Improved fractional order sliding mode active-disturbance-rejection control method for permanent magnet synchronous motor based on improved fractional order superspiral sliding mode observer

Abstract

The invention relates to a permanent magnet synchronous motor improved fractional order sliding mode active-disturbance-rejection control method based on an improved fractional order super-spiral sliding mode observer, and the method specifically comprises the steps: firstly, building a mathematical model of a PMSM in an alpha-beta and d-q coordinate system, designing an improved fractional order super-spiral sliding mode disturbance observer, and estimating the unknown disturbance in a system in real time; and finally, optimizing a steepest function and designing a fractional order tracking differentiator in combination with a fractional order calculus principle. A nonlinear state error feedback law is constructed, nonlinear calculation is carried out on the proportion, differential and integral of an error signal, and the anti-interference capability, the response speed and the control precision of the controller are improved; and combining a fractional order tracking differentiator, a fractional order state observer and a nonlinear feedback control law, and designing a fractional order sliding mode active-disturbance-rejection controller. According to the method, system buffeting is effectively weakened while the convergence speed is increased, and the robustness of the controller under load disturbance is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control technology, and relates to an improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer. Background Technology

[0002] In numerous fields such as modern industrial automation, new energy vehicles, and aerospace, permanent magnet synchronous motors (PMSMs) have become key drive devices due to their significant advantages, including high power density, high efficiency, excellent dynamic response, and speed regulation performance. For example, in new energy vehicles, PMSMs serve as core power components, and their performance directly affects the vehicle's range, power performance, and driving experience. In the field of industrial robotics, the precise position and speed control capabilities of PMSMs ensure the accuracy and stability of robot movements.

[0003] However, permanent magnet synchronous motors are inevitably affected by various complex factors during actual operation. On the one hand, external load disturbances and electromagnetic interference in the motor's operating environment can lead to instability in the motor's operating state; on the other hand, the motor's own parameters (such as stator resistance, inductance, and permanent magnet flux linkage) will be perturbed by factors such as temperature changes and motor aging, all of which seriously affect the control accuracy and dynamic performance of permanent magnet synchronous motors.

[0004] Currently, traditional permanent magnet synchronous motor control strategies, such as field-oriented control (FOC), while capable of speed regulation and control to some extent, exhibit significantly reduced performance under strong disturbances and parameter uncertainties. Some observer-based control strategies, such as traditional sliding mode observers, can estimate and compensate for system disturbances, but suffer from long convergence times, making it difficult to meet high-precision control requirements under rapidly changing operating conditions. Furthermore, ordinary sliding mode control, due to chattering, not only affects the system's control accuracy but may also accelerate wear on motor mechanical components, shortening the motor's lifespan.

[0005] Against this backdrop, combining the improved fractional-order super-twisting sliding mode observer (FOSTSMO) with the improved fractional-order sliding mode self-disturbance rejection control (IFOSMSDRC) strategy has become a new research direction. The improved fractional-order sliding mode self-disturbance rejection control can quickly converge to the desired state within a finite time, overcoming the chattering problem of traditional sliding mode control and improving the dynamic performance of the system. Therefore, the improved fractional-order sliding mode self-disturbance rejection control strategy based on the improved fractional-order super-twisting sliding mode observer can effectively improve the control performance of permanent magnet synchronous motors, meeting the demands of modern industry for high-performance motor control.

[0006] In summary, developing a fractional-order superspiral sliding mode observer and an improved fractional-order sliding mode active disturbance rejection control strategy has significant theoretical implications and broad application prospects. This strategy can not only improve the accuracy and robustness of motor control, but also provide new ideas and methods for the development of motor control technology. Summary of the Invention

[0007] The purpose of this invention is to provide an improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer, which solves the problem of decreased control accuracy and dynamic performance of permanent magnet synchronous motors under complex operating environments due to external disturbances and parameter perturbations.

[0008] The technical solution adopted in this invention is an improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer, which specifically includes the following steps: Step 1: Establish a mathematical model of PMSM under ideal conditions; Step 2: Design an improved fractional-order sliding mode active disturbance rejection controller; Step 3: Design the observer.

[0009] The invention is further characterized by: The specific process of step 1 is as follows: Voltage equation: In a two-phase stationary coordinate system, the voltage equation of a surface-mounted permanent magnet synchronous motor is expressed as: (1) in, u α , u β These are the voltages along the α-axis and β-axis, respectively. i α ,i β These are the currents along the α-axis and β-axis, respectively; R s Stator resistance; E α , E β Let be the back electromotive forces along the α-axis and β-axis, respectively; Equation (1) can be rewritten as the current state equation: (2) back electromotive force E α , E β Represented as: (3) in, Electric angular velocity; For permanent magnet flux linkage; Rotor position; In a synchronous rotating coordinate system, without considering stator core saturation, iron loss, and motor parameter disturbances, the stator voltage equation of a permanent magnet synchronous motor is expressed as: (4) In equation (4), the relationship between inductance and magnetic flux is as follows: (5) in, u d , u q These are the voltages along the d-axis and q-axis, respectively. i d , i d These are the currents along the d-axis and q-axis, respectively. R s Stator resistance; L d , L q These are the inductances along the d-axis and q-axis, respectively. Electric angular velocity; This is the nominal value of the stator flux linkage; , These are the stator flux linkage components along the d and q axes, respectively; Torque equation: Electromagnetic torque is the key physical quantity for energy conversion in a motor, and its expression is: (6) in, For electromagnetic torque, The number of magnetic pole pairs For permanent magnet flux linkage; In surface-mounted PMSM Therefore, the torque equation can be rewritten as: (7) The equation of motion for PMSM is: (8) in, It is mechanical angular velocity; It is the moment of inertia; It is the load torque; It is the coefficient of friction.

