Global finite-time convergence permanent magnet synchronous motor control method based on backstepping method framework

Abstract

The application discloses a global finite time convergence permanent magnet synchronous motor control method based on a backstepping method framework, comprising the following steps: 1) on a MATLAB platform of an upper computer, a permanent magnet synchronous motor control system is designed based on model-based design by using MATLAB / Simulink software; 2) a hardware circuit of a permanent magnet synchronous motor vector control system is built; 3) a finite time nonlinear extended state observer NLESO is designed; and 4) under a recursive control framework of the backstepping method, a super-spiral sliding mode algorithm with a second-order sliding mode characteristic is fused, and a globally finite time stable compound controller is designed. By integrating the observer convergence and the double closed loop stability, the application effectively suppresses the 'chattering' phenomenon of the traditional sliding mode control, and significantly improves the dynamic response speed, the steady state tracking accuracy and the anti-interference robustness of the motor in the whole working condition range.

Description

Technical Field

[0001] This invention relates to permanent magnet synchronous motor drive control technology, and in particular to a global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework. Background Technology

[0002] In high-end equipment fields such as aerospace, robotics, and new energy vehicles, permanent magnet synchronous motors (PMSMs) have become the core power source for servo drive systems due to their high power density, high efficiency, and excellent speed regulation performance. However, such systems often face excitation from varying loads, varying parameters, and external nonlinear disturbances during operation. Due to the inherent characteristics of strong coupling and nonlinearity within the motor, speed fluctuations and current harmonics are easily induced, which not only affect the operating accuracy of the equipment but also reduce the energy conversion efficiency and operational stability of the system. Therefore, designing a motion control scheme with high dynamic response and high precision for permanent magnet synchronous motors has significant scientific research value and engineering practical significance.

[0003] With the development of high-performance control theory, backstepping control based on the "decomposition-synthesis" approach has been widely used due to its ability to effectively handle system nonlinearity and ensure global stability. However, in practical applications, PMSM drive systems exhibit extremely high dynamic complexity. Traditional control modeling is mostly based on asymptotic stability theory, assuming that the system state converges to the equilibrium point in an infinite time. This theoretical assumption ignores the strict requirements of actual operating conditions for response timeliness, resulting in long settling times and slow tracking error decay when facing sudden load changes or during startup. This limitation in convergence characteristics makes it difficult for traditional methods to accurately characterize the dynamic behavior of the system in high-speed transient processes, thus limiting the dynamic performance of servo control.

[0004] Traditional backstepping control, employing linear feedback laws, can only achieve asymptotic convergence of errors, making it difficult to guarantee that the system reaches steady state within a finite time. To improve convergence speed, existing technologies typically introduce sliding mode control or traditional finite-time control laws. However, these methods often exhibit locally finite-time convergence, with limited convergence rates far from the equilibrium point. Pursuing rapid convergence often requires setting extremely high control gains, inevitably leading to voltage saturation and severe control chattering, which harms the lifespan of inverter power devices and affects control smoothness. Although some composite control strategies attempt to compensate for disturbances by introducing observers, the lack of a globally consistent finite-time convergence framework means that the system's convergence performance and robustness remain bottlenecks across the entire operating range, particularly exhibiting inconsistent dynamic response and lack of steady-state accuracy over a wide speed range. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a global finite-time convergent permanent magnet synchronous motor control method based on the backstepping framework. By integrating the observer convergence and dual closed-loop stability into a single design, the method effectively suppresses the "chattering" phenomenon of traditional sliding mode control while significantly improving the dynamic response speed, steady-state tracking accuracy, and anti-interference robustness of the motor across the entire operating range.

[0006] The objective of this invention is achieved as follows: a globally finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework, comprising the following steps:

[0007] Step 1) On the MATLAB platform of the host computer, use MATLAB / Simulink software to design a model-based permanent magnet synchronous motor control system, and perform mathematical modeling and analysis on the nonlinear dynamic characteristics of the permanent magnet synchronous motor in the dq rotating coordinate system.

