Control and parameter intelligent optimization method of impact-resistant high-precision pmsm feeding servo system

Abstract

This invention relates to the field of motor control technology, specifically a method for intelligent optimization of control and parameters of a high-precision, shock-resistant PMSM feed servo system. The method includes the following steps: S1, establishing the physical structure and dynamic model of the PMSM-driven feed system; S2, designing a variable gain fractional-order superspiral sliding mode controller (VGFSTSMC) to achieve finite-time convergence of position tracking error and suppress system jitter by dynamically adjusting the control gain coefficient; S3, designing an adaptive sliding mode disturbance observer (ASMDO) to estimate and compensate for unknown disturbances in real time through adaptive gain adjustment and integral sliding surface; S4, identifying the Stribeck friction model of the system based on the least squares method and using it as the input to the current loop as a friction feedforward compensation (FFC) to reduce system disturbance uncertainty; S5, dynamically optimizing the control parameters of VGFSTSMC and ASMDO using an optimization algorithm to minimize the root mean square error (RMSE) and maximum instantaneous error of the position tracking error; S6, combining VGFSTSMC, ASMDO, FFC, and the optimization algorithm to drive the PMSM to achieve high-precision position control.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, specifically to a control and intelligent parameter optimization method for a high-precision, shock-resistant PMSM feed servo system. Background Technology

[0002] As core equipment in high-end precision manufacturing, Computer Numerical Control (CNC) machine tools directly impact the upper limit of machining accuracy in critical fields such as aerospace and optical devices due to the performance of their feed systems. While the mainstream solution of permanent magnet synchronous motor (PMSM) drive combined with ball screw transmission offers high reliability, it exhibits serious shortcomings when dealing with sudden impact disturbances: millisecond-level mechanical shocks (such as tool breakage) induce 200-800Hz high-frequency resonance through the ball screw, causing back EMF distortion in the coupled motor and resulting in current runaway. Traditional PI controllers, due to response delays, cannot suppress instantaneous displacement deviations. Furthermore, the low-speed stick-slip oscillations caused by nonlinear friction and model mismatch due to mechanical wear lead to a continuous deterioration in positioning accuracy. Currently, there is an urgent need for a highly robust control method capable of real-time compensation for impact disturbances and synchronous suppression of multi-source interference to meet the stringent requirements of micron-level precision machining.

[0003] Existing control schemes generally face the following bottlenecks: Traditional proportional-integral (PI) control relies on accurate models and is sensitive to dynamic disturbances, easily generating steady-state errors; Sliding mode control (SMC), although robust, causes high-frequency chattering due to fixed-gain switching terms, exacerbating mechanical wear; Improved methods such as the superspiral algorithm (STA) suppress chattering through integral terms, but cause small oscillations near stationary targets due to gain redundancy, and it is difficult to balance convergence speed and disturbance rejection capability; Disturbance observation techniques (such as extended state observers) have lag in real-time estimation of complex disturbances, especially during the frictional abrupt change in the startup phase, where error accumulation is significant; Friction feedforward compensation relies on high-precision modeling, but existing piecewise models are not adaptable to nonlinear characteristics and cannot cope with unknown external disturbances.

[0004] To address the aforementioned issues, existing research attempts to improve performance through multimodal control fusion and algorithm optimization, but limitations remain. Fuzzy adaptive control relies on expert experience to set rules, resulting in weak generalization ability; fractional sliding mode, while improving convergence smoothness, offers limited improvement in system robustness; parameter optimization often employs the standard particle swarm optimization (PSO) algorithm, which is prone to getting trapped in local optima and lacks deep coupling with the controller's dynamic characteristics. Furthermore, under high-speed and high-load conditions, the system's nonlinear characteristics intensify, making it difficult for traditional control strategies to balance dynamic response and disturbance rejection capabilities.

[0005] Therefore, how to provide a high-precision and robust servo control method and parameter optimization method for PMSM feed systems is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a high-precision and robust servo control method for a PMSM-driven feed system. By using multiphysics modeling, adaptive disturbance observation, and parameter optimization algorithms, this method solves the problems of difficult jitter suppression, delayed disturbance compensation, and low parameter tuning efficiency in existing technologies.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for intelligent optimization of control and parameters of a shock-resistant, high-precision PMSM feed servo system, comprising the following steps:

[0009] S1. By combining the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism and the closed-loop control model of the grating ruler feedback position, a physical structure and dynamic model of the PMSM drive feed system is established.

