Permanent magnet synchronous motor speed control method based on fractional order terminal sliding mode control

Abstract

The application belongs to the technical field of motor speed regulation control, and particularly relates to a permanent magnet synchronous motor speed control method based on a fractional order terminal sliding mode control, which comprises the following steps: collecting three-phase current signals of a stator winding of a permanent magnet synchronous motor and a motor rotor position, and performing coordinate transformation on the three-phase current signals in combination with the motor rotor position; modeling the permanent magnet synchronous motor; performing current and speed double closed-loop control based on a reconstructed mathematical model of the permanent magnet synchronous motor, so as to realize permanent magnet synchronous motor speed control. The application introduces a fractional order integral sliding surface to improve the approaching rate of motor speed regulation control. Meanwhile, the control method does not need to observe load disturbance, and when external disturbance increases, the control method can adaptively increase control input gain, accurately realizes motor speed control, can be well applied in a permanent magnet synchronous motor vector control system, and accelerates system response speed and improves system robustness.

Description

Technical Field

[0001] This invention belongs to the field of motor speed control technology, specifically relating to a method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control. Background Technology

[0002] Currently, motor speed control methods mainly rely on PI control. However, traditional PI control exhibits poor robustness in the face of system uncertainties and external disturbances, and its control accuracy is also low. Furthermore, PI control requires a high degree of experience in parameter tuning. As described in patent CN 116865615 A ​​– A Vector Control Method for Permanent Magnet Synchronous Motors Based on an Improved Speed ​​PI Controller – when faced with sudden speed changes, its settling time is long and its adjustment accuracy is insufficient. Sliding mode control can effectively address these issues. It exhibits strong robustness to parameter uncertainties and external disturbances, maintaining system stability in the face of these uncertainties. Simultaneously, terminal sliding mode control can push the system state onto the sliding surface within a finite time, thereby achieving precise tracking of the reference signal. Patent CN 116885989 A – A Fractional-Order Sliding Mode Speed ​​Control Method, Electronic Equipment, and Storage Medium for Permanent Magnet Synchronous Motors – provides a sliding mode control method, but its design process is complex, and it requires knowledge of the upper bound of the disturbance when facing unknown disturbances.

[0003] Therefore, in existing motor speed control methods, traditional PI control suffers from low control accuracy when there are large external disturbances or significant changes in the internal parameters of the motor. At the same time, in traditional sliding mode control, the switching term gain of the control system is selected too large, which leads to severe chattering in the system and also has the problem of dependence on the upper limit of the disturbance. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control, comprising the following steps:

[0005] S1: Collect the three-phase current signal of the stator winding of the permanent magnet synchronous motor and the rotor position of the motor. Combine the rotor position with the Clark transformation to convert the three-phase current signal into a two-phase current signal in the α-β coordinate system. Combine the rotor position with the Park transformation to convert the two-phase current signal in the α-β coordinate system into a current signal in the dq coordinate system.

[0006] S2: Obtain the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the dq coordinate system. Construct a mathematical model of the permanent magnet synchronous motor based on the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the two-phase rotating coordinate system.

[0007] S3: Treat the externally applied load torque and the damping effect of the permanent magnet in the motor winding as disturbances, and reconstruct the mathematical model of the permanent magnet synchronous motor to obtain the reconstructed mathematical model of the permanent magnet synchronous motor.

[0008] S4: Based on the reconstructed mathematical model of the permanent magnet synchronous motor, perform dual closed-loop control of current and speed to achieve speed control of the permanent magnet synchronous motor;

[0009] S41: Set the reference speed of the permanent magnet synchronous motor, calculate the outer loop tracking error of the speed based on the actual speed and the reference speed of the permanent magnet synchronous motor, and differentiate the outer loop tracking error of the speed. Based on the reconstructed mathematical model of the permanent magnet synchronous motor, design the fractional-order terminal sliding surface according to the outer loop tracking error of the speed and its derivative.

[0010] S42: Based on the outer loop error of the rotational speed, the equivalent control law of the q-axis current is obtained through the designed fractional-order terminal sliding surface;

[0011] S43: Design an adaptive control law, integrate the adaptive control law into the equivalent control law, and counteract the uncertainty disturbances in system operation to obtain an adaptive fractional-order terminal sliding mode speed controller.