[0008] Step 2) Build the hardware circuit of the permanent magnet synchronous motor vector control system, and use the integrated development environment and real-time simulation tools to establish bidirectional communication between the hardware circuit and the host computer to realize online debugging and real-time monitoring of control parameters;

[0009] Step 3) Design a finite-time nonlinear extended state observer (NLESO). By introducing a nonlinear feedback law containing the fractional power of the observation error, the NLESO captures the total disturbance generated by parameter perturbation, unmodeled dynamics and external loads during system operation in real time, and tracks the disturbance in a finite time, using it as a feedforward compensation component.

[0010] Step 4) Under the backstepping recursive control framework, a super-spiral sliding mode algorithm with second-order sliding mode characteristics is integrated to design a globally finite-time stable composite controller; combined with the finite-time nonlinear extended state observer NLESO, the real-time estimated values ​​of external load and internal system disturbance are decoupled and fed forward compensated; based on the deviation between actual current, speed and reference command, the actual voltage control quantity of the inverter is calculated, and the control signal is output.

[0011] Furthermore, the nonlinear dynamic characteristics of the permanent magnet synchronous motor described in step 1) in the dq rotating coordinate system are mathematically modeled, and the mathematical model is as follows:

[0012]

[0013] in, b0 is the theoretical value of the torque current coefficient, and b1 is the estimated value of b0. For current loop input gain, The mechanical angular velocity of the motor. For q-axis current, This is the q-axis stator voltage. This represents the number of pole pairs of the motor. It is a permanent magnet flux chain. For rotational inertia, For stator inductance; , For the total system disturbance, This represents the internal disturbance term generated by the stator resistance in the current loop;

[0014] For the sake of convenience in theoretical derivation, its mathematical model is rewritten as follows:

[0015]

[0016] in , ; For system state variables, To expand the state variables, for Expected value For q-axis current, This represents the total system disturbance.

[0017] Furthermore, the design of the finite-time nonlinear extended state observer (NLESO) described in step 3) specifically includes:

[0018] Based on the established system state-space equations, an NLESO observation module is designed. Utilizing the motor speed feedback signal and voltage command information, a nonlinear function containing a fractional power error feedback term is constructed to replace the traditional linear proportional term. The design is as follows:

[0019]

[0020] in, , NLESO pairs of state variables , The observed values, For NLESO The observation error, l1 and l2 are the two feedback gains of NLESO, and the two nonlinear functions introduced. , The format is:

[0021]

[0022] Where k f The design of the two nonlinear functions >0 ensures that the linear term gain increases when the error is >0.5, and demonstrates the fast convergence of the nonlinear function when the error is <0.5.

[0023] Furthermore, step 4) specifically includes:

[0024] Design a composite controller with global finite-time convergence within the backstepping framework:

[0025] Design the outer loop control law for speed: Define the motor speed tracking error as e1=ω md -ω m , For ω m The expected value, ω m Let be the mechanical angular velocity of the motor; introduce a nonlinear control law containing the fractional power of the speed error, and construct a virtual control quantity for the speed loop, the expression of which is:

[0026]

[0027] in, and For the controller gain parameter, e1=ω md -ω m ω md For ω m Expected value The observed values ​​are those subject to disturbance.

[0028] For the current loop subsystem, a sliding mode switching surface based on the q-axis current error is defined, and a super-spiral algorithm with second-order sliding mode characteristics is introduced to construct the final control law:

[0029]

[0030] in, and For controller gain parameters; .

[0031] By feeding the total disturbance estimate d2 observed by the finite-time nonlinear extended state observer NLESO into the superspiral sliding mode control algorithm for real-time cancellation, and combining Lyapunov stability theory and homogeneity principle, it is proved that the system possesses finite-time convergence consistency across the entire domain. This control law suppresses high-frequency chattering in sliding mode control through the integral term of the sign function, achieving smooth output of the control voltage.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention is based on the MATLAB platform and adopts the global finite-time composite control development method of permanent magnet synchronous motor based on model design (MBD). The motor is controlled in real time using MATLAB / Simulink software. The hardware platform is built based on the TMS320F28335 processor, and the complex nonlinear backstepping control and observer algorithm is directly downloaded to the hardware for execution through automatic code generation technology. This method realizes efficient collaboration between computer simulation verification and hardware system testing, significantly shortens the development cycle of advanced algorithms, reduces the difficulty of writing complex nonlinear control laws, and thus accelerates the engineering process of high-performance servo systems.

