor based on the optimal control parameters;

[0056] Step 4: Design a fractional-order prediction model and a fractional-order cost function in the current inner loop, and construct a fractional-order model predictive current controller based on the fractional-order prediction model and the fractional-order cost function. The fractional-order model predictive current controller is used to generate the optimal stator voltage control command for the target permanent magnet synchronous motor;

[0057] Step 5: Control the speed and current of the target permanent magnet synchronous motor based on the optimal q-axis current control command and the optimal stator voltage control command respectively, so that the actual speed and current of the target permanent magnet synchronous motor track the given speed and current.

[0058] In the embodiment of the present invention, the permanent magnet synchronous motor is taken as the research object, and the control system of the permanent magnet synchronous motor is a double closed-loop control system. The double closed-loops are respectively a speed outer loop and a current inner loop.

[0059] Specifically, designing a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop includes:

[0060] For a given target signal, define the position tracking error and the speed tracking error;

[0061] Based on the position tracking error and the speed tracking error, construct a fast terminal sliding mode surface that converges within a preset time in the speed outer loop;

[0062] Constrain the parameters in the fast terminal sliding mode surface and introduce a fractional-order differential linear term to make the fast terminal sliding mode surface converge, and obtain a fractional-order sliding mode surface;

[0063] Design a reaching law introducing a fractional-order operator to obtain a fractional-order reaching law for making the double closed-loop control system enter the sliding mode state.

[0064] In the embodiment of the present invention, define the position tracking error as and the speed tracking error as , and the expressions are as follows:

[0065]

[0066]

[0067] Among them, represents the given tracking target signal, represents the mechanical angle of the permanent magnet synchronous motor, represents the change rate of the given tracking target signal, represents the mechanical angular velocity of the permanent magnet synchronous motor;

[0068] Based on the position tracking error and the speed tracking error, a fast terminal sliding mode surface that can converge within a finite time is constructed in the speed outer loop, which is:

[0069]

[0070] Among them, represents the fast terminal sliding mode surface, represents the sliding mode surface gain, , both represent the parameters of the fast terminal sliding mode surface, , are both positive odd numbers and satisfy ;

[0071] By restricting the variation range of the parameters , and introducing a fractional order differential linear term, the fast terminal sliding mode surface can avoid the singular phenomenon and can achieve fast convergence. Furthermore, a fractional order sliding mode surface is designed, and its expression is:

[0072]

[0073] Among them, represents the fractional order sliding mode surface, represents the position tracking error, represents the speed tracking error, represents the fractional order integral operator, represents the differential order, , are both positive real numbers, , both represent the parameters of the fast terminal sliding mode surface, .

[0074] In the embodiment of the present invention, when the tracking error of the double closed-loop control system is far from the equilibrium point, the exponential term in the fractional order sliding mode surface enables the system tracking error to converge rapidly; when the double closed-loop air flocking tracking error is close to the equilibrium point, the linear term in the fractional order sliding mode surface dominates the rapid convergence of the system tracking error. Therefore, introducing a fractional order integral operator in the linear term can make the fractional order sliding mode surface have a faster convergence speed when approaching the equilibrium point.

[0075] In the embodiments of the present invention, in order to ensure that the system quickly and stably enters the sliding mode state, a fractional-order operator is introduced into the reaching law to obtain a fractional-order reaching law, and its expression is:

[0076]

[0077] wherein, represents the fractional-order reaching law, , and all represent undetermined coefficients, and satisfy , , , represents the fractional-order switching term. The fractional-order switching term accelerates the approaching speed when the value is large, and can slow down the approaching rate when s is small, so as to ensure that the approaching speed to the sliding surface is increased without increasing chattering.

[0078] Specifically, the expression of the fractional-order sliding mode controller constructed by combining the fractional-order sliding mode surface and the fractional-order reaching law is:

[0079]

[0080] wherein, represents the fractional-order sliding mode controller, represents the inhomogeneous term in the permanent magnet synchronous motor object model, , represents the motor inertia, represents the given tracking target signal, represents the homogeneous term in the permanent magnet synchronous motor object model, , represents the damping viscous coefficient.

