A method and system for finite-time preset performance fault-tolerant control of permanent magnet synchronous motor under asymmetric constraints

Abstract

The application provides a kind of finite time preset performance fault-tolerant control method and system of permanent magnet synchronous motor under asymmetric constraint, for permanent magnet synchronous motor system with asymmetric time-varying state constraint, unknown lumped disturbance and actuator failure, the constrained system is converted into unconstrained system by nonlinear transformation function, combined with nonlinear disturbance observer and dynamic surface control technology, the finite time preset performance fault-tolerant control law is designed, the position, speed and current tracking error are converged to the range specified by preset performance index within finite time, while ensuring that the motor state does not violate asymmetric time-varying constraint, and can effectively suppress the influence of actuator performance loss and stuck fault on system performance. The application not only considers the actual high-performance control requirements of motor operation, meets the requirements of fast response and performance index, and can ensure the control performance of motor under fault condition, improves the effectiveness and safety of PMSM control.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to a finite-time preset performance fault-tolerant control method and system for permanent magnet synchronous motors under asymmetric constraints. Background Technology

[0002] Permanent magnet synchronous motors, due to their high power density, high efficiency, and excellent dynamic response characteristics, have become core actuators in high-end equipment fields such as industrial robot servo drives, CNC machine tool spindle control, electric vehicle drive systems, and aerospace actuators. However, as application scenarios continue to place higher demands on the safety and dynamic quality of motor systems, traditional control methods are gradually revealing structural limitations when dealing with complex operating conditions.

[0003] Current control designs for permanent magnet synchronous motors (PMSMs) are primarily based on linearized or decoupled models within an integer-order calculus framework. These models struggle to accurately describe the nonlinear electromagnetic characteristics, parameter temperature drift, and strong coupling dynamics caused by sudden load changes during wide-speed operation. This leads to significantly increased model mismatch errors under extreme conditions, hindering further improvements in control accuracy. Regarding state constraint handling, the motor operates under strict physical boundary limitations: rotor position is constrained by mechanical travel, exhibiting asymmetric upper and lower bounds; speed must be limited to a safe threshold to prevent mechanical damage; and stator current exhibits significantly asymmetric tolerance limits in motoring and generating states, dynamically drifting with thermal conditions. While traditional state constraint methods based on obstacle Lyapunov functions can ensure state boundaries are not exceeded, they require the virtual control law to remain within the feasible region, severely limiting the controller's design freedom. More critically, as the system state approaches the constraint boundaries, the control gain tends towards infinity, leading to numerical singularities and actuator saturation risks, severely restricting its engineering feasibility in high-dynamic-response scenarios.

[0004] In terms of disturbance compensation, motor systems are constantly subjected to multi-source uncertainties, including stator resistance temperature drift, dq-axis inductance parameter perturbation, sudden load torque changes, unmodeled friction coefficient characteristics, and inverter dead-zone effects. These factors together constitute lumped disturbances that are difficult to model accurately. Although traditional sliding mode control or robust control has a certain anti-interference capability, it often comes at the cost of sacrificing steady-state accuracy or increasing chattering, making it difficult to simultaneously guarantee tracking accuracy and system smoothness under strong disturbance conditions. In addition, actuator failure is a hardware failure mode that cannot be ignored in motor drive systems. Performance loss faults caused by open circuits in power transistors and jamming bias faults caused by short circuits in windings or abnormal drive signals can instantaneously change the gain of the system control channel or inject unknown biases, directly threatening the safe and stable operation of the system. Most existing preset performance control methods assume that the actuator is in an ideal healthy state and mainly deal with symmetric steady-state constraint problems, making it difficult to achieve unified, reliable, and high-performance control in complex scenarios where asymmetric time-varying constraints, finite-time convergence indices, and actuator failures coexist.

[0005] Therefore, there is an urgent need for an advanced control method that can simultaneously ensure strict satisfaction of asymmetric time-varying state constraints, finite-time preset performance guarantees, accurate compensation for lumped disturbances, and active fault tolerance of actuator failures, in order to overcome the bottleneck of existing technologies in terms of theoretical completeness and engineering applicability. Summary of the Invention

[0006] Purpose of the invention: The technical problem to be solved by the present invention is to provide a finite-time preset performance fault-tolerant control method and system for permanent magnet synchronous motors under asymmetric constraints, addressing the shortcomings of the existing technology.

[0007] The method includes the following steps:

[0008] Step 1: Establish a dynamic model of the permanent magnet synchronous motor (PMSM) in the direct-axis-quadrature-axis dq rotating coordinate system, and define the state variables. ,in For rotor position, The rotor's mechanical speed. The stator current is the d-axis current. The current is the q-axis stator current; the dynamic model considers asymmetric time-varying state constraints and unknown lumped disturbance vectors. The components are respectively , , , And actuator failure, the actuator failure model is represented as Actual input voltage The nominal control input is the voltage actually applied to the motor stator after a fault. The ideal control voltage output by the controller. This is the efficiency loss coefficient matrix. For the biased fault term, the state constraints are time-varying and asymmetric. , Let i be the state variable of the i-th subsystem. Let be the time-varying constraint boundary function of the i-th subsystem. Let be the time-varying upper constraint boundary function of the i-th subsystem;

[0009] Step 2: The original system subject to asymmetric constraints is transformed into an unconstrained system using the nonlinear transformation function NTF. A nonlinear disturbance observer is designed to estimate the lumped disturbance, including external disturbances, neural network approximation errors, and fault terms. The nonlinear transformation function of the i-th subsystem... satisfy ,in Let be the tracking error of the i-th subsystem, i=1,2,3,4, which correspond to the position loop, speed loop, d-axis current loop and q-axis current loop respectively; The transformed tracking error;