[0033] (2) The Finite-Time Nonlinear Extended State Observer (NLESO) designed in this invention significantly improves the ability to capture total system disturbances by introducing a nonlinear element containing fractional power error feedback. Compared with traditional observers, NLESO can achieve steady-state, accurate tracking of parameter perturbations, unmodeled dynamics, and external load fluctuations within a finite time, providing the controller with high-bandwidth and high-effectiveness compensation information. Experimental data show that the observer can control the dynamic fluctuations in rotational speed caused by sudden load changes within 10 r / min, significantly enhancing the steady-state accuracy and anti-interference robustness of the system under full-speed-domain conditions.

[0034] (3) This invention integrates the superspiral sliding mode algorithm (STA) within the backstepping framework, achieving deep coupling and integrated proof of the overall system stability performance and observer convergence characteristics. The introduction of the superspiral structure utilizes its continuous control characteristics to effectively suppress the high-frequency "chattering" phenomenon inherent in traditional sliding mode control while ensuring global finite-time convergence, making the output current smoother. The control strategy based on this architecture can significantly shorten the adjustment time for the system to recover to steady state under different speed ranges and sudden disturbances, improving the dynamic response level while reducing the switching losses of inverter power devices and extending the service life of drive equipment, thus possessing extremely high engineering application and promotion value. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0036] Figure 1 This is a hardware structure block diagram of the motor speed control system based on TMS320F28335 of the present invention.

[0037] Figure 2 This is a schematic diagram of the global finite-time convergent composite controller structure based on the backstepping method framework of the present invention.

[0038] Figure 3 This is the output speed curve of the BS-FADRC no-load variable speed test in this invention.

[0039] Figure 4 This is the output current curve of the BS-FADRC no-load variable speed test in this invention.

[0040] Figure 5 This is the output speed curve of the BS-FADRC loading and unloading experiment in this invention.

[0041] Figure 6 The output current curves of the BS-FADRC load increase / decrease experiment in this invention are shown.

[0042] Figure 7 This is a flowchart illustrating the development process of the model-based design of this invention. Detailed Implementation

[0043] 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.

[0044] A global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework includes the following steps:

[0045] Step 1) On the MATLAB platform of the host computer, use MATLAB / Simulink software to design the permanent magnet synchronous motor control system based on model design (MBD), and perform mathematical modeling and analysis on the nonlinear dynamic characteristics of the permanent magnet synchronous motor in the dq rotating coordinate system.

[0046] This invention is based on the TMS320F28335 chip hardware platform to build a modular DSP design system. The program of this system is automatically converted into code and downloaded to the DSP board for execution.

[0047] The model-based design of this invention is based on Simulink modular design and uses Matlab 2017a. This model-based design is specific to a particular DSP processing chip, specifically the TI C2000 series, model TMS320F28335. The software used for DSP compilation in this invention is the CCSV 6.0 editor. The ControlSuite software of this invention includes various header files and library files for all TI C2000 processors.

[0048] Step 2) Build the hardware circuit of the permanent magnet synchronous motor vector control system, and use the integrated development environment and real-time simulation tools to establish bidirectional communication between the hardware circuit and the host computer to realize online debugging and real-time monitoring of control parameters;

[0049] like Figure 1 As shown, the entire motor control system hardware includes: a host computer, a DSP controller (TMS320F28335 chip), a current sampling module, a rotor position detection module, an inverter power module, a DC power supply module, and a permanent magnet synchronous motor.