[0081] Since the control performance of the fractional-order sliding mode controller is greatly affected by the parameters , , , and , the embodiments of the present invention use the dung beetle algorithm to optimize and tune these parameters, and find the optimal solution to achieve the optimal speed tracking performance of the double closed-loop control system. Among them, the dung beetle algorithm includes the ball-rolling dung beetle, the egg-laying dung beetle, the small dung beetle, and the stealing dung beetle. Each group of parameters of the fractional-order sliding mode controller is used as an individual in the population. The specific optimization process is as follows:

[0082] First, set the maximum number of iterations and the population size;

[0083] Then, randomly initialize the ball-rolling dung beetle, the egg-laying dung beetle, the small dung beetle, and the stealing dung beetle in the dung beetle algorithm;

[0084] Calculate the initial fitness values of the ball-rolling dung beetle, the brooding dung beetle, the small dung beetle, and the kleptoparasitic dung beetle according to the objective function;

[0085] Determine whether the current individual is a ball-rolling dung beetle. If so, update the position of the ball-rolling dung beetle using the position update mechanism of the ball-rolling dung beetle. The expression of the update mechanism is:

[0086]

[0087] where, represents the value of the th group of parameter vectors randomly generated in the fractional-order sliding mode controller at the th iteration; represents the deflection coefficient, ; represents the natural coefficient, , is the worst position in the current population, is the exploration preference parameter of the search space;

[0088] Otherwise, determine whether the current individual is a brooding dung beetle. If so, update the position of the brooding dung beetle using the position update mechanism of the brooding dung beetle. The expression of the update mechanism is:

[0089]

[0090] where, represents the position of the th brooding at the th iteration, , represent two independent random variables; represents the optimal position in the current population; , represent the lower and upper limits of the spawning area;

[0091] Otherwise, determine whether the current individual is a small dung beetle. If so, update the position of the small dung beetle using the position update mechanism of the small dung beetle. The expression of the update mechanism is:

[0092]

[0093] where, , represent the lower and upper limits of the value range of the parameter vector in the fractional-order sliding mode controller; represents a random number following a normal distribution; represents a random number belonging to a uniform distribution;

[0094] Otherwise, determine whether the current individual is a stealing dung beetle. If so, update the position of the stealing dung beetle using the position update mechanism of the stealing dung beetle. The update mechanism expression is:

[0095]

[0096] Where, respectively represent constants and random variables subject to a normal distribution;

[0097] When the entire population has been traversed and the maximum number of iterations has been reached, output the optimal control parameters of the fractional order sliding mode controller.

[0098] Specifically, design a fractional order prediction model and a fractional order cost function in the current inner loop, including:

[0099] Based on the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system, introduce a fractional order differential operator and construct a fractional order voltage balance equation in the current inner loop;

[0100] Adopt a fractional order prediction-correction algorithm to construct a fractional order prediction model of the fractional order voltage balance equation;

[0101] Select the d-q axis voltage vectors and construct a numerical evaluation index expression for the d-q axis voltage vectors;

[0102] Based on the numerical evaluation index expression, introduce the fractional order calculus theory and design a fractional order cost function.

[0103] Specifically, the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system is:

[0104]

[0105] Where, represents the differential operator, represents the d-axis voltage in the synchronous coordinate system, represents the q-axis voltage in the synchronous coordinate system, represents the d-axis current in the synchronous coordinate system, represents the q-axis current in the synchronous coordinate system, represents the stator winding phase resistance, represents the d-axis inductance, represents the q-axis inductance, represents the mechanical angular velocity of the motor, represents the permanent magnet flux linkage.

[0106] Specifically, based on the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system, introduce a fractional order differential operator and construct a fractional order voltage balance equation in the current inner loop, which is:

[0107]

[0108] Among them, represents the stator inductance;

[0109] Specifically, by adopting the fractional prediction correction algorithm, the fractional prediction model for constructing the fractional-order voltage balance equation of the permanent magnet synchronous motor in the above continuous case is:

[0110] ;

[0111] Among them, represents the sampling period of the target permanent magnet synchronous motor control system after discretization, represents the Gamma function, represents the correction coefficient, and its specific form is as follows:

[0112]

[0113] Among them, represents the current step of the prediction correction algorithm, represents the fractional order, and q = α, represents the index factor.

