A permanent magnet synchronous motor steady-state locking adaptive active disturbance rejection control method

Abstract

The application discloses a kind of permanent magnet synchronous motor steady-state locking adaptive active disturbance rejection control method, it is characterized in that, include following steps;Step one: the mechanism model of permanent magnet synchronous motor is established;Step two: permanent magnet synchronous motor coordinate transformation model is constructed;Step three: variable parameter improved ADRC controller mechanism modeling;Step four: build double-layer bayesian tuner architecture;Step five: steady-state locking and adaptive wake-up logic;Step six: execute recursive bayesian optimization algorithm.The application adopts flexible observer configuration strategy and composite cost function including current penalty, significantly reduces the sensitivity of the observer to high-frequency noise under the premise of ensuring dynamic noise immunity, realizes the fast response of servo system in dynamic process and improves the smoothness of steady-state operation and reduces operating noise in steady-state process.

Description

Technical Field

[0001] This invention belongs to the field of ADRC parameter adaptive control technology for permanent magnet synchronous motors, and specifically relates to a steady-state locking adaptive active disturbance rejection control method for permanent magnet synchronous motors. Background Technology

[0002] High-end equipment manufacturing, represented by aerospace, precision CNC machining, and industrial robots, is a core indicator of a nation's industrialization level. As the "heart" of the actuators, the performance of the servo control system directly determines the processing accuracy and response speed of the equipment. Driven by both energy efficiency and environmentally friendly production models, traditional hydraulic and pneumatic servo systems have been gradually replaced by electrified drives. In this process, AC permanent magnet synchronous motors (PMSMs), with their high power density, excellent torque-to-inertia ratio, and compact structural design, have become the preferred power source for high-precision fields such as semiconductor packaging, laser cutting, and the main drive system of new energy vehicles.

[0003] However, as applications evolve towards ultra-precision and high-dynamic scenarios, existing motor control technologies are facing severe physical limits. In actual operating conditions, servo systems are inevitably affected by the combined effects of sudden changes in load inertia, nonlinear friction, electromagnetic torque pulsation, and complex external disturbances. Traditional linear control strategies (such as PID control) often struggle to achieve a balance between "fast response" and "no overshoot" when facing multi-source strongly coupled disturbances, and their disturbance rejection capability is extremely limited. Active disturbance rejection control (ADRC), as a nonlinear control strategy that does not rely on an accurate model of the controlled object, estimates and compensates for the "total disturbance" inside and outside the system in real time through an extended state observer (ESO), providing an effective theoretical framework for solving the above problems. The control performance of ADRC is highly dependent on the configuration of controller bandwidth and observer bandwidth: the higher the bandwidth, the stronger the disturbance suppression capability, but the noise sensitivity of the system will also increase exponentially.

[0004] While ADRC (Advanced Dynamic Control) offers advantages in disturbance estimation and compensation, adjusting bandwidth parameters in real-time according to time-varying operating conditions remains a critical issue in engineering applications. Existing online parameter tuning methods typically employ stochastic optimization algorithms to search for optimal parameters. However, this dynamic optimization mechanism can become a new source of disturbance after the servo system reaches steady state. Specifically, to maintain sensitivity to environmental changes, optimization algorithms usually retain a certain exploration variance, resulting in slight jumps in control parameters during the steady-state phase, manifesting as high-frequency glitches or jitter in the motor speed waveform. Furthermore, to improve disturbance rejection performance, existing methods often tend to increase the observer bandwidth, which may amplify encoder quantization noise and current sampling noise, leading to problems such as high-frequency howling, increased torque ripple, or decreased system stability margin. These factors reduce the smoothness and control accuracy of the servo system's steady-state operation, increase the risk of vibration and wear on mechanical transmission components, and limit its application in high-precision, low-noise servo control scenarios. The above factors can reduce the smoothness of steady-state operation and control accuracy of servo systems, increase the risk of vibration and wear of mechanical transmission components, and limit their application in high-precision, low-noise servo control scenarios.

[0005] Therefore, there is an urgent need for an ADRC parameter adaptive control method that can balance dynamic disturbance rejection and steady-state smoothness. This method needs to respond quickly to suppress disturbances during load changes, and effectively eliminate random jitter caused by parameter exploration after the system enters steady state. At the same time, it needs to solve the noise amplification problem under high bandwidth, and achieve high-precision, low-noise operation under all working conditions. This is also a core problem that urgently needs to be solved in the current research and development of high-performance servo drive technology. Summary of the Invention

[0006] To overcome the above technical problems, the present invention aims to provide a steady-state locking adaptive active disturbance rejection control method for permanent magnet synchronous motors. After the system enters steady state, the random exploration of the optimization algorithm is forcibly stopped, effectively reducing speed spikes caused by parameter fluctuations. At the same time, a flexible observer configuration strategy and a composite cost function including current penalty are adopted to significantly reduce the observer's sensitivity to high-frequency noise while ensuring dynamic disturbance rejection capability. This enables the servo system to achieve rapid response in dynamic processes and improve the smoothness of steady-state operation and reduce operating noise in steady-state processes.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor includes the following steps;

[0009] Step 1: Taking the permanent magnet synchronous motor as the controlled object, establish the mechanism model of the permanent magnet synchronous motor, obtain the coupling relationship between voltage, current, flux linkage, torque and speed, and provide a basic mathematical description for the entire controlled object;

[0010] The purpose of this step is to establish the basic physical model of the permanent magnet synchronous motor and clarify the inherent coupling relationship between voltage, current, flux linkage, electromagnetic torque and mechanical motion. Its aim is to provide a unified mathematical description basis for subsequent controller design, disturbance observation and parameter optimization.

[0011] Step 2: Constructing the coordinate transformation model of the permanent magnet synchronous motor (PMSM): Based on the mechanism model established in Step 1, the three-phase stationary coordinate system model is transformed into a dq rotating coordinate system model through Clarke transformation and Park transformation, realizing the decoupling of system variables and model normalization, providing a mathematical object that is easy to analyze and control to implement for the controller design in Step 3;

[0012] The coupled, time-varying motor model in a three-phase stationary coordinate system is transformed into a two-phase rotating coordinate system that is easier for control analysis through Clarke and Park transformations; this achieves the conversion of AC quantities to equivalent DC quantities, completes the decoupling of flux components and torque components, and reduces the complexity of system modeling and control design.

[0013] After this step, the original three-phase variables are converted into dq-axis variables, making the system model more regular and linear, providing a suitable object for establishing the linear active disturbance rejection controller in step three.

[0014] Step 3: Mechanism Modeling of the Variable Parameter Improved ADRC Controller: Based on the dq axis model obtained in Step 2, a variable parameter improved ADRC controller is constructed. By extending the state observer, load disturbances, parameter perturbations, and unmodeled dynamics are estimated, and active disturbance rejection control is achieved through state error feedback and disturbance compensation. This enables the controller to have the ability to observe disturbances, provide error feedback, and map bandwidth parameters in real time.