[0012] S44: Input the set outer loop tracking error of the speed into the adaptive fractional-order terminal sliding mode speed controller to obtain the final result as the reference value of the q-axis current. The inner loop of the current uses a proportional-integral controller to control the d-axis current that generates excitation and the q-axis current that generates torque respectively. The α-axis and β-axis voltages in the two-phase stationary coordinate system are obtained through inverse Park transformation.

[0013] S45: Based on the voltages of the α-axis and β-axis in the two-phase stationary coordinate system, a space vector is synthesized using space vector pulse width modulation technology. The space vector is then applied to the motor phase terminals through the inverter, enabling the motor to run at the desired speed. The target speed is accurately tracked based on the q-axis current reference value.

[0014] The beneficial effects of this invention are:

[0015] This invention introduces a fractional-order integral sliding surface to improve the approach rate of motor speed control; at the same time, this control method does not require observation of load disturbances. When the external disturbance increases, this control method can adaptively increase the control input gain, accurately achieving motor speed control. It can be well applied in permanent magnet synchronous motor vector control systems to accelerate system response speed and improve system robustness. Attached Figure Description

[0016] Figure 1 This is an overall schematic diagram of the permanent magnet synchronous motor speed control method based on fractional-order terminal sliding mode control of the present invention;

[0017] Figure 2 The barrier function K of this invention bar Image illustration;

[0018] Figure 3 The following is a simulation comparison curve of the speed step response using the BAF-FTSM control method of the present invention;

[0019] Figure 4 The simulation comparison curves of the speed step response using the traditional SMC control method of the present invention are shown.

[0020] Figure 5 The simulation comparison curves show the speed step response of the permanent magnet synchronous motor speed control method based on fractional-order terminal sliding mode control of the present invention.

[0021] Figure 6 The figure shows a simulation comparison curve of the speed control accuracy using the BAF-FTSM control method of the present invention. Figure 7 Simulation comparison curves of speed control accuracy using the traditional SMC control method of this invention.

[0022] Figure 8 The figure shows a simulation comparison curve of the speed control accuracy of the permanent magnet synchronous motor speed control method based on fractional-order terminal sliding mode control of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] A speed control method for permanent magnet synchronous motors based on fractional-order terminal sliding mode control, such as... Figure 1 As shown, it includes:

[0025] S1: Collect the three-phase current signal of the stator winding of the permanent magnet synchronous motor and the rotor position of the motor. Combine the rotor position with the Clark transformation to convert the three-phase current signal into a two-phase current signal in the α-β coordinate system. Combine the rotor position with the Park transformation to convert the two-phase current signal in the α-β coordinate system into a current signal in the dq coordinate system.

[0026] S2: Obtain the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the dq coordinate system. Construct a mathematical model of the permanent magnet synchronous motor based on the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the two-phase rotating coordinate system.

[0027] S3: Treat the externally applied load torque and the damping effect of the permanent magnet in the motor winding as disturbances, and reconstruct the mathematical model of the permanent magnet synchronous motor to obtain the reconstructed mathematical model of the permanent magnet synchronous motor.

[0028] S4: Based on the reconstructed mathematical model of the permanent magnet synchronous motor, perform dual closed-loop control of current and speed to achieve speed control of the permanent magnet synchronous motor;

[0029] S41: Set the reference speed of the permanent magnet synchronous motor, calculate the outer loop tracking error of the speed based on the actual speed and the reference speed of the permanent magnet synchronous motor, and differentiate the outer loop tracking error of the speed. Based on the reconstructed mathematical model of the permanent magnet synchronous motor, design the fractional-order terminal sliding surface according to the outer loop tracking error of the speed and its derivative.

[0030] S42: Based on the outer loop error of the rotational speed, the equivalent control law of the q-axis current is obtained through the designed fractional-order terminal sliding surface;

[0031] S43: Design an adaptive control law, integrate the adaptive control law into the equivalent control law, and counteract the uncertainty disturbances in system operation to obtain an adaptive fractional-order terminal sliding mode speed controller.