[0010] Step 3: Introduce the preset time performance function PTPF to define the preset performance boundary of the tracking error of the i-th subsystem. Combine coordinate transformation and dynamic surface control (DSC) technology to design control laws and adaptive laws for the position loop, speed loop, d-axis current loop, and q-axis current loop, respectively. The control law design includes finite-time convergence terms. and disturbance compensation term, where the control gain of the i-th subsystem To control the gain, the transformed tracking error of the i-th subsystem The tracking error after transformation is the finite-time exponent of the i-th subsystem. For finite time index, For the preset performance function, ;

[0011] Step 4: Design a fault-tolerant control law to compensate for actuator failures and jamming faults. By introducing a fault compensation term, ensure that the system still meets the preset performance indicators when actuator failures occur.

[0012] Step 5: Prove the finite-time stability of the closed-loop system based on Lyapunov stability theory. Prove that the designed controller can guarantee that all closed-loop signals converge within a finite time, the motor state always satisfies the asymmetric time-varying constraint and does not exceed the preset boundary, and the tracking error meets the preset performance index within a preset time.

[0013] Step 1 includes:

[0014] Establish a dynamic model of the PMSM motor in the dq rotating coordinate system:

[0015] ,

[0016] in, These are the stator d-axis current and q-axis current, respectively. The rotor's mechanical speed. For rotor position, These are the stator d-axis voltage input and q-axis voltage input, respectively. These are the d-axis inductance and the q-axis inductance, respectively. For stator resistance, For extreme logarithms, Let J be the magnetic flux linkage of the permanent magnet, J be the moment of inertia, and B be the coefficient of friction. For load torque, The d-axis represents the unknown lumped disturbance. The q-axis lumped perturbation is unknown. The unknown lumped disturbance of the rotational speed loop; dt represents the time derivative;

[0017] Using d-axis current reference value The vector control strategy obtains the state variables. Define control input ,in This is the d-axis stator voltage input. The input voltage is the q-axis stator voltage; consider the actuator fault model. ,in This is the efficiency coefficient matrix. The d-axis efficiency loss coefficient. The q-axis efficiency loss coefficient is... This is a bias fault. This represents the d-axis offset fault component. Let be the q-axis offset fault component; then the system dynamic equations under the effects of fault and disturbance are:

[0018] ,

[0019] ,

[0020] ,

[0021] in, for The derivative of For system dynamic functions, For input matrix functions, For the lumped disturbance of the unknown location ring. The lumped disturbance vector includes external disturbances, parameter perturbations, and fault biases; the state constraints satisfy... It is a time-varying constraint boundary function.

[0022] The specific construction process of the nonlinear transformation function in step 2 includes:

[0023] For the tracking error of the i-th subsystem Introduce a nonlinear transformation function:

[0024] ,

[0025] when Time-varying constraint boundary function of the i-th subsystem hour, ;when The time-varying upper constraint boundary function of the i-th subsystem hour, Therefore, if If the original tracking error remains bounded, then... Strictly meet the constraints ;symbol Indicates approaching;

[0026] The derivative yields the dynamic error after transformation:

[0027] ,

[0028] in , , for The derivative of Let i be the transformation gain of the i-th subsystem. for The derivative of For the constraint boundary change rate compensation term of the i-th subsystem, for The derivative of for The derivative of .

[0029] The nonlinear perturbation observer (NDO) design process in step 2 includes:

[0030] For the lumped disturbance of the i-th subsystem This includes external disturbances, radial basis function (RBF) neural network approximation errors, and fault equivalent terms. The NDO is designed as follows:

[0031] ,

[0032] in, Let i be the disturbance estimate of the i-th subsystem. Let the observer gain of the i-th subsystem be , For the i-th subsystem, For weight estimation in a radial basis function (RBF) neural network, For radial basis function vectors, For the input vector of the RBF neural network, The known dynamic function of the i-th subsystem;

[0033] right Taking the derivative yields the dynamics of the perturbation estimation error:

[0034] ,

[0035] in Let be the observation error of the i-th subsystem. for The derivative of This is the approximation error.

[0036] The preset time performance function in step 3 is defined as follows:

[0037] For the i-th subsystem, the PTPF is selected as follows:

[0038] ,

[0039] ,

[0040] Where e is the natural constant, , , , For design parameters, , , Define the preset convergence time; define the performance error of the i-th subsystem. ;

[0041] Define the intermediate control quantity of the d-axis and q-axis intermediate control quantity This is used for subsequent control law design.