[0010] The specific process of step 2 is as follows: Step 2.1, from Step 1, we know that the mathematical form of the motion equation of the permanent magnet synchronous motor is: (9) The torque equation is: (10) Substituting the torque equation (10) into the motor motion equation (9), we get: (11) make Theoretical value of total system disturbance Then equation (11) can be rewritten as: (12) Design a second-order nonlinear active disturbance rejection controller for the motor speed loop; Step 2.2: Design an improved fractional-order sliding mode active disturbance rejection controller.

[0011] In step 2.1, the design process of the second-order nonlinear active disturbance rejection controller for the motor speed loop is divided into three parts, as follows: Part 1: The tracking differentiator designed based on the given motor speed, using a linear tracking differentiator to handle the given motor speed: (13) In equation (13), where, , The given speed of the motor The tracking signal and its differential signal, It is the velocity factor; Part Two: The mechanical angular velocity collected by the external speed sensor of the motor is converted into electrical angular velocity, and then a nonlinear extended state observer of the motor is established according to equation (12): (14) In equation (14), Used to monitor motor speed. Used to observe total motor disturbance. To measure the error between the observed rotational speed and the actual rotational speed; Part Three: The speed tracking signal output from the tracking differentiator is subtracted from the speed observation signal in the observer, and a nonlinear PID combination is performed to transform the motor speed controller into a standard integral series type. The nonlinear error feedback control law is as follows: (15) In equation (15), To set the control quantity; The error value between the speed tracking signal given to the q-axis current and the observed speed.

[0012] The specific process of step 2.2 is as follows: The steps involve improving the extended state observer in equation (14), which is then rewritten as follows: (16) In equation (16), To determine the optimal control function, the following is adopted: To make nonlinear functions Instead, the following error equations are constructed for the speed and total disturbance of the permanent magnet synchronous motor: (17) Differentiating both sides of the error equation (17) simultaneously, we have: (18) Substituting equation (16) into equation (18), we get: (19) Based on the error equation (17), the following fractional sliding surface equation is constructed: (20) right s Differentiate, and we get : (twenty one) Design a fractional sliding mode reaching law, mathematically in the form of: (twenty two) Combining equations (21) and (22), the expression for the fractional-order sliding mode active disturbance rejection controller is obtained as follows: (twenty three) in, k 1. k 2 is the sliding surface parameter and k 1. k 2 are all greater than zero.

[0013] The specific process of step 3 is as follows: Step 3.1: Construct a fractional-order superspiral sliding mode observer; Step 3.2: Construct an improved fractional-order superspiral sliding mode observer.

[0014] Step 3.3, design adaptive sliding mode gain.

[0015] The specific process of step 3.1 is as follows: To estimate the value of the extended back electromotive force, the traditional FOHSSMO is designed as follows: (twenty four) in, , These are stator current observations. , Input for the observer; Subtracting equation (24) from equation (2) yields the stator current error. , for: (25) In mathematical terms, fractional sliding surfaces are typically designed as follows: (26) in, Describes a fractional calculus operator. a , t Let represent the upper and lower limits of the calculus operator, respectively. T It indicates the order of calculus.

[0016] The basic dynamic equations of the superhelical observer are: (27) By combining fractional sliding mode with superhelical sliding mode, a sliding surface combination is achieved. This is done by embedding fractional integral terms into the sliding surface of the superhelical observer, forming a new sliding surface expression: (28) have to: (29) in, s For state variables, y As an intermediate quantity, K 1. K 2 represents the sliding mode gain.

[0017] The specific process of step 3.2 is as follows: Design a piecewise exponential function, expressed as: (30) In equation (30), a Boundary layer thickness; Based on the proposed piecewise exponential switching function, by combining equations (24) and (29), the mathematical model of the improved fractional-order super-spiral sliding mode observer can be obtained as follows: (31) In equation (31), , Represented as: (32) in, K 1. K 2 represents the sliding mode gain.

[0018] The specific process of step 3.3 is as follows: Design the adaptive sliding mode gain coefficient. K 1 and K 2 is: (33) In the formula, c This is the basic gain quantity.