[0015] The aim is to enable the controller to not only have the ability to estimate and compensate for load disturbances and parameter perturbations in real time, but also to accept the bandwidth parameters output by subsequent optimization algorithms, so as to achieve adaptive adjustment of control performance according to changes in operating conditions. The third-order ESO is used to estimate the total disturbance more smoothly and accurately, the flexible observer configuration function is used to suppress noise amplification under high bandwidth, and the parameterized control law transforms the Bayesian tuning results into actual control inputs.

[0016] Step 4: Build a two-layer Bayesian tuner architecture: Build a two-layer Bayesian tuner architecture on top of the underlying control loop constructed in Step 3, process feedback signals such as speed error and current ripple, and construct a cost function to transform it into an optimization objective for the controller bandwidth parameters.

[0017] Outside the underlying ADRC control loop, an independent upper-level Bayesian decision unit is constructed to perceive, evaluate, and make parameter decisions on the system's operating status; this achieves functional layering of control execution and parameter optimization, so that the tuner does not directly participate in driving modulation, but indirectly adjusts the performance of the underlying controller by outputting the controller bandwidth parameter;

[0018] Further improvements were made to the signal preprocessing, composite cost function construction, and flexible observer parameter mapping, so that the optimization objective takes into account both speed tracking error and quadrature-axis current ripple, thereby establishing a quantitative trade-off between dynamic response and operational stability.

[0019] Step 5: Steady-state locking and adaptive wake-up logic; Implement steady-state locking and adaptive wake-up management for the Bayesian tuner in Step 4, freeze the optimization output when the system is in steady state, and reactivate the optimization process when the system is disturbed, so as to ensure that the parameter adaptation process takes into account both steady-state smoothness and dynamic response.

[0020] A runtime state management mechanism is set up for the upper-level Bayesian tuner. A dual-threshold hysteresis state machine is used to determine whether the system is in a steady state or a disturbed state, and to decide whether to freeze or reactivate the parameter optimization process. The purpose is to solve the parameter jitter and speed spike problems caused by the continuous exploration of the online stochastic optimization algorithm in the steady state stage, while retaining the system's ability to re-optimize when external disturbances or sudden changes in instructions occur.

[0021] It freezes the exploration variance and bandwidth output when the error meets the locking condition, and restarts the recursive Bayes update when the error exceeds the wake-up threshold. Therefore, it is essentially the "switch" and "state manager" of the entire adaptive mechanism.

[0022] Step Six: Execute the recursive Bayesian optimization algorithm; as the actual online optimization execution unit, it recursively updates the probability distribution and generates new candidate bandwidth parameters in the activation state determined in Step Five. After physical constraints and smoothing, the parameters are output to the ADRC controller in Step Three. The low-complexity recursive update ensures that it can be embedded in the motor control chip for real-time operation.

[0023] When the system is in an active state, the controller bandwidth parameters are recursively optimized online based on the real-time performance evaluation results, including Gaussian distribution initialization, posterior update, Thompson sampling, physical constraint limitation, and output smoothing. Under the premise of satisfying the system safety boundary, better controller bandwidth parameters are continuously searched to enable the underlying ADRC to obtain better dynamic disturbance rejection performance and steady-state performance under different operating conditions. Low-complexity recursive updates ensure that it can be embedded in the motor control chip for real-time operation.

[0024] Steps four and six construct performance evaluation indicators based on speed error and quadrature-axis current ripple, and generate controller bandwidth parameters through recursive Bayesian optimization to achieve adaptive adjustment of controller parameters as the operating conditions change; Step five freezes the optimized output in the steady state stage through a dual-threshold hysteresis state machine, and reactivates the parameter optimization process when there is a disturbance or a given change, thus forming a steady-state locking adaptive disturbance rejection control method for permanent magnet synchronous motors.

[0025] Step one specifically involves:

[0026] By using the stator voltage balance equation, flux linkage equation, electromagnetic torque equation, and mechanical motion equation, the system's input, output, state variables, and disturbance propagation path are determined; thus providing a theoretical basis for the total disturbance modeling and compensation in the subsequent active disturbance rejection controller; and serving as the foundation for ESO design and Bayesian tuned feedback objects;

[0027] The stator voltage balance equation, flux linkage equation, electromagnetic torque equation, and mechanical motion equation have a progressive relationship from electricity to magnetism, from magnetism to torque, and from torque to motion.

[0028] The stator voltage balance equation describes the dynamic coupling relationship between stator voltage, current, flux linkage, and speed, forming the basis for establishing the electromagnetic dynamic model of the motor. The flux linkage equation characterizes the coupling relationship between current and permanent magnet flux linkage, providing flux linkage expressions for the voltage and torque equations. The electromagnetic torque equation establishes the conversion relationship between electromagnetic energy and mechanical output torque based on the flux linkage and current relationship, characterizing the mechanism of control input on torque output. The mechanical motion equation further describes the dynamic relationship between electromagnetic torque, load torque, friction damping, and speed change, establishing the connection between speed response and disturbance. These four equations are sequentially connected, forming a complete mechanism model of the permanent magnet synchronous motor from the electrical side to the mechanical side, providing a unified controlled object basis for subsequent extended state observer design, disturbance compensation, and Bayesian tuning.

[0029] Step two specifically involves:

[0030] The Clarke transform and the Park transform have a continuous relationship of first reducing dimensions and then rotating to decouple them;

[0031] The Clarke transform first converts the current, voltage, or flux linkage signals in a three-phase stationary coordinate system into orthogonal components in a two-phase stationary coordinate system, achieving dimensionality reduction from three-phase AC quantities to two-phase orthogonal quantities and providing a mathematical basis for subsequent coordinate rotation. The Park transform, based on the Clarke transform result, further transforms the two-phase stationary coordinate system variables into a dq coordinate system that rotates synchronously with the rotor, converting the originally time-varying, strongly coupled AC quantities into relatively constant DC quantities under steady-state conditions. The order of these two transformations is irreversible; the Clarke transform is the prerequisite for the Park transform, and the Park transform is a crucial step in decoupling the flux and torque components. Through these two stages of transformation, the permanent magnet synchronous motor can be transformed from a complex three-phase coupled system into a dq-axis equivalent model that facilitates the design and parameter optimization of a linear active disturbance rejection controller.

[0032] Step three specifically involves:

[0033] Based on the PMSM mathematical model obtained in steps one and two, an improved linear active disturbance rejection controller that supports online bandwidth variation is established, including a third-order extended state observer, a flexible observer bandwidth configuration function, a state error feedback control law, and disturbance compensation coefficient correction.