[0042] The control laws for each subsystem in step 3 are designed as follows:

[0043] Position loop control law (desired speed command) :

[0044] ,

[0045] in, For the desired location trajectory The derivative of For the nonlinear transformation function of the first subsystem, The tracking error of the first subsystem. This is the preset performance function for the first subsystem. for The derivative of For the control gain of the first subsystem, The transformed tracking error of the first subsystem. For the finite-time exponent of the first subsystem, This is the disturbance estimate for the first subsystem;

[0046] Speed ​​subsystem control law (desired q-axis current command) for:

[0047] ,

[0048] in, For rotational inertia, This represents the number of pole pairs of the motor. It is a permanent magnet flux linkage. For the filter speed, for The derivative of The coefficient of friction, The rotor's mechanical speed. For load torque, This is the nonlinear transformation function of the second subsystem. The tracking error of the second subsystem. This is the preset performance function for the second subsystem. for The derivative of For the control gain of the second subsystem, The transformed tracking error of the second subsystem. For the finite-time exponent of the second subsystem, This is the disturbance estimate for the second subsystem;

[0049] d-axis fault-tolerant control law:

[0050] ,

[0051] in, For d-axis control voltage, For d-axis inductance, It is the q-axis inductance. This is the nonlinear transformation function of the third subsystem. The tracking error of the third subsystem. This is the preset performance function for the third subsystem. for The derivative of For the control gain of the third subsystem, The transformed tracking error of the third subsystem. For the finite-time exponent of the third subsystem, This is the disturbance estimate for the third subsystem;

[0052] q-axis fault-tolerant control law:

[0053] ,

[0054] in, This is the lower bound of the q-axis efficiency loss coefficient. For symbolic functions, This is the upper bound of the q-axis fault offset term;

[0055] The filtered outputs of each subsystem are obtained using a first-order filter, where the filter parameters of the i-th subsystem are... is the time constant.

[0056] The fault-tolerant control law in step 4 is designed as follows:

[0057] The final fault-tolerant control input is:

[0058] ,

[0059] ,

[0060] in, This is the lower bound of the d-axis efficiency loss coefficient. This is the lower bound of the q-axis efficiency loss coefficient. This is the upper bound of the d-axis fault offset term. This is the upper bound of the q-axis fault bias term.

[0061] In step 3, the design process of the adaptive law includes:

[0062] For the i-th subsystem:

[0063] ,

[0064] in, for The derivative of the i-th subsystem, the adaptive gain of the i-th subsystem. The correction coefficient of the i-th subsystem The correction item Used to suppress parameter drift caused by external disturbances and ensure the consistent eventual boundedness of the weight estimation in the RBF neural network.

[0065] The finite-time stability proof in step 5 includes:

[0066] Constructing the global Lyapunov function:

[0067] ,

[0068] in, Let Σ be the global Lyapunov function, and let Σ denote the summation operation. For the weight estimation error of the RBF neural network, Let i be the adaptive gain of the i-th subsystem. Let be the filtering error of the i-th subsystem;

[0069] Prove the derivative of V satisfy ,in , For positive integers, Since is a bounded constant, it can be proven that the system is semi-global, practically finite-time stable, and the convergence time satisfies:

[0070] ;

[0071] Where T is the convergence time. Lyapunov function The value at the initial moment, It is a positive constant;

[0072] The asymmetric time-varying state constraints of PMSM include: rotor position constraints. , Let be the time-varying constraint boundary function of the first subsystem. The time-varying upper constraint boundary function for the first subsystem; rotational speed constraint. , The time-varying constraint boundary function for the second subsystem. The time-varying upper constraint boundary function for the second subsystem; d-axis current constraint. , The time-varying constraint boundary function for the third subsystem. The time-varying upper constraint boundary function for the third subsystem; q-axis current constraint. , The time-varying constraint boundary function for the fourth subsystem. The constraint boundary function is the time-varying function of the fourth subsystem; the constraint boundary changes with time.

[0073] This invention also provides a finite-time preset performance fault-tolerant control system for permanent magnet synchronous motors under asymmetric constraints, comprising the following modules:

[0074] The nonlinear transformation module is used to convert a PMSM motor system subject to asymmetric time-varying constraints into an unconstrained system through a nonlinear transformation function;

[0075] The disturbance observation module is used to estimate lumped disturbances, including external load disturbances, parameter perturbations, and equivalent disturbances caused by actuator failures, through a nonlinear disturbance observer.

[0076] The preset performance control module is used to limit the convergence time and overshoot of the tracking error through a preset time performance function, so as to ensure that the tracking error converges within the preset boundary.

[0077] The fault-tolerant control module is used to compensate for actuator failures and jamming faults through the designed fault-tolerant control law, ensuring that preset performance indicators are still met in the event of actuator failure.

[0078] The dynamic surface control module is used to avoid repeated differentiation of the control law by introducing a first-order filter, thereby reducing computational complexity.

[0079] The system is designed directly based on a coupled dynamic model in the dq rotating coordinate system and is used to execute the method described.

[0080] The actuator malfunctions include:

[0081] d-axis efficiency loss coefficient or q-axis efficiency loss coefficient The fault-free condition;

[0082] The failure level of the d-axis is Or the failure level of the q-axis is Partial failure and malfunction situations;

[0083] The failure level of the d-axis is And the d-axis offset fault component Or the failure level of the q-axis is And the q-axis offset fault component The stuck fault situation.

[0084] Beneficial Effects: Compared with existing technologies, this invention transforms a motor system subject to asymmetric time-varying constraints into an unconstrained system by introducing a nonlinear transformation function. This fundamentally overcomes the feasibility limitations and boundary singularity problems of traditional obstacle Lyapunov function methods, freeing controller design from the stringent requirement that the virtual control law must always be within the constraint interval. This significantly expands the degrees of freedom in control design and improves the safety of numerical implementation. The proposed nonlinear transformation framework can uniformly handle state constraints with asymmetric upper and lower bounds and dynamic changes over time, making it suitable for practical engineering conditions with significant asymmetric constraints, such as motor current, speed, and position.