[0114] In the embodiment of the present invention, the selected d-q axis voltage vector is the optimal voltage vector, and the optimal voltage vector is the d-q axis voltage vector that minimizes the deviation between the model predicted current and the input control command current. The numerical evaluation index expression for constructing the d-q axis voltage vector is:

[0115]

[0116] Among them, represents the numerical evaluation index, represents the d-axis control command output by the speed outer loop control, represents the q-axis current control command output by the speed outer loop control. If the double closed-loop control system adopts the field-oriented control strategy, then .

[0117] Specifically, the expression of the fractional cost function is:

[0118]

[0119] Among them, represents the fractional cost, represents the termination time set by the fractional prediction correction algorithm, represents the starting time set by the fractional prediction correction algorithm, It represents the fractional order when converting the summation relationship in the numerical evaluation index into fractional order integral operation. It represents the q-axis current control command output by the speed outer loop control. It represents the d-axis control command output by the speed outer loop control. It represents the sampling moment. It represents the weight factor and satisfies the following relational expression:

[0120]

[0121] Among them, It represents the Nth-order Legendre polynomial.

[0122] In the embodiment of the present invention, the numerical evaluation basis of the permanent magnet synchronous motor double closed-loop control system model is:

[0123]

[0124] Among them, It represents the simulation time array recorded in the model. It represents the simulation termination time in the model. It represents the input value of the speed controller, that is, the deviation between the speed given value and the feedback.

[0125] In order to verify the effectiveness of the control method provided by the embodiment of the present invention, a surface-mounted permanent magnet synchronous motor with parameters shown in Table 1 below is selected as the control object:

[0126] Table 1

[0127]

[0128] The given speed control command is a stepped wave input. Under the action of the provided control method, the mechanical angular velocity of the control object and the q-axis current in the synchronous coordinate system Figure 3 The response waveforms are shown in (a) and (b) of

[0129] In the embodiment of the present invention, a fractional-order sliding mode surface and a fractional-order reaching law are designed in the speed outer loop of the target permanent magnet synchronous motor, and a fractional-order sliding mode controller is constructed based on the fractional-order sliding mode surface and the fractional-order reaching law; the dung beetle algorithm is used to tune the parameters of the fractional-order sliding mode controller to obtain the optimal control parameters of the fractional-order sliding mode controller, and the fractional-order sliding mode controller generates an optimal q-axis current control command based on the optimal control parameters; a fractional-order prediction model and a fractional-order cost function are designed in the current inner loop of the target permanent magnet synchronous motor, and a fractional-order model predictive current controller is constructed based on the fractional-order prediction model and the fractional-order cost function, and the fractional-order model predictive current controller is used to generate an optimal stator voltage control command; based on the optimal q-axis current control command and the optimal stator voltage control command, the speed and current of the target permanent magnet synchronous motor are controlled respectively, so that the actual speed and current of the target permanent magnet synchronous motor track the given speed and current; compared with the prior art, the embodiment of the present invention introduces fractional-order operators into the traditional sliding mode controller and model predictive current controller, and improves the control accuracy of the speed of the permanent magnet synchronous motor by suppressing the speed fluctuation of the permanent magnet synchronous motor, providing a sufficient basis and reliability guarantee for the fault-tolerant control mechanism of high-performance permanent magnet synchronous motors.