[0034] The relationship between the state equation of the improved third-order extended state observer, the bandwidth configuration function of the flexible observer, the bandwidth parameterized state error feedback control law, and the correction of the disturbance compensation coefficient;

[0035] The improved third-order extended state observer's state equation is used to estimate the motor speed, rate of change of speed, and total system disturbance in real time, serving as the core of the entire ADRC's state perception. The flexible observer bandwidth configuration function establishes a mapping relationship between the observer bandwidth and internal gain based on the controller bandwidth, thereby suppressing noise amplification under high bandwidth while ensuring dynamic performance. The bandwidth-parameterized state error feedback control law generates control inputs based on the target speed, actual speed, and observer output state, enabling the controller bandwidth parameters to directly affect the closed-loop response speed and control stiffness. The disturbance compensation coefficient correction further performs model-assisted correction on the control input channel, improving the observer's decoupling accuracy from the control action and reducing the disturbance estimation burden. These four parts are sequentially connected: first, the third-order extended state observer obtains the state and total disturbance estimates; then, the flexible bandwidth configuration function determines the observer parameters; next, the state error feedback control law generates the control quantity; and finally, the disturbance compensation coefficient completes the correction and compensation, thus forming an improved ADRC controller structure that supports online parameter tuning.

[0036] Step four specifically involves:

[0037] The system constructs a two-layer supervised control topology, implements signal sensing and high-pass filtering preprocessing, constructs a composite cost function with energy stability constraints, and performs flexible observer parameter mapping.

[0038] The two-layer supervised control topology is used to connect the Bayesian tuner to the traditional ADRC control loop as an independent upper-level decision-making unit, decoupling the lower-level control execution from the upper-level parameter optimization. Signal sensing and high-pass filtering preprocessing are used to collect speed error and quadrature-axis current signals and extract ripple information that reflects electromagnetic torque fluctuations, providing effective input for performance evaluation. The composite cost function, based on the preprocessed signal, comprehensively quantifies the speed tracking accuracy and current ripple stability, serving as the basis for the Bayesian optimization algorithm to judge the current bandwidth quality. Flexible observer parameter mapping further transforms the single controller bandwidth output by the upper-level tuner into the complete observer and control parameters required by the lower-level ADRC, enabling the optimization results to truly affect the controller. The order of these four components is as follows: first, build the two-layer topology; then, collect and process the feedback signal; subsequently, complete the performance evaluation through the composite cost function; finally, output new bandwidth parameters based on the evaluation and optimization results and map them to the lower-level controller, thus forming a closed-loop adaptive parameter tuning mechanism.

[0039] Step five specifically involves:

[0040] Establish a dual-threshold hysteresis state machine, execute steady-state dead-zone locking action, and execute adaptive mutation wake-up action;

[0041] The dual-threshold hysteresis state machine is used to set the locking and wake-up thresholds based on the magnitude of the speed error, establishing a switching criterion between the locked and active states to prevent frequent jittering switching in the critical region. The steady-state dead-zone locking action is executed when the error is continuously below the locking threshold, freezing the exploration variance of the Bayesian optimization algorithm and keeping the controller bandwidth parameter unchanged, thus physically cutting off random disturbances introduced by online optimization. The adaptive mutation wake-up action is executed when the error exceeds the wake-up threshold, releasing the exploration variance and activating recursive Bayesian updates, allowing the system to re-enter the parameter optimization state to cope with external disturbances or given changes. The relationship between these three is as follows: the dual-threshold hysteresis state machine is responsible for making state decisions; the steady-state dead-zone locking action is responsible for suppressing parameter jitter under stable operating conditions; and the adaptive mutation wake-up action is responsible for restoring parameter adaptation capability during sudden changes in operating conditions. Together, they ensure that the system balances steady-state smoothness and dynamic disturbance immunity.

[0042] Step six specifically involves:

[0043] Initialize the Gaussian probability distribution model, perform recursive posterior probability updates, implement Thompson sampling and physical constraints, and perform output smoothing filtering.

[0044] Specifically, the initial Gaussian probability distribution model is used to provide the initial mean and variance of the controller's optimal bandwidth parameters, determining the initial search range of the optimization algorithm; the recursive posterior probability update is used to correct the mean and variance of the probability distribution based on the composite cost function of the current period and the historical performance comparison results, achieving a dynamic balance between utilization and exploration; Thompson sampling and physical constraints are used to extract new candidate bandwidth parameters from the updated probability distribution and limit them within a preset safety range to ensure that the optimization results meet the physical realizability of the control system; and the output smoothing filter process performs low-pass smoothing on the final candidate bandwidth to suppress the impact of parameter jumps on the motor mechanical transmission chain and control loop.

[0045] The above four steps are interconnected and indispensable: first, an optimization starting point is established through initialization; then, new posterior cognition is obtained through recursive updates; subsequently, safe candidate parameters are generated using Thompson sampling; and finally, the discrete optimization results are transformed into a continuous and actionable controller bandwidth output through smoothing filtering.

[0046] In summary, steps one and two are used to establish the mathematical model and coordinate transformation basis of the controlled object; step three is used to construct an improved ADRC controller with adjustable parameters; step four is used to establish an upper-level Bayesian tuning evaluation and mapping mechanism; step five is used to perform steady-state locking and disturbance wake-up management of the online optimization process; and step six is ​​used to execute specific recursive Bayesian parameter optimization in the active state. Finally, an adaptive control method with closed-loop coupling between modeling, control, evaluation, management and optimization is formed.

[0047] The beneficial effects of the present invention.

[0048] This invention theoretically reduces the additional disturbances introduced by online optimization in the steady-state phase by monitoring rotational speed errors and performing physical-level parameter freezing. Compared with existing technologies, under the conditions of this embodiment, it can reduce the amplitude of steady-state rotational speed fluctuations (whose steady-state accuracy is mainly affected by factors such as sensor accuracy, mechanical assembly errors, and sampling noise), improve the smoothness of the steady-state rotational speed curve, and significantly enhance the control accuracy and quietness of the precision servo system.

[0049] This invention establishes a low-sensitivity linear mapping relationship, which reduces the observer gain level and noise sensitivity compared to traditional high-proportion observer bandwidth configurations. This improvement helps maintain the stability of the current loop operation and reduces the risk of electromagnetic whistling and driver overheating when the Bayesian algorithm pushes the controller bandwidth to over 250 rad / s to cope with load changes.

[0050] This invention introduces a cross-axis current ripple penalty term that has undergone high-pass filtering into the cost function. This achieves an automatic quantitative trade-off between "speed accuracy" and "torque stability". Simulation and experimental data show that, under the same dynamic response speed and conditions, it helps to reduce cross-axis current ripple and is beneficial to reducing fatigue load on the motor and mechanical transmission components.