[0085] By integrating finite-time control theory with a preset performance control strategy, this invention ensures that the tracking errors of each subsystem converge to a preset neighborhood within a pre-defined finite time. The convergence time is independent of the system's initial state, and the overshoot and convergence rate of the transient process can be flexibly tuned through performance function parameters, thus achieving quantitative controllability of transient and steady-state performance. Regarding fault-tolerant control, the unified fault-tolerant control law designed in this invention does not rely on real-time diagnosis by fault detection and isolation units. It can automatically activate a compensation mechanism when the actuator experiences performance loss or jammed bias faults. Through the synergistic effect of a disturbance observer and neural adaptive control, it suppresses fault-equivalent disturbances, maintains the preset performance indicators of the system under fault conditions, and significantly improves the reliability and safety of the motor drive system.

[0086] Furthermore, the joint architecture of the nonlinear disturbance observer and the RBF neural network can accurately estimate and compensate for lumped disturbances, including parameter perturbations, external load disturbances, and actuator fault equivalents, effectively enhancing the system's robustness against multi-source uncertainties. The introduction of dynamic surface control technology avoids the computational bloat caused by repeated differentiation of the virtual control law in backstep design, reducing the controller's implementation complexity and facilitating real-time deployment on embedded drive platforms. In summary, this invention achieves an organic unity between asymmetric time-varying constraint satisfaction, finite-time convergence guarantee, actuator fault tolerance, and disturbance robustness, providing effective theoretical support and technical solutions for the safe and reliable operation of permanent magnet synchronous motors in high-end equipment. Attached Figure Description

[0087] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0088] Figure 1 This is a schematic diagram of the PMSM motor system described in an embodiment of the present invention.

[0089] Figure 2 This is a flowchart of the finite-time control method according to an embodiment of the present invention.

[0090] Figure 3 The actual rotor position of this invention and desired rotor position A schematic diagram of the curve.

[0091] Figure 4 The tracking error of this invention and its constraint variables A schematic diagram of the curve.

[0092] Figure 5a The actual d-axis control voltage under fault-free conditions of this invention and d-axis nominal control voltage A schematic diagram of the curve.

[0093] Figure 5b The actual q-axis control voltage under fault-free conditions of this invention and q-axis nominal control voltage A schematic diagram of the curve.

[0094] Figure 6a The actual control voltage of the d-axis under partial failure conditions of the actuator in this invention. and d-axis nominal control voltage A schematic diagram of the curve.

[0095] Figure 6b The actual control voltage of the q-axis under partial fault conditions of the actuator in this invention. and q-axis nominal control voltage A schematic diagram of the curve.

[0096] Figure 7a The actual control voltage of the d-axis when the actuator is stuck is the present invention. and d-axis nominal control voltage A schematic diagram of the curve.

[0097] Figure 7b The actual control voltage of the q-axis when the actuator of this invention is stuck. and q-axis nominal control voltage A schematic diagram of the curve. Detailed Implementation

[0098] This invention provides a finite-time preset performance fault-tolerant control method for permanent magnet synchronous motors under asymmetric constraints, comprising the following steps:

[0099] Step 1: Establish the dynamic equation model of the PMSM motor system in the dq rotating coordinate system:

[0100] ,

[0101] in, These are the stator d-axis current and q-axis current, respectively. The rotor's mechanical speed. For rotor position, These are the stator d-axis voltage input and q-axis voltage input, respectively. These are the d-axis inductance and the q-axis inductance, respectively. For stator resistance, For extreme logarithms, Let J be the magnetic flux linkage of the permanent magnet, J be the moment of inertia, and B be the coefficient of friction. For load torque, The d-axis represents the unknown lumped disturbance. The q-axis lumped perturbation is unknown. The unknown lumped disturbance of the rotational speed loop; dt represents the time derivative.

[0102] like Figure 1 The diagram shown is a schematic of a permanent magnet synchronous motor (PMSM) system according to an embodiment of the present invention. The PMSM is described using a fourth-order state-space model in a direct-axis-quadrature-axis dq rotating coordinate system, including... , , , Four state variables. In the diagram, the ABC three-phase permanent magnet synchronous motor controller receives stator voltage, torque coefficient, rotor position, and rotor speed signals, and outputs d-axis control voltage signals and q-axis control voltage signals; d-axis voltage... q-axis voltage and load torque As the input to the PMSM system model, after being processed by the permanent magnet synchronous motor model, the output rotor position is determined. Rotor speed d-axis current and q-axis current Electromagnetic torque With back electromotive force Generated by a permanent magnet magnetic field source.

[0103] Using d-axis current reference value The vector control strategy, according to claim 1, has state variables. Define control inputs ,in This is the d-axis stator voltage input. The input voltage is the q-axis stator voltage; consider the actuator fault model. ,in This is the efficiency coefficient matrix. The d-axis efficiency loss coefficient. The q-axis efficiency loss coefficient is... This is a bias fault. This represents the d-axis offset fault component. Let the fault component be the q-axis offset. Then, the system dynamic equations under the fault and disturbance effects are:

[0104] ,

[0105] ,

[0106] ,

[0107] in, Let f(x) be the derivative of x, f(x) be the system dynamic function, and g(x) be the input matrix function. For the lumped disturbance of the unknown location ring. The lumped disturbance vector includes external disturbances, parameter perturbations, and fault biases; the state constraints satisfy... It is a time-varying constraint boundary function.

[0108] The system is subject to asymmetric time-varying state constraints as follows:

[0109] ,

[0110] ,

[0111] ,

[0112] ,

[0113] in , It is a time-varying constraint boundary function.