[0019] The beneficial effects of this invention are as follows: 1. Permanent magnet synchronous motors (PMSMs) are often affected by various disturbances in practical applications, such as load changes, parameter uncertainties, and external interference. Traditional control methods often struggle to maintain system stability and performance in the face of these disturbances. However, a control strategy based on a fractional-order superspiral sliding mode observer can estimate and compensate for these disturbances in real time, thereby significantly improving the system's robustness. Through accurate estimation of disturbances, the controller can adjust the control input in a timely manner, ensuring stable operation of the motor under various operating conditions.

[0020] 2. The combination of fractional calculus and superslip sliding mode control not only retains the advantages of both technologies but also creates more efficient observation performance, demonstrating significant advantages in speed estimation, angle observation, and anti-interference capabilities. This combination, through innovative mathematical model design, effectively solves the chattering problem of traditional sliding mode observers while improving the system's convergence speed and robustness, providing more advanced observation technology solutions for fields such as motor control and new energy systems.

[0021] 3. The proposed novel piecewise function replaces the traditional switching function, which can effectively suppress chattering while avoiding the phase delay problem caused by the introduction of filters.

[0022] 4. Energy efficiency is a crucial consideration in motor control. A control strategy based on a fractional-order superspiral sliding mode observer can reduce energy loss by optimizing the motor's operating state. For example, when the load changes, the controller can quickly adjust the motor's output power, avoiding energy waste caused by over-supply. Furthermore, this strategy can also reduce energy consumption by improving the motor's operating efficiency, thereby achieving energy savings.

[0023] 5. This invention employs fractional-order calculus theory to design the sliding surface. By introducing non-integer-order differential operators, the degrees of freedom in system design are increased. Compared with traditional integer-order sliding mode control, fractional-order sliding surfaces can more accurately describe the dynamic characteristics of the system, effectively suppress sliding mode chattering, and improve the system's tracking accuracy and anti-interference capability.

[0024] 6. The fractional-order tracking differentiator, by optimizing the steepest-speed function and combining it with the principles of fractional calculus, can quickly and smoothly track changes in the input signal. When the motor receives a new speed command, the fractional-order tracking differentiator can rapidly generate a smooth transition signal, enabling the motor to respond quickly to command changes and shorten the rise time.

[0025] 6. An improved fractional-order sliding mode active disturbance rejection controller monitors the internal state and external disturbances of the system in real time through a fractional-order state observer. When the system is subjected to disturbances such as load changes or grid voltage fluctuations, the fractional-order state observer can quickly capture the disturbance information and adjust the control output in a timely manner through a nonlinear state error feedback law to effectively compensate for the disturbance.

[0026] 7. Because the system can track the reference signal more accurately, unnecessary energy loss is reduced, improving the operating efficiency of the permanent magnet synchronous motor. In industrial production, the energy-saving effect of the motor is of great significance for reducing production costs. Rapid response and precise control allow the motor to operate at a more reasonable operating point, avoiding energy waste caused by over-adjustment and further improving the system's energy utilization efficiency.

[0027] 8. An improved fractional-order superspiral sliding mode observer combined with an improved fractional-order sliding mode active disturbance rejection control strategy forms a stable closed-loop control system. The observer's accurate estimation of the system state and disturbances provides more precise information for the sliding mode controller, enabling the controller to adjust the control input in a timely manner according to the actual situation, thereby enhancing the stability of the closed-loop system. During motor operation, it can effectively suppress system oscillations and instability, ensuring stable motor operation under various working conditions. Attached Figure Description

[0028] Figure 1 This is the overall control block diagram of the improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order super-helical sliding mode observer of the present invention; Figure 2 This is a block diagram of the controller in the improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer, as described in this invention. Figure 3 This is a basic structural block diagram of a traditional fractional-order superspiral sliding mode observer; Figure 4 This is a diagram illustrating the switching function of a piecewise function; Figure 5 This is a basic structural block diagram of the improved fractional-order superhelical sliding mode observer in the improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on the improved fractional-order superhelical sliding mode observer of the present invention; Figure 6(a) shows the speed and torque waveforms when the load torque undergoes a sudden change under PI control. Figure 6(b) shows the speed and torque waveforms when the load torque undergoes a sudden change under the control of the improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on the improved fractional-order super-helical sliding mode observer of the present invention. Figure 7(a) shows the speed and torque waveforms when the load torque undergoes a sudden load reduction under PI control. Figure 7(b) shows the speed and torque waveforms when the load torque undergoes a sudden load reduction under the control of the improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on the improved fractional-order super-helical sliding mode observer of the present invention. Figure 8(a) shows the speed and torque waveforms when the speed setpoint jumps from 1000 r / min to 1200 r / min under PI control. Figure 8(b) shows the speed and torque waveforms when the speed setpoint jumps from 1000 r / min to 1200 r / min under the control of the improved fractional-order sliding mode active disturbance rejection control method of permanent magnet synchronous motor based on the improved fractional-order super-helical sliding mode observer of the present invention. Figure 9(a) shows the speed and torque waveforms when the given speed of the motor changes abruptly from 0 N·m to 10 N·m after the motor has stabilized and the given speed is kept at 1200 r / min under PI control. Figure 9(b) shows the speed and torque waveforms when the given speed of the permanent magnet synchronous motor is abruptly changed after the motor is stabilized and the load torque is increased from 0 N·m to 10 N·m under the control of the improved fractional sliding mode active disturbance rejection control method of the permanent magnet synchronous motor based on the improved fractional sliding mode observer of the present invention, while maintaining the given speed of the motor at 1200 r / min. Detailed Implementation

[0029] The following detailed description is provided in conjunction with specific implementation methods.