[0032] S44: Input the set outer loop tracking error of the speed into the adaptive fractional-order terminal sliding mode speed controller to obtain the final result as the reference value of the q-axis current. The inner loop of the current uses a proportional-integral controller to control the d-axis current that generates excitation and the q-axis current that generates torque respectively. The α-axis and β-axis voltages in the two-phase stationary coordinate system are obtained through inverse Park transformation.

[0033] S45: Based on the voltages of the α-axis and β-axis in the two-phase stationary coordinate system, a space vector is synthesized using space vector pulse width modulation technology. The space vector is then applied to the motor phase terminals through the inverter, enabling the motor to run at the desired speed. The target speed is accurately tracked based on the q-axis current reference value.

[0034] To obtain the mathematical model of the surface-mounted permanent magnet synchronous motor without considering the effects of rotor magnetic circuit saturation and core losses, the stator voltage equation, electromagnetic torque equation, and mechanical motion equation are derived based on the current signal in the dq coordinate system, including:

[0035] Stator voltage equation:

[0036]

[0037] Electromagnetic torque equation:

[0038]

[0039] Equations of motion for machines:

[0040]

[0041] Among them, u d u q These are the dq-axis components of the stator voltage, i d i q These are the dq-axis components of the stator current, where R is the stator resistance and ω is the dq-axis component. e L is the electric angular velocity. d L q These are the dq-axis inductance components, ψ f It is a permanent magnet flux linkage. For the differentiation operation; T e P represents electromagnetic torque. n L is the number of pole pairs of a permanent magnet synchronous motor. d L q These are the dq-axis components of the stator inductance; J is the moment of inertia, ω m T is the rotor's mechanical angular velocity. L Where is the load torque and B is the damping coefficient.

[0042] A mathematical model of a permanent magnet synchronous motor is constructed based on the stator voltage equation, electromagnetic torque equation, and mechanical motion equation of the current signal in a two-phase rotating coordinate system, including:

[0043]

[0044] Among them, i q For the q-axis component of the stator current, u q L is the q-axis component of the stator voltage. s For stator inductance, For the differentiation operation, R is the stator resistance, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f For permanent magnet flux linkage, ω m Where J is the rotor's mechanical angular velocity, and T is the moment of inertia. e T represents electromagnetic torque. L Where is the load torque and B is the damping coefficient.

[0045] Treating the externally applied load torque and the damping effect of the permanent magnet in the motor windings as disturbances, the constructed mathematical model of the permanent magnet synchronous motor is reconstructed to obtain the reconstructed mathematical model of the permanent magnet synchronous motor, including:

[0046]

[0047] Where, ω m The rotor's mechanical angular velocity, For the differentiation operation, J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f For permanent magnet flux linkage, i qF is the q-axis component of the stator current. M T represents the total uncertainty in the speed control of the permanent magnet synchronous motor. L Where is the load torque and B is the damping coefficient.

[0048] Set the reference speed for the permanent magnet synchronous motor, and calculate the outer loop tracking error based on the actual speed of the permanent magnet synchronous motor and the reference speed, including:

[0049] The actual speed ω of the permanent magnet synchronous motor is obtained through an encoder. m The reference speed of the motor is defined as ω. ref The outer loop tracking error e1 = ω is calculated based on the actual speed and reference speed of the permanent magnet synchronous motor. ref -ω m .

[0050] Based on the reconstructed mathematical model of the permanent magnet synchronous motor, a fractional-order terminal sliding surface is designed according to the outer loop tracking error of the speed and its derivative, including:

[0051]

[0052] Where s is a fractional-order terminal sliding surface. The reference speed ω of the motor ref The second derivative of P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. F is the first derivative of the q-axis component of the stator current. M The total uncertainty in the speed control of the permanent magnet synchronous motor is given by 'a', where 'a' is the outer loop tracking error coefficient. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. Let t0 be the fractional integral term, t0 be the lower limit of integration, t be the upper limit of integration, r be the order of integration, RL be the fractional calculus form, a1 be the exponent, 0 < a1 < 1, and sgn() be the sign function.