[0114] Step 2: Design of Nonlinear Transformation Function (NTF) and Disturbance Observer (NDO);

[0115] Step 2.1: For the tracking error of the i-th subsystem (i=1,2,3,4), introduce the NTF function:

[0116] ,

[0117] when Time-varying constraint boundary function of the i-th subsystem At that time, the tracking error after the transformation of the i-th subsystem ;when The time-varying upper constraint boundary function of the i-th subsystem hour, Therefore, if If the original tracking error remains bounded, then... Strictly meet the constraints .

[0118] The derivative yields the dynamic error after transformation:

[0119] ,

[0120] in, , , for The derivative of Let i be the transformation gain of the i-th subsystem. for The derivative of For the constraint boundary change rate compensation term of the i-th subsystem, for The derivative of for The derivative of .

[0121] Step 2.2: NDO Design;

[0122] Define the tracking error after transformation of each subsystem and aggregated disturbances This includes external disturbances, coupling uncertainties, and neural network approximation errors.

[0123] Design NDO:

[0124] ,

[0125] in, Let i be the dynamic estimate of the i-th subsystem. Let the observer gain of the i-th subsystem be , For the i-th subsystem, For weight estimation in a radial basis function (RBF) neural network, For radial basis function vectors, The input vector for the radial basis function neural network is... Let be the known dynamic function of the i-th subsystem.

[0126] right Taking the derivative yields the dynamics of the perturbation estimation error:

[0127] ,

[0128] in For observation error, for The derivative of This is the approximation error.

[0129] like Figure 2 The flowchart shown is a finite-time preset performance fault-tolerant control method according to an embodiment of the present invention. Based on nonlinear transformation and dynamic surface control (DSC) technology, the virtual control law, the actual control law, the first-order filter and the disturbance observer are recursively designed, and the finite-time stability of the closed-loop system is verified by constructing a Lyapunov function.

[0130] Step 3: Design the controller; including the following steps:

[0131] Step 3.1: Design the preset performance function PTPF;

[0132] For the i-th subsystem, the PTPF is selected as follows:

[0133] ,

[0134] ,

[0135] Where e is the natural constant, , , , For design parameters, , , Define the preset convergence time; define the performance error. ;

[0136] Define the intermediate control quantity of the d-axis and q-axis intermediate control quantity This is used for subsequent control law design.

[0137] Step 3.2: Design the position loop control law;

[0138] Define position tracking error , This represents the actual rotor position of the first subsystem. The tracking error of the first transformed subsystem for the desired position trajectory. Differentiation yields :

[0139] ,

[0140] in, The transformation gain of the first subsystem. yes The derivative of This is the compensation term for the rate of change of the constraint boundary of the first subsystem.

[0141] By using an RBF neural network to approximate an unknown nonlinear function, a position loop control law (desired speed command) is designed. :

[0142] ,

[0143] in, For the control gain of the first subsystem, For the finite-time exponent of the first subsystem, , To approximate unknown nonlinearities using RBF neural networks, The transformed tracking error of the first subsystem. This is the output of the disturbance observer.

[0144] To avoid By repeatedly differentiating, a first-order filter is introduced:

[0145] ,

[0146] ,

[0147] in, Let be the time constant of the first-order filter of the first subsystem. The desired rotational speed after filtering. for The derivative of .

[0148] Define the filtering error of the first subsystem Its dynamics are as follows:

[0149] ,

[0150] in, for derivative, It is a continuous and bounded function.

[0151] Design Adaptive Law:

[0152] ,

[0153] in, For the first radial basis function (RBF) neural network weight estimation, for The derivative of the first subsystem, the adaptive gain of the first subsystem. The correction coefficient of the first subsystem The correction item Used to suppress parameter drift caused by external disturbances and ensure the consistent eventual boundedness of the weight estimation in the RBF neural network.

[0154] Construct the first Lyapunov function:

[0155] ,

[0156] in, The weight estimation error of the RBF neural network in the first subsystem.

[0157] right Differentiating and substituting into the control law, we can obtain the following using Young's inequality:

[0158] ,

[0159] in, The positive convergence coefficients of the first subsystem are... is the bounded compensation constant of the first subsystem.

[0160] Step 3.3: Design the speed loop control law;

[0161] Define speed tracking error Tracking error of the second transformed subsystem Differentiation yields :

[0162] ,

[0163] in, The transformation gain of the second subsystem. This is the compensation term for the rate of change of the constraint boundary of the second subsystem.

[0164] d-axis current reference value Under the control strategy, , Coupling terms are incorporated into the lumped disturbance, and the unknown terms are approximated using an RBF neural network to design the desired q-axis current command. :

[0165] ,

[0166] in, For the control gain of the second subsystem, For the finite-time exponent of the second subsystem, , Used to compensate for lumped disturbances in the speed loop and ensure the stability of the recursive design.

[0167] Introduce a first-order filter:

[0168] ,

[0169] in, The time constant of the first-order filter in the second subsystem is... This represents the desired q-axis current after filtering.

[0170] Define the filtering error of the second subsystem. Construct the second Lyapunov function and similarly prove its stability.

[0171] Step 3.4: Design of d-axis current loop control law

[0172] Define d-axis current tracking error (in Tracking error of the third transformed subsystem. Differentiation yields :

[0173] ,

[0174] in, The transformation gain of the third subsystem. This is the compensation term for the rate of change of the constraint boundary of the third subsystem.