[0030] This invention relates to an improved fractional-order sliding mode self-disturbance rejection control (IFOSMSDRC) method for permanent magnet synchronous motors based on an improved fractional-order super-twisting sliding mode observer (FOSTSMO). By designing an improved fractional-order super-twisting sliding mode observer, the invention utilizes the memory characteristics and nonlocality of fractional calculus to more accurately estimate unknown disturbances in the system, thereby improving the accuracy and speed of disturbance estimation. Furthermore, an improved fractional-order sliding mode self-disturbance rejection control strategy is employed to reduce chattering problems inherent in traditional sliding mode control, accelerate system state convergence, and enable the permanent magnet synchronous motor to quickly and accurately track a given speed and torque.

[0031] Example 1 This invention presents an improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors (PMSMs) based on an improved fractional-order superspiral sliding mode observer. First, based on the fundamental electromagnetic principles of the motor, a mathematical model of the PMSM in a three-phase stationary coordinate system is established and transformed to an α-β, dq coordinate system. The physical meaning and interrelationships of each parameter are then clarified. Based on the established motor model, a PMSM mathematical model considering parameter variations is developed. To address the mismatch disturbances caused by external load disturbances and parameter changes in the PMSM, an improved fractional-order superspiral sliding mode observer is designed to estimate the unknown components, thereby enhancing the anti-interference performance of the speed control system. Then, based on the dynamic characteristics of the motor, an improved sliding mode active disturbance rejection controller is designed to ensure effective operation without relying on an accurate model. A control law is designed to achieve precise control of the motor's speed and position.

[0032] Example 2 This invention relates to an improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superhelical sliding mode observer. The specific steps are as follows: Step 1: Establish a mathematical model of PMSM under ideal conditions; Step 2: Improve the design of the fractional-order sliding mode active disturbance rejection controller; Step 3, Observer Design.

[0033] Example 3 The specific process of step 1 is as follows: As a high-performance motor, the model analysis of permanent magnet synchronous motors is crucial for achieving precise control. A permanent magnet synchronous motor utilizes a magnetic field generated by permanent magnets, which interacts with the rotating magnetic field generated by alternating current flowing through the stator windings, thereby producing electromagnetic torque and driving the rotor to rotate. Its operation is based on the laws of electromagnetic induction and Ampere's force; through rational design of the motor structure and control current, efficient and precise operation can be achieved.

[0034] Voltage equation: In a two-phase stationary coordinate system, the surface-mounted permanent magnet synchronous motor ( The voltage equation for () can be expressed as: (1) in, u α , u β These are the voltages along the d-axis and q-axis, respectively. i α , i β These are the currents along the α-axis and β-axis, respectively; R s Stator resistance; E α , E β Let be the back electromotive forces along the α-axis and β-axis, respectively.

[0035] Equation (1) can be rewritten as the current state equation: (2) back electromotive force E α , E β Represented as: (3) in Electric angular velocity; For permanent magnet flux linkage; This indicates the rotor position.

[0036] In a synchronous rotating coordinate system (d, q coordinate system), without considering stator core saturation, iron loss, and motor parameter disturbances, the stator voltage equation of a permanent magnet synchronous motor can be expressed as: (4) In equation (4), the relationship between inductance and magnetic flux is as follows: (5) in, u d , u q These are the voltages along the d-axis and q-axis, respectively.i d , i d These are the currents along the d-axis and q-axis, respectively. R s Stator resistance; L d , L q These are the inductances along the d-axis and q-axis, respectively. Electric angular velocity; This is the nominal value of the stator flux linkage; , These are the stator flux linkage components along the d and q axes, respectively.

[0037] Torque equation: Electromagnetic torque is the key physical quantity for energy conversion in a motor, and its expression is: (6) in, For electromagnetic torque, The number of magnetic pole pairs It is a permanent magnet flux linkage.

[0038] In surface-mounted PMSM Therefore, the torque equation can be rewritten as: (7) The equation of motion for PMSM is: (8) in, It is mechanical angular velocity; It is the moment of inertia; It is the load torque; It is the coefficient of friction.