[0051] This invention employs a recursive posterior probability update and a Thompson sampling strategy to reduce computational complexity to a minimum. It operates at constant frequency and requires no storage of large historical matrices. This makes it feasible to embed this complex adaptive algorithm into commercial motor control chips, reducing reliance on high-performance host computers and helping to lower hardware costs and system modification complexity.

[0052] This invention achieves rapid switching between "sleep and wake-up" states under set sampling periods and threshold conditions by monitoring error thresholds. When a load step or a given sudden change is detected, the system can switch from a locked state to an active state in a short time and update the bandwidth parameters. Theoretically, its recovery time for sudden disturbances is shorter than that of traditional fixed parameter control, effectively solving the problem of control performance degradation caused by time-varying loads in scenarios such as aerospace servos and industrial robots. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of a three-phase AC permanent magnet synchronous motor.

[0054] Figure 2 A simplified model of a three-phase AC permanent magnet synchronous motor.

[0055] Figure 3 is a schematic diagram of coordinate transformation.

[0056] Figure 4 This is a diagram showing the internal signal flow of a Bayesian tuner.

[0057] Figure 5 The process of optimizing the recursive Bayesian algorithm.

[0058] Figure 6 This is a Simulink controller model.

[0059] Figure 7 The simulation results for the controller are shown in the figure.

[0060] Figure 8 This is the overall methodology flowchart.

[0061] Figure 9 This is the flowchart of the core algorithm logic. Detailed Implementation

[0062] 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.

[0063] A steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor includes the following steps;

[0064] Step 1: Constructing the mechanism model of a permanent magnet synchronous motor (PMSM):

[0065] This implementation uses a three-phase permanent magnet synchronous motor (PMSM) as the controlled object. To facilitate the design and analysis of the controller, the motor is first modeled based on the following assumptions: the stator and rotor core reluctance and magnetic circuit saturation are ignored; eddy current and hysteresis losses are neglected; the three-phase current is an ideal sine wave during steady-state operation; and the air gap magnetic field has a sinusoidal distribution.

[0066] By using Clarke and Park transformations, the motor model in a stationary three-phase coordinate system (ABC) is transformed into a mathematical model in a synchronous rotating coordinate system (dq), thereby decoupling the magnetic field from the torque.

[0067] The schematic diagram of the three-phase permanent magnet synchronous motor modeled in this paper is as follows: Figure 1 As shown, its simplified model is as follows Figure 2 As shown, A, B, and C represent the three-phase stator windings of the permanent magnet synchronous motor, which are located on the stator, while the permanent magnets are located on the rotor. The stator windings are arranged in space with a 120° electrical angle phase difference, and the rotor axis is angularly out of phase with the stator direct axis. And it is assumed that the quadrature axis leads the direct axis in the counterclockwise direction of rotor rotation. The motor windings in the diagram are connected in a star configuration (i.e., Y-connection). A star connection means that one end of each of the three phases is connected together to form a common terminal (N line, also called the neutral line). The rotor uses surface-mounted permanent magnets. Assuming that the three-phase permanent magnet synchronous motor has one pair of poles, the rotor position electrical angle at any given time... It is equal to the product of the rotor's mechanical angle and the number of pole pairs.

[0068] 1. Stator voltage balance equation

[0069]

[0070] In the formula: The dq-axis stator voltage component; For the dq-axis stator current components; This refers to the stator winding resistance. For dq axis inductance; The rotor's electric angular velocity; The dq-axis flux linkage component describes the dynamic coupling relationship between stator voltage, current, and rotational speed. This is the physical basis for the design of the ADRC Extended State Observer (ESO). Based on the dynamic response characteristics in this equation, the ESO unifies unmodeled dynamics (such as parameter perturbations) and external disturbances (such as load abrupt changes) as a unified observation of the "total disturbance" for compensation, thus providing a linearized controlled object for the Bayesian tuner.

[0071] 2. Magnetic flux linkage equation

[0072] The stator flux linkage equation describes the coupling relationship between current and flux linkage:

[0073]

[0074] In the formula: Rotor flux generated by permanent magnets.

[0075] 3. Electromagnetic torque equation

[0076] Electromagnetic torque is a core indicator of a motor's output power. In the dq coordinate system, electromagnetic torque... It can be represented as:

[0077]

[0078] In the formula: This represents the number of pole pairs in the motor. For the surface-mounted permanent magnet synchronous motor (SPMSM) used in this embodiment, since... Since the reluctance torque component is zero, the above equation can be simplified to:

[0079]

[0080] This formula shows that, Under the vector control strategy, electromagnetic torque and quadrature axis current Proportional. Therefore, in the Bayesian optimization cost function of this invention, a... As a penalty, it is essentially a suppression of electromagnetic torque pulsation and control energy consumption.

[0081] 4. Equations of motion for machines

[0082] The mechanical dynamics equations of an electric motor describe the dynamic characteristics of speed as torque changes:

[0083]

[0084] In the formula: It is the moment of inertia; This is the load torque; It is the coefficient of viscous friction; This represents the mechanical angular velocity. This equation is directly related to the speed tracking error. With electromagnetic torque It is the direct feedback object for parameter optimization in Bayesian tuners.

[0085] Step 2: Construct a coordinate transformation model for a permanent magnet synchronous motor (PMSM);

[0086] In the mathematical model derived in the three-phase stator coordinate system, there are complex coupling relationships between the parameters of the motor, which is not suitable for dynamic analysis. Therefore, a coordinate transformation can be used to replace the stator windings fixed on the stator with a set of virtual d-q axis windings that rotate at the rotor speed (electric angular velocity), thus simplifying the mathematical model.

[0087] Depending on the coordinate system, common mathematical models of permanent magnet synchronous motors (PMSMs) can be categorized into models based on the ABC three-phase natural coordinate system, models based on the α−β stationary coordinate system, and models based on the d−q rotating coordinate system. The d−q rotating coordinate system is called the rotor reference coordinate system. Ideally, the direction of the N pole of the permanent magnet in the rotor of the PMSM is defined as the d-axis, representing the direct-axis component of the stator current; the q-axis is perpendicular to the rotor flux direction, representing the quadrature-axis component of the stator current, and the two are orthogonal. While the ABC coordinate system does not require coordinate transformation, its equations are relatively complex, with many variables and high coupling, making calculations more complicated. Even after transforming from the ABC coordinate system to the α−β coordinate system, the model parameters still change over time, complicating the control system design. Therefore, to facilitate later controller design, the mathematical model in the synchronous rotating coordinate system d−q is typically chosen for motor modeling. The transformation from the stationary coordinate system to the rotor reference coordinate system is shown in Figure 3.