[0175] Design d-axis intermediate control quantity :

[0176] ;

[0177] in, For the control gain of the third subsystem, For the finite-time exponent of the third subsystem, , For the RBF neural network weight estimation of the third subsystem, This is the RBF vector of the third subsystem. This is the input vector of the RBF neural network for the third subsystem. This is the disturbance estimate for the third subsystem.

[0178] Step 3.5: Design the q-axis current loop and fault-tolerant control law;

[0179] Define q-axis current tracking error Tracking error of the fourth transformed subsystem Differentiation yields :

[0180] ,

[0181] in, The transformation gain of the fourth subsystem. This is the compensation term for the rate of change of the constraint boundary of the fourth subsystem.

[0182] Design q-axis intermediate control quantity :

[0183] ,

[0184] in, For the control gain of the 4th subsystem, For the finite-time exponent of the fourth subsystem, , For the RBF neural network weight estimation of the fourth subsystem, This is the RBF vector of the 4th subsystem. This is the input vector of the RBF neural network for the fourth subsystem. This is the disturbance estimate for the fourth subsystem.

[0185] The final fault-tolerant control input is:

[0186] ,

[0187] in, This is the lower bound of the d-axis efficiency loss coefficient. This is the lower bound of the q-axis efficiency loss coefficient. This is the upper bound of the d-axis fault offset term. This is the upper bound of the q-axis fault offset term. It is a symbolic function.

[0188] This control law structure has the following characteristics: when the actuator fails, i.e. or When, in the denominator and To ensure that the control gain automatically increases to compensate for performance loss; when a jamming fault occurs on the d-axis, i.e. and Or the q-axis may jam. and At that time, the perturbation observer and the neural adaptive mechanism work together to compensate for the bias perturbation.

[0189] Step 4: Analyze stability;

[0190] Constructing the global Lyapunov function:

[0191] ,

[0192] Taking the derivative with respect to V and combining it with the design of the four-step subsystem, we get:

[0193] ,

[0194] in For positive integers, are bounded constants. Let be the weight estimation error of the RBF neural network for the i-th subsystem.

[0195] According to the finite-time stability criterion, when the selected parameters satisfy... At that time, there were:

[0196] ,

[0197] in, For positive integers, Let V be the value of the global Lyapunov function at the initial time.

[0198] This proves that the closed-loop system is semi-global, practically finite-time stable, and the convergence time T satisfies:

[0199] ;

[0200] Step 5: Performance Guarantee and Constraint Satisfaction;

[0201] According to the boundedness of NTF, when When bounded, the original tracking error Strictly meet That is, the position, rotational speed, d-axis current, and q-axis current are all within the asymmetric time-varying constraint boundary.

[0202] Based on the properties of PTPF, the tracking error of each subsystem within a preset time... The tracking error converges to a preset neighborhood. The original tracking error and the transformed error satisfy the Lipschitz relation, therefore the tracking error for all states meets the preset performance index.

[0203] Step 6: Set simulation verification parameters;

[0204] System parameters are set to stator resistance. d-axis inductance H-axis and q-axis inductance H, permanent magnet flux Wb, polar logarithm Moment of inertia J = 0.01 kg·m², coefficient of viscous friction B = 0.01 N·m·s / rad, load torque N·m.

[0205] The state constraints are set to an asymmetric time-varying form, and the position constraints satisfy... rad; speed constraint boundary is dynamically adjusted by performance function; d-axis current constraint A; The q-axis current constraint boundary is dynamically adjusted by the performance function.

[0206] The controller parameter is the position loop gain. Speed ​​loop gain d-axis current loop gain q-axis current loop gain DSC filter time constant , , , Correction coefficient NDO observer gain Disturbance estimation limit RBF adaptive gain Weighted amplitude limit PPC transformation error limiting Control voltage limiting V, V.

[0207] Preset performance function parameters: Location layer , , ; velocity layer , , , d-axis current layer , , , q-axis current layer , , , .

[0208] RBF neural network settings: number of nodes in each subsystem l=11, width b=1, and center points are evenly distributed in [-1.5,1.5], [-2.5,2.5], [-2,2] and [-5,5] respectively.

[0209] Simulation scenario:

[0210] Scenario 1 (Normal Operation): Expected Location Trajectory rad, initial position rad, initial rotational speed rad / s, initial current A, A. The results show that the position, rotational speed, d-axis current, and q-axis current always satisfy the asymmetric constraints, and the position tracking error converges within the preset boundaries.

[0211] Scenario 2 (LOE Fault): Inject a performance loss fault at t=10s, with a bias term of κ=0.5 (50% performance loss). The controller automatically increases the nominal control voltage to compensate for performance loss, while the position tracking error remains within the preset performance limits.

[0212] Scenario 3 (LIP Failure): A stuck failure is injected at t=10s. Bias fault item V. The fault-tolerant control law compensates for fault biases through a disturbance observer and a neural adaptive mechanism, ensuring the system remains stable and its state does not violate constraints.

[0213] To verify the effectiveness of the control method described in this invention, the following results were obtained through simulation experiments: Figure 3 As shown, the actual rotor position of the present invention With the desired rotor position The curve shows that the system has good position tracking performance; such as Figure 4 As shown, this represents the tracking error of the present invention. and its constraint variables The curve shows that the tracking error remains within the preset performance boundaries; for example... Figure 5a and Figure 5bThe figures show the actual control voltage of the d-axis under fault-free conditions. and nominal control voltage and q-axis actual control voltage and nominal control voltage The curve; such as Figure 6a and Figure 6b The figures show the actual control voltage of the d-axis under partial actuator failure conditions. and nominal control voltage and the actual control voltage of the q-axis and nominal control voltage The curve shows that the controller automatically increases the nominal control voltage to compensate for performance loss; such as Figure 7a and Figure 7b The figures show the actual control voltage of the d-axis under actuator jamming fault conditions. and nominal control voltage and the actual control voltage of the q-axis and nominal control voltage The curves show that the fault-tolerant control law compensates for fault biases through a disturbance observer and a neural adaptive mechanism. The simulation results verify the effectiveness and reliability of this invention under asymmetric time-varying constraints, finite-time convergence, and actuator fault conditions.