[0039] Example 4 The specific process of step 2 is as follows: Step 2.1, Design of a traditional nonlinear active disturbance rejection controller; From step 1, we know that the mathematical form of the motion equation of the permanent magnet synchronous motor is: (9) The torque equation is: (10) Substituting the torque equation from equation (10) into the motor motion equation from equation (9), we get: (11) make Theoretical value of total system disturbance Then equation (11) can be rewritten as: (12) Based on equation (12) and the basic principles and structure of active disturbance rejection control, a second-order nonlinear active disturbance rejection controller for the motor speed loop is designed. Its structure consists of three parts: Part 1: The tracking differentiator designed based on the given motor speed. To further reduce the parameters to be adjusted in the nonlinear active disturbance rejection controller, a linear tracking differentiator is selected to handle the given motor speed. (13) In equation (13), where, , The given speed of the motor The tracking signal and its differential signal, It is the velocity factor.

[0040] Part Two: The mechanical angular velocity collected by the external speed sensor of the motor is converted into electrical angular velocity, and then a nonlinear extended state observer of the motor is established according to equation (12): (14) In equation (14), Used to monitor motor speed. Used to observe the total disturbance of the motor.

[0041] Part Three: The speed tracking signal output from the tracking differentiator is subtracted from the speed observation signal in the observer, and a nonlinear PID combination is performed to transform the motor speed controller into a standard integral series type. The nonlinear error feedback control law is as follows: (15) In equation (15), To set the control quantity; This is the given value for the q-axis current.

[0042] Step 2.2, improve the design of fractional-order sliding mode active disturbance rejection controller; As can be seen from the expressions of each part of the nonlinear active disturbance rejection controller in step 2.1, apart from the tracking differentiator, the second-order nonlinear active disturbance rejection controller has 8 parameters to be adjusted, which is very complex and has no obvious physical meaning, which brings certain difficulties to the practical application of nonlinear active disturbance rejection.

[0043] Based on the design principles and steps of velocity nonlinear active disturbance rejection controllers and sliding mode controllers, the extended state observer of equation (14) is improved, and equation (14) can be rewritten as follows: (16) In equation (16), To determine the optimal control function, the following is adopted: To make nonlinear functions This reduces the number of parameters to be adjusted. The following error equations are constructed for the speed and total disturbance of the permanent magnet synchronous motor: (17) Differentiating both sides of the error equation (17) simultaneously, we have: (18) Substituting equation (16) into equation (18), we get: (19) To minimize the number of parameters to be adjusted, a fractional-order sliding surface is used. Based on the error equation of equation (17), the following fractional-order sliding surface equation is constructed: (20) In equation (20), k 1. k 2 is the sliding surface parameter and k 1. k Both 2 are greater than zero, for s Differentiate, and we get : (twenty one) A fractional sliding surface ensures rapid convergence of the motor's state variables during sliding. To reduce sliding chattering, a fractional sliding mode reaching law is designed, with the following mathematical form: (twenty two) In the designed reaching law, the fractional-order switching term exist s When the value is large, the approach speed increases. s Slowing down the approach speed when the speed is low can ensure that the approach speed is increased without increasing chattering.

[0044] Combining equations (21) and (22), the expression for the fractional-order sliding mode active disturbance rejection controller can be obtained as follows: (twenty three) Example 5 The specific process of step 3 is as follows: Step 3.1, the construction of the fractional-order superspiral sliding mode observer, the specific process is as follows: To estimate the value of the extended back electromotive force, the traditional FOHSSMO is designed as follows: (twenty four) in, , These are stator current observations. , Input for the observer.

[0045] Subtracting equation (24) from equation (2) yields the stator current error. , for: (25) Fractional-order superspiral sliding mode observers are based on fractional calculus theory. By introducing non-integer derivative / integral operators, they extend the theoretical framework of traditional integer-order sliding mode observers. Fractional calculus possesses memory properties, enabling it to better describe the historical states of a system, thereby improving the observation accuracy of complex dynamic systems. Mathematically, fractional-order sliding surfaces are typically designed as follows: (26) in, Describes a fractional calculus operator. a , t Let represent the upper and lower limits of the calculus operator, respectively. T It indicates the order of calculus.

[0046] The Superspiral Sliding Mode Observer (STSMO) is a second-order sliding mode control algorithm. Its core idea is to suppress chattering by introducing an integral term. The basic dynamic equation of the Superspiral Observer is: (27) in, s For state variables, y As an intermediate quantity, K 1. K 2 represents the sliding mode gain.

[0047] This design combines fractional sliding mode with superhelical sliding mode to achieve sliding surface integration. By embedding fractional integral terms into the sliding surface of the superhelical observer, a new sliding surface expression is formed: (28) We can obtain: (29) Figure 3 The diagram shows the structure of a traditional superspiral sliding mode observer. It can be seen that due to the presence of the switching function, the estimated back EMF is a high-frequency signal, which easily causes system chattering. To mitigate this problem, a low-pass filter is usually introduced to eliminate high-frequency chattering. However, the low-pass filter causes phase delay, significantly slowing down the tracking speed.

[0048] Step 3.2, improve the construction of the fractional-order superspiral sliding mode observer, specifically: to solve the chattering and phase delay problems, a new piecewise exponential function is proposed, which can be expressed as: (30) In equation (30), aThis represents the boundary layer thickness.