[0088] 1. Clarke Transform

[0089] As shown in Figure 3(a), the three vectors ABC are projected onto the α-axis and β-axis respectively, transforming the three-phase stationary coordinate system ABC into a two-phase stationary coordinate system. - This is called the Clarke transform. The Clarke transform converts three-phase symmetrical sinusoidal currents... , , Converted into two-phase sinusoidal current , Based on the coordinate transformation relationship, make The axis coincides with the axis of phase A. Axis ahead With the axis at 90°, to ensure that the amplitudes of current, voltage, and flux linkage remain unchanged before and after the Clarke transformation, the coefficients of the transformed current matrix are 23. The two-phase current equations for the equal-amplitude Clarke transformation are as follows:

[0090]

[0091] This invention achieves dimensionality reduction of motor physical quantities. It transforms three-dimensional alternating current quantities with a 120° mutual difference into two-dimensional orthogonal current quantities, providing an orthogonal basis for subsequent rotational transformations. This is the first "barrier" for the current sampling signal to enter the control system in this invention, ensuring that the signal received by the subsequent Bayesian tuner is accurate and reliable. A signal is an effective state quantity that has been rigorously mathematically reconstructed.

[0092] 2. Park Transformation

[0093] As shown in Figure 3(b), it consists of two phases - The transformation from a stationary coordinate system to a two-phase d-q rotating coordinate system (stator magnetic field rotating coordinate system) is called the Park transformation. The d-axis and... The included angle of the axis is

[0094]

[0095] Through the Park transform, the originally time-varying AC signal is transformed into a steady-state DC signal. This allows the AC motor to be controlled as an equivalent DC motor. Controlling magnetic flux, Control torque. Only when... Only in a coordinate system can the system model possess a relatively stable form, allowing the use of a linear active disturbance rejection controller (LADRC) to adjust the speed loop. Bayesian tuner optimized bandwidth. Essentially, it adjusts the response speed of this DC model.

[0096] Step 3: Mechanism Modeling of the Variable Parameter Improved ADRC Controller:

[0097] Traditional Active Disturbance Rejection Control (ADRC) typically uses fixed gain parameters, failing to balance dynamic response and steady-state noise immunity. This invention constructs an improved linear active disturbance rejection controller (LADRC) that supports dynamic bandwidth input. Unlike conventional second-order ESOs that handle the speed loop, this embodiment employs a third-order extended state observer, treating the system as a second-order model for control (considering unmodeled dynamics such as current loop delay), to achieve higher-precision disturbance estimation capabilities. A real-time mapping mechanism between the bandwidth parameter and the controller's internal gain is also established.

[0098] 1. State equations of the improved third-order extended state observer (LESO)

[0099]

[0100] This is the core sensing unit of the ADRC controller. In the formula... The actual speed of the motor , For control input (i.e., quadrature axis current command) ). Observe the motor speed. Observe the differential of the motor speed (i.e., acceleration). The total disturbance of the observation system (including load torque) (Friction, parameter perturbations, and unmodeled dynamics).

[0101] Compared to traditional second-order ESOs, this invention employs a third-order structure, adding an integral state variable, which enables control over the "total disturbance" in high-frequency noise environments. A smoother and more accurate estimate provides high-quality data support for subsequent disturbance compensation.

[0102] 2. Flexible observer bandwidth configuration function

[0103]

[0104] This is the key formula for suppressing steady-state noise and "eliminating glitches" in this invention. Traditional engineering experience typically sets the observer bandwidth. This will lead to observer gain. With the cubic order of bandwidth ( The noise level increases dramatically, greatly amplifying the sensor noise. This formula forces a lock-in. This establishes a flexible configuration relationship with "low sensitivity".

[0105] It serves as a bridge connecting the upper-level Bayesian tuner and the lower-level ESO. When the Bayesian algorithm dynamically adjusts the controller bandwidth... At this time, the formula ensures the observer bandwidth. It always operates in the low-noise amplification region, which reduces the impact of high-frequency noise on the control loop through parameter configuration.

[0106] 3. Bandwidth-parameterized state error feedback control law:

[0107]

[0108] In this embodiment, to simplify the calculation and to accommodate the characteristics of a third-order ESO, the following simplified form is adopted (ignoring the differential term or incorporating it into the perturbation):

[0109]

[0110] This is the formula for generating control signals. For the target speed, Torque-to-current conversion factor ( ). In the molecule The item is responsible for eliminating speed errors (PD control function). This term is responsible for canceling the total observed disturbance in real time. This formula shows that the controller's response speed (stiffness) is directly derived from the output of the Bayesian tuner. Decision. Changed in real time. The system can smoothly switch between "high stiffness disturbance rejection" and "low stiffness flexible silence" modes.

[0111] 4. Disturbance compensation coefficient Correction:

[0112] Settings can be configured based on offline recognition results:

[0113]

[0114] Achieve model-assisted linearization. The accuracy of ESO determines the control input The degree of decoupling. In this model, accurate It can reduce ESO estimation The burden of this allows the Bayesian algorithm to focus on handling external load disturbances rather than spending computing power to compensate for model parameter deviations, thus further improving the convergence speed of optimization.

[0115] Step 4: Construct a two-layer Bayesian tuner architecture:

[0116] 1. Construct a two-layer supervisory control topology:

[0117] This invention builds an independent Bayesian tuner in parallel on top of the traditional ADRC control loop for permanent magnet synchronous motors. This tuner does not directly participate in the modulation of the motor voltage or duty cycle; instead, it acts as a decision-making center, receiving feedback on the motor's operating status and outputting macroscopic control parameters—the controller bandwidth. This two-layer decoupled architecture helps maintain the real-time performance of the lower-level control and improves the flexibility of upper-level parameter decision-making. Even if the upper-level algorithm pauses updates, the lower-level controller can still maintain stable operation of the parameters at the last moment.

[0118] 2. Implement signal sensing and high-pass filtering preprocessing:

[0119] The tuner collects the speed tracking error in real time through the sensor interface. and cross-axis current Two signals. To accurately assess control stability, the system analyzes the acquired quadrature-axis current. A first-order high-pass filter is performed to remove the DC component generated by the load torque, retaining only the AC ripple component that reflects the electromagnetic torque fluctuations. .

[0120] First, the DC component is estimated using a low-pass filter. Then, the ripple component is extracted using differential extraction:

[0121]

[0122] In the formula, These are the filter coefficients. The sampling period.

[0123] Subsequently, the system divides the error signal and the current ripple signal by the rated speed respectively. and rated current Normalization is performed to eliminate dimensional differences and reduce their impact on cost function calculation.