[0214] This invention provides a finite-time preset performance fault-tolerant control method and system for permanent magnet synchronous motors under asymmetric constraints. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A finite-time preset performance fault-tolerant control method for a permanent magnet synchronous motor under asymmetric constraints, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the permanent magnet synchronous motor (PMSM) in the direct-axis-quadrature-axis dq rotating coordinate system, and define the state variables. ,in For rotor position, The rotor's mechanical speed. The stator current is the d-axis current. The current is the q-axis stator current; the dynamic model considers asymmetric time-varying state constraints and unknown lumped disturbance vectors. The components are respectively , , , And actuator failure, the actuator failure model is represented as Actual input voltage The nominal control input is the voltage actually applied to the motor stator after a fault. The ideal control voltage output by the controller. This is the efficiency loss coefficient matrix. For the biased fault term, the state constraints are time-varying and asymmetric. , Let i be the state variable of the i-th subsystem. Let be the time-varying constraint boundary function of the i-th subsystem. Let be the time-varying upper constraint boundary function of the i-th subsystem; Step 2: The original system subject to asymmetric constraints is transformed into an unconstrained system using the nonlinear transformation function NTF. A nonlinear disturbance observer is designed to estimate the lumped disturbance, including external disturbances, neural network approximation errors, and fault terms. The nonlinear transformation function of the i-th subsystem... satisfy ,in Let be the tracking error of the i-th subsystem, i=1,2,3,4, which correspond to the position loop, speed loop, d-axis current loop and q-axis current loop respectively; The transformed tracking error; Step 3: Introduce the preset time performance function PTPF to define the preset performance boundary of the tracking error of the i-th subsystem. Combine coordinate transformation and dynamic surface control (DSC) technology to design control laws and adaptive laws for the position loop, speed loop, d-axis current loop, and q-axis current loop, respectively. The control law design includes finite-time convergence terms. and disturbance compensation term, where the control gain of the i-th subsystem To control the gain, the transformed tracking error of the i-th subsystem The tracking error after transformation is the finite-time exponent of the i-th subsystem. For finite time index, For the preset performance function, ; Step 4: Design a fault-tolerant control law to compensate for actuator failures and jamming faults. By introducing a fault compensation term, ensure that the system still meets the preset performance indicators when actuator failures occur. Step 5: Prove the finite-time stability of the closed-loop system based on Lyapunov stability theory. Prove that the designed controller can guarantee that all closed-loop signals converge within a finite time, the motor state always satisfies the asymmetric time-varying constraint and does not exceed the preset boundary, and the tracking error meets the preset performance index within a preset time.

2. The method according to claim 1, characterized in that, Step 1 includes: Establish a dynamic model of the PMSM motor in the dq rotating coordinate system: ， in, These are the stator d-axis current and q-axis current, respectively. The rotor's mechanical speed. For rotor position, These are the stator d-axis voltage input and q-axis voltage input, respectively. These are the d-axis inductance and the q-axis inductance, respectively. For stator resistance, For extreme logarithms, Let J be the magnetic flux linkage of the permanent magnet, J be the moment of inertia, and B be the coefficient of friction. For load torque, The d-axis represents the unknown lumped disturbance. The q-axis lumped perturbation is unknown. The unknown lumped disturbance of the rotational speed loop; dt represents the time derivative; Using d-axis current reference value The vector control strategy obtains the state variables. Define control input ,in This is the d-axis stator voltage input. The input voltage is the q-axis stator voltage; consider the actuator fault model. ,in This is the efficiency coefficient matrix. The d-axis efficiency loss coefficient. The q-axis efficiency loss coefficient is... This is a bias fault. This represents the d-axis offset fault component. Let be the q-axis offset fault component; then the system dynamic equations under the effects of fault and disturbance are: ， ， ， in, for The derivative of For system dynamic functions, For input matrix functions, For the lumped disturbance of the unknown location ring. The lumped disturbance vector includes external disturbances, parameter perturbations, and fault biases; the state constraints satisfy... It is a time-varying constraint boundary function.

3. The method according to claim 2, characterized in that, The specific construction process of the nonlinear transformation function in step 2 includes: For the tracking error of the i-th subsystem Introduce a nonlinear transformation function: ， when Time-varying constraint boundary function of the i-th subsystem hour, ;when The time-varying upper constraint boundary function of the i-th subsystem hour, Therefore, if If the original tracking error remains bounded, then... Strictly meet the constraints ;symbol Indicates approaching; The derivative yields the dynamic error after transformation: ， in , , for The derivative of Let i be the transformation gain of the i-th subsystem. for The derivative of For the constraint boundary change rate compensation term of the i-th subsystem, for The derivative of for The derivative of .