[0049] The characteristic curve of this function is as follows: Figure 4 As shown. Within the boundary layer, the piecewise exponential switching function constructed in this invention exhibits continuity; however, outside the boundary layer, it displays saturation characteristics.

[0050] Based on the proposed piecewise exponential switching function, by combining equations (24) and (29), the mathematical model of the improved fractional-order superspiral sliding mode observer can be obtained as follows: (31) In equation (31), , It can be further described as: (32) The proposed novel piecewise function replaces the traditional switching function, which can effectively suppress chattering while avoiding the phase delay problem caused by the introduction of filters.

[0051] Step 3.3, the design of adaptive sliding mode gain, the specific process is as follows: The value of the sliding mode gain coefficient directly determines the steady-state error and response speed of the sliding mode control system, and is usually a constant. However, when the rotational speed changes, a fixed value cannot maintain good control performance. Therefore, an adaptive sliding mode gain coefficient can be designed by utilizing the relationship between the motor back electromotive force and the rotational speed. K 1 and K 2 is: (33) In the formula, c This is the basic gain quantity.

[0052] As can be seen from equation (33), when the rotational speed changes, the sliding mode gain coefficient will change with the speed, thereby achieving stability at different rotational speeds. Figure 5 This is a block diagram of the FOHSSMO structure.

[0053] Example 6 To verify the effectiveness of the control method designed in this invention, experiments were conducted on a Hardware-In-the-Loop (HIL) experimental platform. The sampling frequency of HIL was set to 20kHz. The experimental platform was connected to an oscilloscope via an adapter board. Then, the simulation circuit built in Simulink was loaded into the MT6020 and RCP1050 via a host computer for experimental verification.

[0054] Power is defined as positive when voltage and current are in the same direction. The simulation parameters are set as shown in Table 1.

[0055] Table 1 PMSM parameters

[0056] Operating Condition 1: Motor speed under steady-state conditions as set in the experiment oh e 500r / grid T e The torque was set at 10 N·m / division. After the motor ran stably, the load torque was increased from 0 N·m to 10 N·m in a jump. The comparison results of the speed and torque jump experiment under the two control strategies are shown in Figure 6(a).

[0057] oh e , T e These represent the rotational speed and electromagnetic torque of the permanent magnet synchronous motor, respectively. To verify the performance of the control strategy proposed in this invention, it is compared with a PI control strategy.

[0058] According to the data in Figure 6(a), under the PI control strategy, when the load torque of the permanent magnet synchronous motor jumps from 0 N·m to 10 N·m, the motor speed... oh e The overshoot reached as high as 1197 r / min, and gradually recovered to a steady state after a transient process of 38.92 ms; the motor electromagnetic torque T e The amplitude changed by 18 N·m and recovered to steady-state operation after a transient process of 74.7 ms.

[0059] As shown in Figure 6(b), under the control strategy of this invention, the motor speed caused by the load torque jump is... oh e The overshoot is smaller compared to PI control, and the motor speed... oh e Almost no jitter and quickly maintain steady-state operation under the new conditions; transient process oh e The transition time is 23.3 ms, and the amplitude change is only 24 r / min. The electromagnetic torque fluctuation amplitude caused by sudden load changes is significantly reduced, with a fluctuation amplitude of only 9 N·m and a transient time reduced to 24.73 ms, which is lower than that of PI control. Therefore, during the process of load torque change, the system under the control strategy of this invention has better transient performance, faster response speed, and better steady-state performance.

[0060] Operating Condition 2: Motor speed under steady-state conditions as set in the experiment oh e 500r / grid T eThe torque was set at 10 N·m / division. After the motor ran stably, the load torque was increased from 15 N·m to 10 N·m in a jump. The comparison results of the speed and torque jump experiment under the two control strategies are shown in Figure 7(a) and Figure 7(b).

[0061] In the picture, oh e , T e These represent the rotational speed and electromagnetic torque of the permanent magnet synchronous motor, respectively. To verify the performance of the control strategy proposed in this invention, it is compared with a PI control strategy.

[0062] According to the data in Figure 7(a), under the PI control strategy, when the load torque of the permanent magnet synchronous motor jumps from 15 N·m to 10 N·m, the motor speed... oh e The overshoot reached as high as 1197 r / min, and gradually recovered to a steady state after a transient process of 58.3 ms; the motor electromagnetic torque T e The amplitude changed by 27 N·m and recovered to steady-state operation after a transient process of 43.7 ms.

[0063] As shown in Figure 7(b), under the control strategy of this invention, the motor speed caused by the load torque jump is... oh e The overshoot is smaller compared to PI control, and the motor speed... oh e The jitter is small and it quickly maintains steady-state operation under the new conditions; transient process oh e The transition time is 18.6 ms, and the amplitude change is only 49 r / min; the electromagnetic torque fluctuation amplitude caused by sudden load changes is significantly reduced, with a fluctuation amplitude of only 11.7 N·m and a transient time reduced to 17 ms, which is lower than that of PI control. Therefore, during the process of load torque reduction and sudden change, the system under the control strategy of this invention has better transient performance, faster response speed, and can also enable the system to have better steady-state performance.