[0124]

[0125] 3. Construct a composite cost function constrained by energy stability:

[0126] To address the issue of system oscillations caused by traditional adaptive control's sole pursuit of error minimization, this embodiment constructs an integral cost function that includes an energy penalty term. This function is applied in each evaluation cycle. Within this calculation, the sum of the squared speed error and the squared weighted current ripple is accumulated:

[0127]

[0128] in, The number of sampling points within the evaluation period. Error squared term. The guided algorithm seeks parameters with faster response times, while the current ripple square term... This forces the algorithm to avoid the parameter region that triggers high-frequency howling. This is achieved by adjusting the noise suppression weights. In this embodiment, a value of 0.2 is used to achieve a quantitative trade-off between dynamic response speed and steady-state operation stability.

[0129] 4. Perform flexible observer parameter mapping:

[0130] Bayesian tuner outputs a single controller bandwidth. Subsequently, a parameter mapping module transforms it into the complete parameter set required by the ADRC controller. To reduce the risk of high-frequency noise amplification, this invention employs a flexible observer configuration strategy, establishing the following bandwidth constraint relationship to force the bandwidth of the extended state observer to be... Locked to 2.0 times the controller bandwidth:

[0131]

[0132] Based on this proportional relationship, the system uses the pole placement method to simultaneously calculate the three internal gains of the observer. :

[0133]

[0134] This strategy will increase higher-order gains. The value decreased significantly (compared to) The traditional configuration has been reduced to approximately This ensures that the observer maintains low noise sensitivity during the adaptive optimization process.

[0135] The internal signal flow diagram of the entire Bayesian tuning process is shown below. Figure 4 As shown.

[0136] Step 5: Steady-state locking and adaptive wake-up logic:

[0137] 1. Establish a dual-threshold hysteresis state machine

[0138] To address the inherent drawback of online optimization algorithms introducing random noise in steady-state conditions, this embodiment designs a logic state machine that includes "locked states" and "active states." The system sets two non-overlapping thresholds: a lower locking threshold... Higher wake-up threshold This hysteresis design reduces the likelihood of frequent switching of the system under critical conditions, ensuring the stability of the control mode.

[0139] 2. Perform steady-state dead-zone locking action:

[0140] The system monitors the absolute value of the speed tracking error in real time. When the error is detected to be below the lockout threshold for a continuous period (e.g., 0.5 seconds), the system will lock the position. When the logic unit determines that the system has entered a steady state, it immediately triggers a locking action. At this point, the system forcibly reduces the exploration variance within the Bayesian algorithm. Setting the value to zero stops the random number generator and freezes the controller bandwidth parameter to the output value of the previous time step. This measure physically eliminates the source of random disturbances introduced by the algorithm, reduces speed fluctuations in the steady-state phase, and improves the smoothness of the speed curve.

[0141] 3. Execute adaptive mutation wake-up action:

[0142] To maintain the system's adaptability to environmental changes, the system continuously monitors error signals. When a speed error exceeds the wake-up threshold, the system will initiate a wake-up process. When (typically caused by a sudden load change or a given step jump), the logic unit determines that the system has been significantly disturbed and immediately triggers an unlocking action. At this point, the system will explore the variance. The system is reset to its initial value, and the recursive Bayesian update algorithm is reactivated. This mechanism gives the system an "alert" capability, enabling it to quickly switch from a dormant state to an optimization state and rapidly suppress external disturbances.

[0143] Step Six: Execute the Recursive Bayesian Optimization Algorithm:

[0144] The flowchart of the recursive Bayesian optimization algorithm for this step is as follows: Figure 5 As shown.

[0145] 1. Initialize the Gaussian probability distribution model:

[0146] When the system is in an active state, a lightweight recursive probabilistic model is used instead of a complex full-history regression. The algorithm assumes optimal bandwidth parameters. It follows a Gaussian distribution, and its probability density function can be expressed as:

[0147]

[0148] Algorithm initializes the mean of the distribution and variance The initial mean was set to a conservative, safe bandwidth, and the initial variance was set to a moderate exploration range to ensure system stability during the initial startup phase of the algorithm.

[0149] 2. Perform recursive posterior probability update:

[0150] In each control cycle Within the algorithm, the cost function value of the current period is compared. The cost of historical best And recursively update the distribution parameters according to the following rules. and :

[0151]

[0152] In the formula, This is the variance shrinkage factor (0.9 in this example), used to accelerate convergence when a better solution is found; The variance expansion factor (1.1 in this example) is used to expand the search range when trapped in local maxima. If the current performance is better than the historical best, the algorithm executes the "exploitation" strategy, moving the distribution mean to the current parameter value and shrinking the variance proportionally; if the current performance is worse than the historical best, the algorithm executes the "exploration" strategy, keeping the mean unchanged (backoff) and fine-tuning the expansion of the variance. This recursive update mechanism reduces computational complexity, making it compatible with the computing power of microprocessors.

[0153] 3. Implement Thompson sampling and physical constraints:

[0154] Based on the updated probability distribution, the algorithm uses the Thompson sampling method to generate candidate bandwidth parameters for the next time step. :

[0155]

[0156] To prevent the generated parameters from exceeding the physical limits of the motor or causing system divergence, the algorithm imposes hard constraints on the candidate parameters, forcibly limiting them to a preset safe range. Within, the final candidate values ​​are obtained. :

[0157]

[0158] This step ensures the safety of the adaptive process and reduces the risk of extreme parameters adversely affecting the hardware.

[0159] 4. Perform output smoothing filtering:

[0160] To avoid abrupt changes in discrete optimization parameters in the time domain, which could impact the motor's mechanical transmission, a discrete first-order low-pass filter is connected in series at the output of the algorithm. This filter transforms the "step-like" parameter sequence generated by the algorithm into a continuous and smooth control command through a weighted averaging method. :

[0161]

[0162] In the formula, This is a smoothing factor. This measure achieves a smooth transition from algorithmic numerical optimization to physical flexible control, reducing the impact of abrupt changes during parameter adjustment.

[0163] The ADRC parameter adaptive control method based on steady-state locking strategy and flexible observer proposed in this invention has broad application prospects in the fields of aerospace and high-end equipment manufacturing, and shows significant technical advantages, especially in the following scenarios:

[0164] 1. Energy management and smooth drive of hybrid-electric propulsion aircraft engines (HEPS):

[0165] In series or parallel hybrid aero-engines, the electric motor frequently assists the gas turbine in rapid load adjustments. The adaptive wake-up mechanism of this invention ensures that the electric motor can respond quickly to sudden changes in thrust demand in a very short time, reducing thrust fluctuations and impact risks during power switching. At the same time, the steady-state locking technology improves the smoothness of the motor's output torque during cruise, reduces the possibility of electromagnetic interference caused by current ripple, and enhances the electromagnetic compatibility of airborne electronic equipment.