[0130] The above is the preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A control method for a permanent magnet synchronous motor, characterized in that, Including: Step 1: Select a target permanent magnet synchronous motor, the double closed-loop control system of the target permanent magnet synchronous motor includes a speed outer loop and a current inner loop; Step 2: Design a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop, and construct a fractional-order sliding mode controller based on the fractional-order sliding mode surface and the fractional-order reaching law. The expression of the fractional-order sliding mode surface is: Among them, represents the fractional-order sliding mode surface, represents the position tracking error, represents the velocity tracking error, represents the fractional-order integral operator, represents the differential order, and both represent positive real numbers, and both represent the parameters of the fast terminal sliding mode surface, ; Step 3: Use the dung beetle algorithm to tune the parameters of the fractional-order sliding mode controller to obtain the optimal control parameters of the fractional-order sliding mode controller. The fractional-order sliding mode controller generates the optimal q-axis current control command of the target permanent magnet synchronous motor based on the optimal control parameters; Step 4: Design a fractional-order prediction model and a fractional-order cost function in the current inner loop, and construct a fractional-order model predictive current controller based on the fractional-order prediction model and the fractional-order cost function. The fractional-order model predictive current controller is used to generate the optimal stator voltage control command of the target permanent magnet synchronous motor; Designing a fractional-order prediction model and a fractional-order cost function in the current inner loop includes: Based on the voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system, introduce a fractional-order differential operator and construct a fractional-order voltage balance equation in the current inner loop; Use the fractional-order predictor-corrector algorithm to construct the fractional-order prediction model of the fractional-order voltage balance equation; Select the d-q axis voltage vector and construct the numerical evaluation index expression of the d-q axis voltage vector; Introduce the fractional-order calculus theory based on the numerical evaluation index expression and design a fractional-order cost function; Step 5: Control the speed and current of the target permanent magnet synchronous motor based on the optimal q-axis current control command and the optimal stator voltage control command respectively, so that the actual speed and current of the target permanent magnet synchronous motor track the given speed and current.

2. The control method of the permanent magnet synchronous motor according to claim 1, wherein Designing a fractional-order sliding mode surface and a fractional-order reaching law in the speed outer loop includes: For a given target signal, define the position tracking error and the speed tracking error; Based on the position tracking error and the speed tracking error, construct a fast terminal sliding mode surface that converges within a preset time in the speed outer loop; Constrain the parameters in the fast terminal sliding mode surface and introduce a fractional-order differential linear term to make the fast terminal sliding mode surface converge to obtain a fractional-order sliding mode surface; Design a reaching law introducing a fractional-order operator to obtain a fractional-order reaching law for making the double closed-loop control system enter the sliding mode state.

3. The control method of the permanent magnet synchronous motor according to claim 2, characterized in that, The expression of the fractional-order reaching law is: Among them, represents the fractional-order reaching law, represents the fast terminal sliding mode surface, , and both represent undetermined coefficients, represents the fractional-order switching term.

4. The control method of the permanent magnet synchronous motor according to claim 3, characterized in that, The expression of the fractional-order sliding mode controller is: ； Among them, represents the fractional-order sliding mode controller, represents the inhomogeneous term in the permanent magnet synchronous motor object model, , represents the moment of inertia of the motor, represents the given tracking target signal, represents the homogeneous term in the permanent magnet synchronous motor object model, , represents the damping viscous coefficient.

5. The control method of the permanent magnet synchronous motor according to claim 4, characterized in that, The voltage balance equation of the target permanent magnet synchronous motor in the d-q coordinate system is: Among them, represents a differential operator, represents the d-axis voltage in the synchronous coordinate system, represents the q-axis voltage in the synchronous coordinate system, represents the d-axis current in the synchronous coordinate system, represents the q-axis current in the synchronous coordinate system, represents the stator winding phase resistance, represents the d-axis inductance, represents the q-axis inductance, represents the mechanical angular velocity of the permanent magnet synchronous motor, represents the permanent magnet flux linkage.

6. The control method of the permanent magnet synchronous motor according to claim 5, characterized in that, The fractional-order voltage balance equation is: Among them, represents the stator inductance.

7. The control method of the permanent magnet synchronous motor according to claim 6, characterized in that The fractional-order prediction model is: Among them, represents the sampling period of the discretized target permanent magnet synchronous motor control system, represents the Gamma function, represents the correction coefficient.

8. The control method of the permanent magnet synchronous motor according to claim 7, characterized in that, The expression of the fractional-order cost function is: Among them, represents the fractional-order cost, represents the termination time set by the fractional-order prediction-correction algorithm, represents the starting time set by the fractional-order prediction-correction algorithm, represents the fractional-order order when converting the summation relationship in the numerical evaluation index into a fractional-order integral operation, represents the q-axis current control command output by the outer speed loop control, represents the d-axis control command output by the outer speed loop control, represents the weighting factor, represents the sampling time.

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