[0064] Operating Condition 3: Motor Speed ​​in Steady State (as set in the experiment) oh e 500r / grid T e The speed setpoint was 10 N·m / division. After the motor ran stably, the speed setpoint was increased from 1000 r / min to 1200 r / min for a jump. The comparison results of the speed and torque jump experiment under the two control strategies are shown in Figure 8(a) and Figure 8(b).

[0065] In the picture, oh e , Te These represent the rotational speed and electromagnetic torque of the permanent magnet synchronous motor, respectively. To verify the performance of the control strategy proposed in this invention, it is compared with a PI control strategy.

[0066] According to the data in Figure 8(a), under the PI control strategy, when the setpoint for the permanent magnet synchronous motor speed jumps from 1000 r / min to 1200 r / min, the motor speed... oh e The overshoot reached as high as 1256 r / min, and gradually recovered to a steady state after a transient process of 72.72 ms; the motor electromagnetic torque T e The amplitude changed by 22 N·m and recovered to steady-state operation after a transient process of 43.7 ms.

[0067] As shown in Figure 8(b), under the control strategy of this invention, the motor speed caused by a given speed jump is... oh e The overshoot is smaller compared to PI control, and the motor speed... oh e The jitter is small and it quickly maintains steady-state operation under the new conditions; transient process oh e The transition time is 40.2 ms, and the amplitude change is only 236 r / min. The electromagnetic torque fluctuation amplitude caused by the sudden change in given speed is significantly reduced, with a fluctuation amplitude of only 8.8 N·m and a transient time reduced to 28.03 ms, which is lower than that of PI control. Therefore, during the process of load torque reduction and sudden change, the system under the control strategy of this invention has better transient performance, faster response speed, and can also enable the system to have better steady-state performance.

[0068] Operating Condition 4: Motor Speed ​​in Steady State (as set in the experiment) oh e 500r / grid T e With a given speed of 1200 r / min and a given torque of 10 N·m / division, after the motor has stabilized, the load torque is increased from 0 N·m to 10 N·m in a jump. The comparison results of the speed and torque jump experiments under the two control strategies are shown in Figure 9(a) and Figure 9(b).

[0069] In the picture, oh e , T e These represent the rotational speed and electromagnetic torque of the permanent magnet synchronous motor, respectively. To verify the performance of the control strategy proposed in this invention, it is compared with a PI control strategy.

[0070] According to the data in Figure 9(a), under the PI control strategy, when the load torque of the permanent magnet synchronous motor jumps from 0 N·m to 10 N·m, the motor speed... oh e The overshoot reached as high as 1123 r / min, and gradually recovered to a steady state after a transient process of 56.5 ms; the motor electromagnetic torque T e The amplitude changed by 20 N·m and recovered to steady state after a transient process of 41.3 ms.

[0071] As shown in Figure 9(b), under the control strategy of this invention, the motor speed caused by the load torque jump is... oh e The overshoot is smaller compared to PI control, and the motor speed... oh e Almost no jitter and quickly maintain steady-state operation under the new conditions; transient process oh e The transition time is 20.21 ms, and the amplitude change is only 20 r / min. The electromagnetic torque fluctuation amplitude caused by sudden load changes is significantly reduced, with a fluctuation amplitude of only 9.18 N·m and a transient time reduced to 17.87 ms, which is lower than that of PI control. Therefore, at a given speed of 1200 r / min, during the process of load torque jump, the system under the control strategy of this invention has better transient performance, faster response speed, and can also enable the system to have better steady-state performance.

Claims

1. An improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer, characterized in that: Specifically, the steps include the following: Step 1: Establish a mathematical model of PMSM under ideal conditions; Step 2: Design an improved fractional-order sliding mode active disturbance rejection controller; Step 3: Design the observer.

2. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 1, characterized in that: The specific process of step 1 is as follows: Voltage equation: In a two-phase stationary coordinate system, the voltage equation of a surface-mounted permanent magnet synchronous motor is expressed as: （1） in, u α , u β These are the voltages along the d-axis and q-axis, respectively. i α , i β These are the currents along the α-axis and β-axis, respectively; R s Stator resistance; E α , E β Let be the back electromotive forces along the α-axis and β-axis, respectively; Equation (1) can be rewritten as the current state equation: （2） back electromotive force E α , E β Represented as: （3） in, Electric angular velocity; For permanent magnet flux linkage; Rotor position; In a synchronous rotating coordinate system, without considering stator core saturation, iron loss, and motor parameter disturbances, the stator voltage equation of a permanent magnet synchronous motor is expressed as: （4） In equation (4), the relationship between inductance and magnetic flux is as follows: （5） in, u d , u q These are the voltages along the d-axis and q-axis, respectively. i d , i d These are the currents along the d-axis and q-axis, respectively. R s Stator resistance; L d , L q These are the inductances along the d-axis and q-axis, respectively. Electric angular velocity; This is the nominal value of the stator flux linkage; , These are the stator flux linkage components along the d and q axes, respectively; Torque equation: Electromagnetic torque is the key physical quantity for energy conversion in a motor, and its expression is: （6） in, For electromagnetic torque, The number of magnetic pole pairs For permanent magnet flux linkage; In surface-mounted PMSM Therefore, the torque equation can be rewritten as: （7） The equation of motion for PMSM is: （8） in, It is mechanical angular velocity; It is the moment of inertia; It is the load torque; It is the coefficient of friction.

3. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 2, characterized in that: The specific process of step 2 is as follows: Step 2.1, from Step 1, we know that the mathematical form of the motion equation of the permanent magnet synchronous motor is: （9） The torque equation is: （10） Substituting the torque equation (10) into the motor motion equation (9), we get: （11） make Theoretical value of total system disturbance Then equation (11) can be rewritten as: （12） Design a second-order nonlinear active disturbance rejection controller for the motor speed loop; Step 2.2: Design an improved fractional-order sliding mode active disturbance rejection controller.

4. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 3, characterized in that: In step 2.1, the design process of the second-order nonlinear active disturbance rejection controller for the motor speed loop is divided into three parts, as follows: Part 1: The tracking differentiator designed based on the given motor speed, using a linear tracking differentiator to handle the given motor speed: （13） In equation (13), where, , The given speed of the motor The tracking signal and its differential signal, It is the velocity factor; Part Two: The mechanical angular velocity collected by the external speed sensor of the motor is converted into electrical angular velocity, and then a nonlinear extended state observer of the motor is established according to equation (12): （14） In equation (14), Used to monitor motor speed. Used to observe total motor disturbance; Part Three: The speed tracking signal output from the tracking differentiator is subtracted from the speed observation signal in the observer, and a nonlinear PID combination is performed to transform the motor speed controller into a standard integral series type. The nonlinear error feedback control law is as follows: （15） In equation (15), To set the control quantity; This is the given value for the q-axis current.

5. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer according to claim 4, characterized in that: The specific process of step 2.2 is as follows: The steps involve improving the extended state observer in equation (14), which is then rewritten as follows: （16） In equation (16), To determine the optimal control function, the following is adopted: To make nonlinear functions Instead, the following error equations are constructed for the speed and total disturbance of the permanent magnet synchronous motor: （17） Differentiating both sides of the error equation (17) simultaneously, we have: （18） Substituting equation (16) into equation (18), we get: （19） Based on the error equation (17), the following fractional sliding surface equation is constructed: （20） right s Differentiate, and we get : （21） Design a fractional sliding mode reaching law, mathematically in the form of: （22） Combining equations (21) and (22), the expression for the fractional-order sliding mode active disturbance rejection controller is obtained as follows: （23） in, k 1. k 2 is the sliding surface parameter and k 1. k 2 are all greater than zero.

6. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 5, characterized in that: The specific process of step 3 is as follows: Step 3.1: Construct a fractional-order superspiral sliding mode observer; Step 3.2: Construct an improved fractional-order superspiral sliding mode observer; Step 3.3, design adaptive sliding mode gain.

7. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 6, characterized in that: The specific process of step 3.1 is as follows: To estimate the value of the extended back electromotive force, the traditional FOHSSMO is designed as follows: （24） in, , These are stator current observations. , Input for the observer; Subtracting equation (24) from equation (2) yields the stator current error. , for: （25） In mathematical terms, fractional sliding surfaces are typically designed as follows: （26） in, Describes a fractional calculus operator. a , t Let represent the upper and lower limits of the calculus operator, respectively. T Indicates the order of calculus; The basic dynamic equations of the superhelical observer are: （27） By combining fractional sliding mode with superhelical sliding mode, a sliding surface combination is achieved. This is done by embedding fractional integral terms into the sliding surface of the superhelical observer, forming a new sliding surface expression: （28） have to: （29） in, s For state variables, y As an intermediate quantity, K 1. K 2 represents the sliding mode gain.

8. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 7, characterized in that: The specific process of step 3.2 is as follows: Design a piecewise exponential function, expressed as: （30） In equation (30), a Boundary layer thickness; Based on the proposed piecewise exponential switching function, by combining equations (24) and (29), the mathematical model of the improved fractional-order superspiral sliding mode observer can be obtained as follows: （31） In equation (31), , Represented as: （32） in, K 1. K 2 represents the sliding mode gain.

9. The improved fractional-order sliding mode active disturbance rejection control method for permanent magnet synchronous motors based on an improved fractional-order superspiral sliding mode observer as described in claim 8, characterized in that: The specific process of step 3.3 is as follows: design the adaptive sliding mode gain coefficient. K 1 and K 2 is: （33） In the formula, c This is the basic gain quantity.

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