[0166] 2. Precision control of the airborne electromechanical actuation system for multi-electric aircraft:

[0167] More-electric aircraft extensively use electromechanical actuators to replace hydraulic actuators in driving control surfaces, landing gear, and thrust reversers. The flexible observer strategy of this invention effectively suppresses high-frequency noise amplification under high bandwidth, alleviates the "high-frequency howling" and overheating problems commonly seen in high-stiffness position servo systems, effectively extends the fatigue life of the mechanical transmission chain, and reduces maintenance costs.

[0168] 3. High-efficiency and quiet operation of aviation fuel pumps and lubricating oil pumps:

[0169] Fuel metering pumps and oil pumps in aircraft engines are typically driven by permanent magnet synchronous motors, requiring extremely high precision and stability in flow control. The composite cost function of this invention directly reduces pump torque pulsation by suppressing quadrature-axis current ripple, thereby reducing pressure pulsation and flow-induced noise in the fluid pipeline. This is of great significance for improving the supply stability of the engine fuel system and reducing the overall noise level of the aircraft.

[0170] 4. Attitude stabilization control of electric vertical takeoff and landing (eVTOL) aircraft:

[0171] eVTOL aircraft rely on multiple distributed motors for attitude adjustment, making them extremely sensitive to motor synchronization and response speed. The recursive Bayesian algorithm of this invention has extremely low computational complexity and can be directly embedded into a low-cost distributed motor controller (MCU), reducing dependence on central flight control computing resources. This enables independent online self-tuning of multiple motor parameters, improving the aircraft's attitude robustness under complex weather conditions such as strong gusts.

[0172] like Figure 6As shown, the Simulink simulation model of the control method of this invention mainly consists of a given signal input module, a Bayesian-ADRC adaptive tuning module, an ADRC speed outer loop control module, a current inner loop adjustment module, a coordinate inverse transformation module, an SVPWM modulation module, an inverter drive module, a permanent magnet synchronous motor body module, and a state feedback measurement module. Its working process is as follows: First, the given speed signal and the actual feedback signal from the motor are input into the control system; then, the Bayesian-ADRC tuning module adjusts the key parameters of the controller online according to the speed error and the system operating state, and applies the adjustment result to the ADRC speed outer loop; after the speed outer loop outputs the torque current, it works together with the current inner loop to complete the dq-axis current adjustment; then, the inverter drive signal is generated by the inverse Park transformation and SVPWM module to drive the permanent magnet synchronous motor; simultaneously, the motor speed, rotor position, and related state variables are measured in real time and fed back to the controller and tuner, forming a closed-loop control circuit. The figure visually reflects the overall implementation structure of the present invention from "online parameter optimization - control law generation - motor drive execution - state feedback update", and can be used to verify the feasibility of the proposed steady-state locking strategy, flexible observer design and recursive Bayesian online optimization mechanism in permanent magnet synchronous motor control system.

[0173] like Figure 7 The figure shows the simulation results of the controller modeled according to the present invention. The dashed line represents the given motor speed, and the solid line represents the actual motor speed. As can be seen from the figure, after the system starts, the actual speed can quickly track the increase of the given speed and reach the target speed of 1000 r / min in about 0.4 s, indicating that the control method proposed in this invention has good start-up response capability and tracking accuracy. After entering the steady-state stage, the actual speed generally coincides with the given speed, indicating that the method can maintain high speed control accuracy under steady-state conditions. The magnified area in the figure further shows the detailed response process around 0.5 s. It can be seen that after a short transient fluctuation at this moment, the system quickly recovers to stability, and the speed deviation is suppressed and converges back to near the target speed in a short time. This indicates that the variable parameter improved ADRC controller proposed in this invention, combined with the steady-state locking and adaptive wake-up mechanism, can maintain strong anti-disturbance capability, small steady-state error, and good dynamic recovery performance under the presence of disturbances or parameter switching.

[0174] like Figure 8The diagram shows the overall flowchart of an adaptive active disturbance rejection control (ADRC) method for permanent magnet synchronous motors based on a steady-state locking strategy and a flexible observer proposed in this invention. The process first constructs a decoupled model of the permanent magnet synchronous motor and an improved ADRC controller to establish the mathematical model of the controlled object and the underlying closed-loop control framework. Then, a two-layer supervised Bayesian tuner architecture is built to separate the parameter optimization layer from the underlying ADRC execution layer. Based on this, the system acquires and preprocesses feedback signals in real time to extract speed errors and related state information. Next, steady-state locking and adaptive wake-up logic are executed to determine whether the current system is in a parameter frozen state or an online optimization activation state. Then, a parameter decision mechanism is executed based on the current state to select key controller parameters online. Next, safety constraints, smoothing processing, and mapping reconstruction are applied to the generated parameters to ensure that parameter updates meet physical realizability and control continuity requirements. Finally, the updated parameters are applied to the underlying ADRC controller and closed-loop control is run. The control results are then fed back to the front-end signal acquisition and processing unit, thus forming a complete closed-loop iterative optimization process.

[0175] like Figure 9 The diagram shows the control loop flowchart of the steady-state locking and adaptive wake-up collaborative recursive Bayesian parameter tuning proposed in this invention. At the beginning of each control cycle, step 1 is executed first to collect and extract features from the system feedback signal to obtain the speed error. and cross-axis current ripple characteristics Then, in step 2, it is determined whether the system meets the steady-state locking condition, that is, whether the absolute value of the speed error is less than the preset locking threshold. And whether the duration is greater than the stability determination time. When the steady-state locking condition is met, proceed to step 3 to execute the steady-state dead-zone locking action, setting the exploration variance to zero and maintaining the current controller bandwidth parameter. This remains unchanged to prevent parameter jitter and speed fluctuations caused by continuous random searching during the steady-state phase of the system.

[0176] Furthermore, if the system does not meet the steady-state locking condition, proceed to step 4 to further determine whether the sudden awakening condition is met, i.e., whether the absolute value of the speed error is greater than the preset awakening threshold. When this condition is met, an adaptive reset wake-up action is performed in step 5 to restore the exploration variance to its initial value. This allows the Bayesian optimizer to regain its exploration capabilities. Afterwards, regardless of whether it enters directly from an unlocked state or from a woken-up state, the system calculates a composite cost function in step 6 that includes speed error and current ripple indices. In step 7, recursive Bayesian posterior update and Thompson sampling are performed to generate new candidate controller bandwidth parameters. To ensure the feasibility of parameter changes and the continuity of control, step 8 performs amplitude limiting and smoothing filtering on the candidate outputs; step 9 then reconstructs the observer parameters based on the flexible observer mapping relationship, for example, setting the observer bandwidth to... It then updates the underlying controller parameters synchronously and returns to the next control loop.