[0050] The host computer is used to build a speed control model for a permanent magnet synchronous motor in the MATLAB / Simulink environment. The speed control model for a permanent magnet synchronous motor includes a coordinate transformation module, a finite-time nonlinear extended state observer module, an inverse step speed loop control module, a super-spiral sliding mode current loop control module, and a PWM generation module.

[0051] The host computer converts the permanent magnet synchronous motor speed control model into embedded C code through automatic code generation, and downloads the embedded C code to the DSP controller for real-time execution.

[0052] The current sampling module is used to collect the three-phase stator current of the permanent magnet synchronous motor and input the sampling signal into the DSP controller;

[0053] The rotor position detection module is used to acquire the rotor position and / or speed of the permanent magnet synchronous motor and input the rotor position and / or speed signals into the DSP controller;

[0054] The DSP controller is used to perform coordinate transformation, finite-time nonlinear extended state observation, backstepping speed loop control, super-helical sliding mode current loop control, and PWM signal generation based on the three-phase stator current, rotor position, and / or speed signals.

[0055] The inverter power module is used to receive the PWM drive signal output by the DSP controller and output three-phase drive voltage to the permanent magnet synchronous motor according to the PWM drive signal;

[0056] The host computer has a bidirectional communication connection with the DSP controller, which is used to send the speed setpoint, observer parameters, backstep control parameters and super-helical sliding mode control parameters to the DSP controller, and to receive the motor speed, current, position, disturbance estimate and control voltage information uploaded by the DSP controller.

[0057] The output of the finite-time nonlinear extended state observer module is connected to the backstepping speed loop control module and the super-spiral sliding mode current loop control module, so as to use the total disturbance estimate as both the speed loop virtual control compensation and the current loop voltage control compensation.

[0058] This invention utilizes a module built with MATLAB / Simulink software to automatically generate C code, which is then directly downloaded to a DSP for real-time motor control. The DSP samples the rotor information of the PMSM (Motor Motor Surgery Unit) to calculate the motor's speed and position. Finally, a vector control algorithm is used to obtain a voltage space vector PWM (Pulse Width Modulation) signal, which drives the inverter's power switching devices through an isolation circuit. The bus voltage is converted into modulated current or voltage by the inverter module, achieving real-time control of the motor's speed and position.

[0059] Step 3) Design a finite-time nonlinear extended state observer (NLESO). By introducing a nonlinear feedback law containing the fractional power of the observation error, the NLESO captures the total disturbance generated by parameter perturbation, unmodeled dynamics and external loads during system operation in real time, and tracks the disturbance in a finite time, using it as a feedforward compensation component.

[0060] The nonlinear dynamic characteristics of a permanent magnet synchronous motor in the dq rotating coordinate system are mathematically modeled, and the mathematical model is as follows:

[0061]

[0062] in, b0 is the theoretical value of the torque current coefficient, and b1 is the estimated value of b0. For current loop input gain, The mechanical angular velocity of the motor. For q-axis current, This is the q-axis stator voltage. This represents the number of pole pairs of the motor. It is a permanent magnet flux chain. Let L be the moment of inertia and L be the stator inductance. , For the total system disturbance, This represents the internal disturbance term generated by the stator resistance in the current loop.

[0063] For the sake of convenience in theoretical derivation, its mathematical model is rewritten as follows:

[0064]

[0065] in , ; For system state variables, To expand the state variables, for Expected value For q-axis current, This represents the total system disturbance.

[0066] The design of the finite-time nonlinear extended state observer (NLESO) specifically includes:

[0067] Based on the established system state-space equations, an NLESO observation module is designed. Utilizing the motor speed feedback signal and voltage command information, a nonlinear function containing a fractional power error feedback term is constructed to replace the traditional linear proportional term. The design is as follows:

[0068]

[0069] in, , NLESO pairs of state variables , The observed values, For NLESO The observation error, l1 and l2 are the two feedback gains of NLESO, and the two nonlinear functions introduced. , The format is:

[0070]

[0071] Where k f The design of the two nonlinear functions ensures that the linear term gain increases when the error is >0.5, and demonstrates the fast convergence of the nonlinear function when the error is <0.5.