[0053] The total uncertainty in the speed control of a permanent magnet synchronous motor is set to S = 0. By inputting the outer loop error of the rotational speed into the designed fractional-order terminal sliding surface, the equivalent control law of the q-axis current is obtained, including:

[0054]

[0055] Among them, u eq Here, D is the equivalent control law for the q-axis current, and D is the fractional-order convergence factor of the terminal sliding surface. J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. The reference speed ω of the motor ref The second derivative, where a is the outer loop tracking error coefficient of the rotational speed. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. Let t0 be the fractional integral term, t0 be the lower limit of integration, t be the upper limit of integration, r be the order of integration, RL be the fractional calculus form, a1 be the exponent, 0 < a1 < 1, and sgn() be the sign function.

[0056] Design adaptive control laws, including:

[0057] Definition: If there exists a positive constant near zero, the adaptive barrier function on a closed interval is defined as a continuous even function.

[0058]

[0059] And it has the following properties:

[0060] (1) In the interval [0, ε], the barrier function K bar (x) is strictly monotonically increasing.

[0061] (2) Within the domain x∈[-ε,ε], the range is:

[0062] K bar (x)∈[0,+∞)

[0063] (3)

[0064] Barrier function K bar The graph of the function (x) is as follows Figure 2 As shown, when ε is 1, the barrier function K bar As can be seen from this figure, when the sliding mode s converges towards the origin in the region [-ε, ε], the gain K is adaptively switched to handle the occurrence of uncertain disturbances. bar The gain will be significantly increased until it can offset the system's uncertainty disturbances; simultaneously, as the sliding mode s decreases to zero, the switching gain K will be increased. bar This will also be reduced accordingly to avoid oversaturation of system control input;

[0065] In practical vector control systems, since the upper bound of system uncertainty is difficult to obtain accurately, the following adaptive switching control law is designed when the upper bound of system uncertainty is unknown:

[0066]

[0067] Among them, u as Here, D is the adaptive control law, and D is the fractional-order terminal sliding surface convergence factor. J is the moment of inertia, P nψ is the number of pole pairs of the permanent magnet synchronous motor. f denoted as permanent magnet flux linkage, k as adaptive switching control gain, s as fractional-order terminal sliding surface, and sgn() as sign function;

[0068] The adaptive switching control gain k is:

[0069]

[0070]

[0071]

[0072] In the formula, η is the coefficient of the adaptive law integral term, η>0, K1 is the control gain of the adaptive law at time 0-t, K1(0)≥0, K bar For barrier functions, The time when |S(0)| first reaches the region [-ε / 2, ε / 2] when switching control gain K1.

[0073] Incorporating the adaptive control law into the equivalent control law, the overall control law is:

[0074]

[0075] The set outer loop tracking error of the rotational speed is input into the adaptive fractional-order terminal sliding mode speed controller, and the final result is used as the q-axis current reference value, including:

[0076]

[0077] Among them, i' q Here, D is the q-axis current reference value, and D is the fractional-order terminal sliding surface convergence factor. J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. The reference speed ω of the motor ref The second derivative, where a is the outer loop tracking error coefficient of the rotational speed. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. is the fractional integral term, t0 is the lower limit of integration, t is the upper limit of integration, r is the order of integration, RL is the fractional calculus form, a1 is the exponent, 0 < a1 < 1, k is the adaptive switching control gain, and sgn() is the sign function.

[0078] In this embodiment, a MATLAB simulation model is used to simulate the speed control method of permanent magnet synchronous motor based on fractional-order terminal sliding mode control of the present invention.

[0079] The parameters of the MATLAB simulation model are shown in Table 1 below:

[0080] Table 1 Simulation Model Parameters

[0081]

[0082]

[0083] The step response speed curves of the BAF-FTSM control method, the traditional SMC control method, and the control method of this invention are respectively as follows: Figure 3 , 4 As shown in Figure 5, the simulation comparison curves of speed control accuracy are as follows: Figure 6 , 7 As shown in Figure 8; in the initial stage, the given speed is 1000 r / min and the given load torque is 0 N·m; from Figure 6 , 7 As shown in Figure 8, the BAF-FTSM control method reaches the given speed in 0.02s after motor start-up without overshoot. In contrast, the traditional SMC control method exhibits a 22.2% overshoot after reaching the given speed, and the subsequent time to reach the given speed is 0.083s. The PI speed control scheme shows a 31.8% overshoot after reaching the given speed, and the subsequent time to reach the given speed is 0.057s. A load torque of 10 N·m is applied to the system at 0.2s. The BAF-FTSM control method returns to the target speed in 0.015s, with a speed fluctuation of 26 r / min. The traditional SMC control method has a speed fluctuation error of 91 r / min and takes 0.074s to return to the target speed. The PI speed control method has a speed fluctuation of 101 r / min and takes 0.044s to return to the target speed.