Claims

1. A steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor, characterized in that, Includes the following steps; Step 1: Taking the permanent magnet synchronous motor as the controlled object, establish the mechanism model of the permanent magnet synchronous motor and obtain the coupling relationship between voltage, current, flux linkage, torque and speed; Step 2: Based on the mechanism model established in Step 1, the three-phase stationary coordinate system model is converted into a dq rotating coordinate system model through Clarke transformation and Park transformation; Step 3: Based on the dq axis model obtained in Step 2, construct a variable parameter improved ADRC controller. Estimate load disturbances, parameter perturbations, and unmodeled dynamics by extending the state observer, and achieve active disturbance rejection control through state error feedback and disturbance compensation. Step 4: Build a two-layer Bayesian tuner architecture on top of the underlying control loop constructed in Step 3, process feedback signals such as speed error and current ripple, and construct a cost function to transform it into an optimization objective for the controller bandwidth parameters. Step 5: Implement steady-state locking and adaptive wake-up management for the Bayesian tuner in Step 4, freezing the optimization output when the system is in a steady state and reactivating the optimization process when the system is disturbed; Step six recursively updates the probability distribution under the active state determined in step five and generates new candidate bandwidth parameters. After physical constraints and smoothing, the parameters are output to the ADRC controller in step three. The low-complexity recursive update ensures that it can be embedded in the motor control chip for real-time operation.

2. The method for steady-state locking adaptive active disturbance rejection control of a permanent magnet synchronous motor according to claim 1, characterized in that, Step one specifically involves: The input, output, state variables, and disturbance propagation path of the system are determined by the stator voltage balance equation, flux linkage equation, electromagnetic torque equation, and mechanical motion equation. The stator voltage balance equation, flux linkage equation, electromagnetic torque equation, and mechanical motion equation have a progressive relationship from electricity to magnetism, from magnetism to torque, and from torque to motion. Among them, the stator voltage balance equation is used to describe the dynamic coupling relationship between stator voltage, current, magnetic flux and rotational speed; the magnetic flux equation is used to characterize the coupling relationship between current and permanent magnet magnetic flux; the electromagnetic torque equation establishes the conversion relationship between electromagnetic energy and mechanical output torque based on the relationship between magnetic flux and current; the mechanical motion equation describes the dynamic relationship between electromagnetic torque, load torque, friction damping and rotational speed change, and is used to establish the connection between rotational speed response and disturbance.

3. The method for steady-state locking adaptive active disturbance rejection control of a permanent magnet synchronous motor according to claim 2, characterized in that, Step two specifically involves: The Clarke transform and the Park transform have a continuous relationship of first reducing dimensions and then rotating to decouple them; Among them, the Clarke transform first transforms the current, voltage or flux linkage signals in the three-phase stationary coordinate system into orthogonal components in the two-phase stationary coordinate system, realizing the dimensionality reduction processing from three-phase AC quantities to two-phase orthogonal quantities; The Park transformation, based on the Clarke transformation, further transforms the two-phase stationary coordinate system variables into the dq coordinate system that rotates synchronously with the rotor, thus converting the originally time-varying, strongly coupled AC quantities into relatively constant DC quantities under steady-state conditions.

4. The steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor according to claim 3, characterized in that, Step three specifically involves: Based on the PMSM mathematical model obtained in steps one and two, an improved linear active disturbance rejection controller that supports online bandwidth variation is established, including a third-order extended state observer, a flexible observer bandwidth configuration function, a state error feedback control law, and disturbance compensation coefficient correction. The improved third-order extended state observer state equation is used to estimate the motor speed, the rate of change of speed, and the total system disturbance in real time; The flexible observer bandwidth configuration function is used to establish a mapping relationship between the observer bandwidth and internal gain based on the controller bandwidth, thereby suppressing noise amplification under high bandwidth while ensuring dynamic performance; The state error feedback control law with bandwidth parameterization generates control input based on the target speed, actual speed, and observer output state, enabling the controller bandwidth parameter to directly affect the closed-loop response speed and control stiffness. The correction of the disturbance compensation coefficient further assists in the model-aided correction of the control input channel.

5. The steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor according to claim 4, characterized in that, Step four specifically involves: The system constructs a two-layer supervised control topology, implements signal sensing and high-pass filtering preprocessing, constructs a composite cost function with energy stability constraints, and performs flexible observer parameter mapping. Among them, the two-layer supervisory control topology is used to connect the Bayesian tuner to the traditional ADRC control loop as an independent upper-level decision unit, so that the lower-level control execution and the upper-level parameter optimization are decoupled from each other. Signal sensing and high-pass filtering preprocessing are used to acquire speed error and cross-axis current signals, and extract ripple information that can reflect electromagnetic torque pulsation, providing effective input for performance evaluation; The composite cost function, based on the preprocessed signal, comprehensively quantifies the speed tracking accuracy and current ripple stability, serving as the basis for the Bayesian optimization algorithm to evaluate the current bandwidth performance. Flexible observer parameter mapping further transforms the single controller bandwidth output by the upper-level tuner into the complete observer and control parameters required by the lower-level ADRC, enabling the optimization results to truly apply to the controller.

6. The steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor according to claim 5, characterized in that, Step five specifically involves: Establish a dual-threshold hysteresis state machine, execute steady-state dead-zone locking action, and execute adaptive mutation wake-up action; Among them, the dual-threshold hysteresis state machine is used to set the locking threshold and the wake-up threshold according to the magnitude of the speed error, establish the switching criteria between the locked state and the active state, and prevent the system from frequently jittering and switching in the critical region. The steady-state dead zone locking action is executed when the detected error is continuously lower than the locking threshold. It is used to freeze the exploration variance of the Bayesian optimization algorithm and keep the controller bandwidth parameter unchanged, thus physically cutting off the random disturbances introduced by online optimization. The adaptive mutation wake-up action is executed when the error exceeds the wake-up threshold. It is used to release the exploration variance and activate the recursive Bayes update, so that the system can re-enter the parameter optimization state to cope with external disturbances or given changes.

7. The steady-state locking adaptive active disturbance rejection control method for a permanent magnet synchronous motor according to claim 6, characterized in that, Step six specifically involves: Initialize the Gaussian probability distribution model, perform recursive posterior probability updates, implement Thompson sampling and physical constraints, and perform output smoothing filtering. The initial Gaussian probability distribution model is used to provide the initial mean and variance of the controller's optimal bandwidth parameters and to determine the initial search range of the optimization algorithm. Recursive posterior probability update is used to correct the mean and variance of the probability distribution based on the comparison results of the composite cost function of the current period and the historical performance, so as to achieve a dynamic balance between utilization and exploration. Thompson sampling and physical constraints are used to extract new candidate bandwidth parameters from the updated probability distribution and limit them within a preset safety range to ensure that the optimization results meet the physical realizability of the control system. The output smoothing filter process performs low-pass smoothing on the final candidate bandwidth to suppress the impact of parameter jumps on the motor mechanical transmission chain and control loop.

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