[0072] Define ESO state variables The observation error is The relationship between the two observation errors can be obtained as follows:

[0073]

[0074] It can be seen that the nonlinear ESO introduces fractional power and nonlinear term gains. When the estimation error is far from the origin, it can quickly converge to the vicinity of the origin with the high-speed exponential convergence property of the linear term. Then, other nonlinear terms in the definition of the nonlinear function ensure that the estimation error converges to zero from a small neighborhood of the origin in a finite time.

[0075] For the error feedback law, a Lyapunov function incorporating the ESO estimation error can be designed using a quadratic form function as follows:

[0076]

[0077] in, , It is a symmetric positive definite matrix. Through calculation, The derivative with respect to time is

[0078]

[0079] Where the matrix coefficients are

[0080]

[0081] and Matrix A and B are respectively

[0082]

[0083] Assuming total disturbance term The absolute value of the derivative has an upper limit. Then you can get Define a new function as

[0084]

[0085] Based on the aforementioned results, the Lyapunov function The derivative can be written as

[0086]

[0087] The following inequalities can be derived from the yapunov function:

[0088]

[0089] in For matrix eigenvalues, for The Euclidean norm.

[0090] A simple calculation was performed again to obtain The square of the Euclidean norm is

[0091]

[0092] From this, we can infer that The upper and lower limits are

[0093]

[0094] Furthermore, the derivative of the Lyapunov function can be rewritten as...

[0095]

[0096] According to the Bhat-Bernstein finite-time stability theorem, under the premise of satisfying the above equation, the system state variables... In a limited time It converges to zero, and There exists a strict upper limit.

[0097]

[0098] in This represents the initial state of the system. The right-hand side of the derivative of the Lyapunov function contains... The fractional power term and the linear term are both present. The fractional power term is the dominant component of the finite-time convergence process, while the addition of the linear term does not affect the finite-time convergence property or the upper limit of the convergence time.

[0099] In this design, ESO controls the system state variables. , The observation error can converge to zero in a finite time, and can complete the total disturbance. Timely and stable tracking.

[0100] Step 4) Under the backstepping recursive control framework, a super-spiral sliding mode algorithm with second-order sliding mode characteristics is integrated to design a globally finite-time stable composite controller; combined with the finite-time nonlinear extended state observer NLESO, the real-time estimated values ​​of external load and internal system disturbance are decoupled and fed forward compensated; based on the deviation between actual current, speed and reference command, the actual voltage control quantity of the inverter is calculated, and the control signal is output.

[0101] Design a composite controller with global finite-time convergence within the backstepping framework:

[0102] Design the outer loop control law for speed: Define the motor speed tracking error as e1=ω md -ω m , For ω m The expected value, ω m Let be the mechanical angular velocity of the motor; introduce a nonlinear control law containing the fractional power of the speed error, and construct a virtual control quantity for the speed loop, the expression of which is:

[0103]

[0104] in, and For the controller gain parameter, e1=ωmd -ω m ω md For ω m Expected value The observed values ​​are those subject to disturbance.

[0105] Design Lyapunov functions for

[0106]

[0107] Its derivative is

[0108]

[0109] In current feedback value Approaching a given value When, the above formula is rewritten as

[0110]

[0111] Considering that when the time is greater than At that time, the observation error of ESO on the disturbance term The above formula can be rewritten as

[0112]

[0113] Define error back, The derivative form is

[0114]

[0115] The first term in the above formula Although it contains nonlinear terms, its curve is actually a monotonically increasing odd function. Further calculations and substituting the nonlinear ESO yield the following result.

[0116]

[0117] Define Lyapunov functions for

[0118]

[0119] Its derivative form is

[0120]

[0121] Considering that when the time is greater than At that time, the observation error of ESO on the disturbance term The above formula can be rewritten as

[0122]

[0123] For the current loop subsystem, a sliding mode switching surface based on the q-axis current error is defined, and a super-spiral algorithm with second-order sliding mode characteristics is introduced to construct the final control law:

[0124]

[0125] in, and For controller gain parameters; .