[0084] Figure 4 The comparison of speed control accuracy of the three control methods at 0.3s is given. The BAF-FTSM control method can achieve a speed control accuracy of ±0.2r / min, while the speed control accuracy of the traditional SMC and PI control methods is ±1r / min.

[0085] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control, characterized in that, include: S1: Collect the three-phase current signal of the stator winding of the permanent magnet synchronous motor and the rotor position of the motor. Combine the rotor position with the Clark transformation to convert the three-phase current signal into a two-phase current signal in the α-β coordinate system. Combine the rotor position with the Park transformation to convert the two-phase current signal in the α-β coordinate system into a current signal in the dq coordinate system. S2: Obtain the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the dq coordinate system. Construct a mathematical model of the permanent magnet synchronous motor based on the stator voltage equation, electromagnetic torque equation, and mechanical motion equation based on the current signal in the two-phase rotating coordinate system. S3: Treat the externally applied load torque and the damping effect of the permanent magnet in the motor winding as disturbances, and reconstruct the mathematical model of the permanent magnet synchronous motor to obtain the reconstructed mathematical model of the permanent magnet synchronous motor. S4: Based on the reconstructed mathematical model of the permanent magnet synchronous motor, perform dual closed-loop control of current and speed to achieve speed control of the permanent magnet synchronous motor; S41: Set the reference speed of the permanent magnet synchronous motor, calculate the outer loop tracking error of the speed based on the actual speed and the reference speed of the permanent magnet synchronous motor, and differentiate the outer loop tracking error of the speed. Based on the reconstructed mathematical model of the permanent magnet synchronous motor, design the fractional-order terminal sliding surface according to the outer loop tracking error of the speed and its derivative. S42: Based on the outer loop error of the rotational speed, the equivalent control law of the q-axis current is obtained through the designed fractional-order terminal sliding surface; S43: Design an adaptive control law, integrate the adaptive control law into the equivalent control law, and counteract the uncertainty disturbances in system operation to obtain an adaptive fractional-order terminal sliding mode speed controller. S44: Input the set outer loop tracking error of the speed into the adaptive fractional-order terminal sliding mode speed controller to obtain the final result as the reference value of the q-axis current. The inner loop of the current uses a proportional-integral controller to control the d-axis current that generates excitation and the q-axis current that generates torque respectively. The α-axis and β-axis voltages in the two-phase stationary coordinate system are obtained through inverse Park transformation. S45: Based on the voltages of the α-axis and β-axis in the two-phase stationary coordinate system, a space vector is synthesized using space vector pulse width modulation technology. The space vector is then applied to the motor phase terminals through the inverter, enabling the motor to run at the desired speed. The target speed is accurately tracked based on the q-axis current reference value.

2. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, The stator voltage equation, electromagnetic torque equation, and mechanical motion equation are obtained based on the current signal in the dq coordinate system, including: Stator voltage equation: Electromagnetic torque equation: Equations of motion for machines: Among them, u d u q These are the dq-axis components of the stator voltage, i d i q These are the dq-axis components of the stator current, where R is the stator resistance and ω is the dq-axis component. e L is the electric angular velocity. d L q These are the dq-axis inductance components, ψ f It is a permanent magnet flux linkage. For the differentiation operation; T e P represents electromagnetic torque. n L is the number of pole pairs of a permanent magnet synchronous motor. d L q These are the dq-axis components of the stator inductance; J is the moment of inertia, ω m T is the rotor's mechanical angular velocity. L Where is the load torque and B is the damping coefficient.

3. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, A mathematical model of a permanent magnet synchronous motor is constructed based on the stator voltage equation, electromagnetic torque equation, and mechanical motion equation of the current signal in a two-phase rotating coordinate system, including: Among them, i q For the q-axis component of the stator current, u q L is the q-axis component of the stator voltage. s For stator inductance, For the differentiation operation, R is the stator resistance, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f For permanent magnet flux linkage, ω m Where J is the rotor's mechanical angular velocity, and T is the moment of inertia. e T represents electromagnetic torque. L Where is the load torque and B is the damping coefficient.

4. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, Treating the externally applied load torque and the damping effect of the permanent magnet in the motor windings as disturbances, the constructed mathematical model of the permanent magnet synchronous motor is reconstructed to obtain the reconstructed mathematical model of the permanent magnet synchronous motor, including: Where, ω m The rotor's mechanical angular velocity, For the differentiation operation, J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f For permanent magnet flux linkage, i q F is the q-axis component of the stator current. M T represents the total uncertainty in the speed control of the permanent magnet synchronous motor. L Where is the load torque and B is the damping coefficient.

5. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, Set the reference speed for the permanent magnet synchronous motor, and calculate the outer loop tracking error based on the actual speed of the permanent magnet synchronous motor and the reference speed, including: The actual speed ω of the permanent magnet synchronous motor is obtained through an encoder. m The reference speed of the motor is defined as ω. ref The outer loop tracking error e1 = ω is calculated based on the actual speed and reference speed of the permanent magnet synchronous motor. ref -ω m .

6. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, Based on the reconstructed mathematical model of the permanent magnet synchronous motor, a fractional-order terminal sliding surface is designed according to the outer loop tracking error of the speed and its derivative, including: Where s is a fractional-order terminal sliding surface. The reference speed ω of the motor ref The second derivative of P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. F is the first derivative of the q-axis component of the stator current. M The total uncertainty in the speed control of the permanent magnet synchronous motor is given by 'a', where 'a' is the outer loop tracking error coefficient. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. Let t0 be the fractional integral term, t0 be the lower limit of integration, t be the upper limit of integration, r be the order of integration, RL be the fractional calculus form, a1 be the exponent, 0 < a1 < 1, and sgn() be the sign function.

7. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, By inputting the outer loop error of the rotational speed into the designed fractional-order terminal sliding surface, the equivalent control law of the q-axis current is obtained, including: Among them, u eq Here, D is the equivalent control law for the q-axis current, and D is the fractional-order convergence factor of the terminal sliding surface. J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. The reference speed ω of the motor ref The second derivative, where a is the outer loop tracking error coefficient of the rotational speed. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. Let t0 be the fractional integral term, t0 be the lower limit of integration, t be the upper limit of integration, r be the order of integration, RL be the fractional calculus form, a1 be the exponent, 0 < a1 < 1, and sgn() be the sign function.

8. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, Design adaptive control laws, including: Among them, u as Here, D is the adaptive control law, and D is the fractional-order terminal sliding surface convergence factor. J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f denoted as permanent magnet flux linkage, k as adaptive switching control gain, s as fractional-order terminal sliding surface, and sgn() as sign function.

9. The method for controlling the speed of a permanent magnet synchronous motor based on fractional-order terminal sliding mode control according to claim 1, characterized in that, The set outer loop tracking error of the rotational speed is input into the adaptive fractional-order terminal sliding mode speed controller, and the final result is used as the q-axis current reference value, including: Among them, i q ' is the q-axis current reference value, and D is the fractional-order terminal sliding surface convergence factor. J is the moment of inertia, P n ψ is the number of pole pairs of the permanent magnet synchronous motor. f It is a permanent magnet flux linkage. The reference speed ω of the motor ref The second derivative, where a is the outer loop tracking error coefficient of the rotational speed. Let e1 be the first derivative of the outer loop tracking error of rotational speed, and μ1 be the coefficient of the fractional integral term. is the fractional integral term, t0 is the lower limit of integration, t is the upper limit of integration, r is the order of integration, RL is the fractional calculus form, a1 is the exponent, 0 < a1 < 1, k is the adaptive switching control gain, and sgn() is the sign function.

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