4. The method according to claim 3, characterized in that, The nonlinear perturbation observer (NDO) design process in step 2 includes: For the lumped disturbance of the i-th subsystem This includes external disturbances, radial basis function (RBF) neural network approximation errors, and fault equivalent terms. The NDO is designed as follows: ， in, Let i be the disturbance estimate of the i-th subsystem. Let the observer gain of the i-th subsystem be , For the i-th subsystem, For weight estimation in a radial basis function (RBF) neural network, For radial basis function vectors, For the input vector of the RBF neural network, The known dynamic function of the i-th subsystem; right Taking the derivative yields the dynamics of the perturbation estimation error: ， in Let be the observation error of the i-th subsystem. for The derivative of This is the approximation error.

5. The method according to claim 4, characterized in that, The preset time performance function in step 3 is defined as follows: For the i-th subsystem, the PTPF is selected as follows: ， ， Where e is the natural constant, , , , For design parameters, , , Define the preset convergence time; define the performance error of the i-th subsystem. ; Define the intermediate control quantity of the d-axis and q-axis intermediate control quantity This is used for subsequent control law design.

6. The method according to claim 5, characterized in that, The control laws for each subsystem in step 3 are designed as follows: Position loop control law : ， in, For the desired location trajectory The derivative of For the nonlinear transformation function of the first subsystem, The tracking error of the first subsystem. This is the preset performance function for the first subsystem. for The derivative of For the control gain of the first subsystem, The transformed tracking error of the first subsystem. For the finite-time exponent of the first subsystem, This is the disturbance estimate for the first subsystem; Speed ​​subsystem control law for: ， in, For rotational inertia, This represents the number of pole pairs of the motor. It is a permanent magnet flux linkage. For the filter speed, for The derivative of The coefficient of friction, The rotor's mechanical speed. For load torque, This is the nonlinear transformation function of the second subsystem. The tracking error of the second subsystem. This is the preset performance function for the second subsystem. for The derivative of For the control gain of the second subsystem, The transformed tracking error of the second subsystem. For the finite-time exponent of the second subsystem, This is the disturbance estimate for the second subsystem; d-axis fault-tolerant control law: ， in, For d-axis control voltage, For d-axis inductance, It is the q-axis inductance. This is the nonlinear transformation function of the third subsystem. The tracking error of the third subsystem. This is the preset performance function for the third subsystem. for The derivative of For the control gain of the third subsystem, The transformed tracking error of the third subsystem. For the finite-time exponent of the third subsystem, This is the disturbance estimate for the third subsystem; q-axis fault-tolerant control law: ， in, This is the lower bound of the q-axis efficiency loss coefficient. For symbolic functions, This is the upper bound of the q-axis fault offset term; The filtered outputs of each subsystem are obtained using a first-order filter, where the filter parameters of the i-th subsystem are... is the time constant.

7. The method according to claim 6, characterized in that, The fault-tolerant control law in step 4 is designed as follows: The final fault-tolerant control input is: ， ， in, This is the lower bound of the d-axis efficiency loss coefficient. This is the lower bound of the q-axis efficiency loss coefficient. This is the upper bound of the d-axis fault offset term. This is the upper bound of the q-axis fault bias term.

8. The method according to claim 6, characterized in that, In step 3, the design process of the adaptive law includes: For the i-th subsystem: ， in, for The derivative of the i-th subsystem, the adaptive gain of the i-th subsystem. The correction coefficient of the i-th subsystem .

9. The method according to claim 8, characterized in that, The finite-time stability proof in step 5 includes: Constructing the global Lyapunov function: ， in, Let Σ be the global Lyapunov function, and let Σ denote the summation operation. For the weight estimation error of the RBF neural network, Let i be the adaptive gain of the i-th subsystem. Let be the filtering error of the i-th subsystem; Prove the derivative of V satisfy ,in , For positive integers, Since is a bounded constant, it can be proven that the system is semi-global, practically finite-time stable, and the convergence time satisfies: ； Where T is the convergence time. Lyapunov function The value at the initial moment, It is a positive constant; The asymmetric time-varying state constraints of PMSM include: rotor position constraints. , Let be the time-varying constraint boundary function of the first subsystem. The time-varying upper constraint boundary function for the first subsystem; rotational speed constraint. , The time-varying constraint boundary function for the second subsystem. The time-varying upper constraint boundary function for the second subsystem; d-axis current constraint. , The time-varying constraint boundary function for the third subsystem. The time-varying upper constraint boundary function for the third subsystem; q-axis current constraint. , The time-varying constraint boundary function for the fourth subsystem. The constraint boundary function is the time-varying function of the fourth subsystem; the constraint boundary changes with time.

10. A finite-time preset performance fault-tolerant control system for a permanent magnet synchronous motor under asymmetric constraints, characterized in that, Includes the following modules: The nonlinear transformation module is used to convert a PMSM motor system subject to asymmetric time-varying constraints into an unconstrained system through a nonlinear transformation function; The disturbance observation module is used to estimate lumped disturbances, including external load disturbances, parameter perturbations, and equivalent disturbances caused by actuator failures, through a nonlinear disturbance observer. The preset performance control module is used to limit the convergence time and overshoot of the tracking error through a preset time performance function, so as to ensure that the tracking error converges within the preset boundary. The fault-tolerant control module is used to compensate for actuator failures and jamming faults through the designed fault-tolerant control law, ensuring that preset performance indicators are still met in the event of actuator failure. The dynamic surface control module is used to avoid repeated differentiation of the control law by introducing a first-order filter, thereby reducing computational complexity. The system is designed directly based on a coupled dynamic model in the dq rotating coordinate system and is used to execute the method as described in any one of claims 1 to 9.

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