[0126] The total perturbation estimate obtained by observing the finite-time nonlinear extended state observer NLESO Real-time cancellation is performed in the feedforward super-spiral sliding mode control algorithm, and by combining Lyapunov stability theory and homogeneity principle, it is proved that the system has finite-time convergence consistency in the entire domain. The control law suppresses high-frequency chattering in sliding mode control through the integral term of the sign function, and achieves smooth output of control voltage.

[0127] Therefore, it can be clearly concluded that while the nonlinear extended state observer guarantees the finite-time convergence characteristic of disturbance observation and the super-spiral sliding mode controller guarantees the finite-time stability of the velocity loop and current loop, the entire velocity control system satisfies the global finite-time stability characteristic within the framework of the backstepping method. The control block diagram of this system is as follows: Figure 2 As shown.

[0128] Table 1 Parameters of Motor Speed ​​Control System

[0129]

[0130] A global finite-time control system (BS-FTADRC) based on the backstepping method framework was built on the experimental platform. The system development process is as follows: Figure 7 As shown in Table 1, the parameters of the motor speed control system are as follows. The controller parameters are selected as follows: in NLESO, l1=4000, l2=40000, kf=0.06; in STA, λ=0.03, α=0.06. The experiment simulates the same working conditions as the previous experiment. The output speed curve of the BS-FTADRC no-load speed change experiment obtained from the host computer is shown in Table 1. Figure 3 As shown, the output current i q Curves Figure 4 As shown, the output speed curves of the load increase and decrease experiments are as follows: Figure 5 As shown, the output current i q Curves Figure 6 As shown.

[0131] Analysis of No-Load Transmission Test Results (Corresponding) Figure 3 and Figure 4 Speed ​​tracking performance: From Figure 3As can be seen, BS-FTADRC exhibits the fastest response speed during system startup and speed step transitions (500 r / min to 1000 r / min). Compared to the traditional ADRC-TL and the asymptotically stable BS-TL scheme, this invention, by introducing a finite-time convergence law within the backstepping framework, significantly shortens the settling time and achieves a faster, overshoot-free steady state at the end of the tracking process. Current dynamic response: Figure 4 The corresponding i is displayed q Current curve. During the transient process of a sudden change in rotational speed, the i of the present invention... q The current response is more agile and has less fluctuation. Thanks to the introduction of the super-spiral sliding mode algorithm (STA), the current command maintains good continuity during rapid switching, effectively suppressing the high-frequency switching noise of traditional sliding mode control.

[0132] Analysis of Loading and Unloading Experiment Results (corresponding) Figure 5 and Figure 6 Resistance to load disturbances: Figure 5 The simulation investigated the sudden application and unloading of loads during motor operation. Regarding speed drop, the BS-FTADRC algorithm exhibited the smallest speed drop and the shortest recovery time to steady state when the load abruptly changed. Experimental results show that, through precise finite-time observation and feedforward compensation of disturbances using nonlinear ESO (NLESO), the dynamic speed fluctuation was controlled within 10 r / min, significantly outperforming other comparative algorithms. Steady-state disturbance rejection current characteristics: as shown... Figure 6 This shows that during the load sustaining phase, the i of the present invention q The current can be quickly adjusted and kept stable to balance the load torque. This demonstrates the strong robustness of the composite control system under complex disturbances, ensuring that the motor maintains high-precision steady-state operation even under fluctuating load conditions.

[0133] Based on the experimental results, the BS-FTADRC scheme proposed in this invention exhibits significant technological advantages in the following dimensions: Speed: Utilizing global finite-time stability characteristics, it greatly shortens the start-up and transition time of the speed control system. Robustness: Through real-time compensation for external load and internal parameter perturbations using NLESO, it significantly reduces the system's speed drop and recovery time. Stability: The super-helical sliding mode effectively smooths the control output, reducing control chattering without sacrificing response speed, and providing excellent protection for the motor and power devices.

[0134] The above description of the embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework, characterized in that, Includes the following steps: Step 1) On the MATLAB platform of the host computer, use MATLAB / Simulink software to design a model-based permanent magnet synchronous motor control system, and perform mathematical modeling and analysis on the nonlinear dynamic characteristics of the permanent magnet synchronous motor in the dq rotating coordinate system. Step 2) Build the hardware circuit of the permanent magnet synchronous motor vector control system, and use the integrated development environment and real-time simulation tools to establish bidirectional communication between the hardware circuit and the host computer to realize online debugging and real-time monitoring of control parameters; Step 3) Design a finite-time nonlinear extended state observer (NLESO). By introducing a nonlinear feedback law containing the fractional power of the observation error, the NLESO captures the total disturbance generated by parameter perturbation, unmodeled dynamics and external loads during system operation in real time, and tracks the disturbance in a finite time, using it as a feedforward compensation component. Step 4) Under the backstepping recursive control framework, a super-spiral sliding mode algorithm with second-order sliding mode characteristics is integrated to design a globally finite-time stable composite controller; combined with the finite-time nonlinear extended state observer NLESO, the real-time estimated values ​​of external load and internal system disturbance are decoupled and fed forward compensated; based on the deviation between actual current, speed and reference command, the actual voltage control quantity of the inverter is calculated, and the control signal is output.

2. The global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework according to claim 1, characterized in that, The nonlinear dynamic characteristics of the permanent magnet synchronous motor described in step 1) in the dq rotating coordinate system are mathematically modeled, and the mathematical model is as follows: ； in, b0 is the theoretical value of the torque current coefficient, and b1 is the estimated value of b0. For current loop input gain, The mechanical angular velocity of the motor. For q-axis current, This is the q-axis stator voltage. This represents the number of pole pairs of the motor. It is a permanent magnet flux linkage. For rotational inertia, For stator inductance; , For the total system disturbance, This represents the internal disturbance term generated by the stator resistance in the current loop; For the sake of convenience in theoretical derivation, its mathematical model is rewritten as follows: ； in , , For system state variables, To expand the state variables, for Expected value For q-axis current, This represents the total system disturbance.

3. The global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework according to claim 1, characterized in that, Step 3) describes the design of the finite-time nonlinear extended state observer (NLESO), which specifically includes: Based on the established system state-space equations, an NLESO observation module is designed. Utilizing the motor speed feedback signal and voltage command information, a nonlinear function containing a fractional power error feedback term is constructed to replace the traditional linear proportional term. The design is as follows: ； in, , NLESO pairs of state variables , The observed values, For NLESO The observation error, l1 and l2 are the two feedback gains of NLESO, and the two nonlinear functions introduced. , The format is: ； Where k f The design of the two nonlinear functions >0 ensures that the linear term gain increases when the error is >0.5, and demonstrates the fast convergence of the nonlinear function when the error is <0.

5.

4. The global finite-time convergent permanent magnet synchronous motor control method based on the backstepping method framework according to claim 1, characterized in that, Step 4) specifically includes: Design a composite controller with global finite-time convergence within the backstepping framework: Design the outer loop control law for speed: Define the motor speed tracking error as e1=ω md -ω m , For ω m The expected value, ω m Let be the mechanical angular velocity of the motor; introduce a nonlinear control law containing the fractional power of the speed error, and construct a virtual control quantity for the speed loop, the expression of which is: ； in, and For the controller gain parameter, e1=ω md -ω m ω md For ω m Expected value The observed values ​​are those subject to disturbance. For the current loop subsystem, a sliding mode switching surface based on the q-axis current error is defined, and a super-spiral algorithm with second-order sliding mode characteristics is introduced to construct the final control law: ； in, and For controller gain parameters; ; The total perturbation estimate obtained by observing the finite-time nonlinear extended state observer NLESO Real-time cancellation is performed in the feedforward super-spiral sliding mode control algorithm, and by combining Lyapunov stability theory and homogeneity principle, it is proved that the system has finite-time convergence consistency in the entire domain. The control law suppresses high-frequency chattering in sliding mode control through the integral term of the sign function, and achieves smooth output of control voltage.

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