[0010] S2. Based on the novel variable gain superspiral reaching law and fractional sliding mode function, a variable gain fractional superspiral sliding mode controller VGFSTSMC is designed. By dynamically adjusting the control gain coefficient, the position tracking error is converged in finite time and the system jitter is suppressed.

[0011] S3. Design an adaptive sliding mode disturbance observer (ASMDO) to estimate and compensate for unknown disturbances in real time through adaptive gain adjustment and integral sliding surface.

[0012] S4. The Stribeck friction model of the system is identified based on the least squares method and used as the input of the friction feedforward compensation FFC to the current loop to reduce the uncertainty of system disturbance.

[0013] S5. The control parameters of VGFSTSMC and ASMDO are dynamically tuned using an optimization algorithm to minimize the root mean square error (RMSE) and the maximum instantaneous error of the position tracking error.

[0014] S6. Combine VGFSTSMC, ASMDO, FFC with optimization algorithms to drive PMSM to achieve high-precision position control.

[0015] Furthermore, step S1 is detailed as follows:

[0016] PMSM driven feed system in dq The electromagnetic torque equation in the coordinate system is expressed as:

[0017]

[0018] In the formula, It is magnetic torque; It is the torque constant; This refers to the q-axis stator current.

[0019] Ignoring the elastic deformation of the motor shaft, coupling, lead screw, nut, and other components, and assuming that the transmission chain of the PMSM drive feed system is rigid, the axial position of the worktable... equal to the mechanical angle of the motor shaft The axial equivalent displacement, the dynamic equation of the PMSM-driven feed system is expressed as:

[0020]

[0021] in, The axial movement speed of the feed system's table; This refers to the ball screw transmission ratio. For the lead screw; This is the system's equivalent moment of inertia. It is the equivalent viscous damping coefficient; For disturbance torque;

[0022] Assuming the derivative of the equivalent disturbance torque of the motor shaft is zero, the final dynamic equation of the PMSM drive feed system is expressed as:

[0023] .

[0024] Furthermore, in step S2, the design of the variable gain fractional-order superspiral sliding mode controller VGFSTSMC is as follows:

[0025] Using differential operators:

[0026] ,

[0027] In the formula, It is a time-varying objective function, representing a physical quantity that requires fractional derivatives or integration. It is the time independent variable representing the current moment. It is a temporary variable in integration operations and a time stamp of a past moment; C The domain representing the function used for calculus computation; , which is the fractional order;

[0028] Define the position error of the system noise signal and speed error ,in, It is the target location. It is the target speed. This is the actual axial position of the worktable. This is the actual speed of the workbench;

[0029] Design a fractional-order PID sliding surface It is expressed as follows:

[0030]

[0031] In the formula, are positive weighting coefficients and ; For fractional calculus, ;

[0032] The variable gain superspiral reaching law of VGFSTSMC is expressed as follows:

[0033]

[0034] In the formula, the variable gain coefficient and The expression is as follows:

[0035]

[0036] In the formula, ; The basic gain coefficient; The gain is a sensitivity parameter to the sliding surface. This is the parameter for adjusting the rate of gain change; It is a natural constant;

[0037] and It is a nonlinear stable term that simultaneously satisfies Specifically, it is expressed as follows:

[0038]

[0039] In the formula, It is a sliding surface; It is a continuous variable exponential coefficient, which accelerates the convergence of the system and keeps the changes in the control value smooth; It is a variable exponential adjustment parameter; It is a natural constant; Used to adjust the ratio of different exponential terms to fine-tune the integration step size;

[0040] For sliding surfaces The first derivative of the formula is as follows:

[0041]

[0042] Substitute the dynamic equations of the PMSM-driven feed system into the above equation and solve both sides of the equation. The derivative of order 1, after simplification, yields:

[0043]

[0044] In the formula, For disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current.

[0045] Ignoring unknown lumped disturbance torque Substituting the variable gain superspiral reaching law, we obtain the control law of the variable gain fractional superspiral sliding mode controller as follows:

[0046]

[0047] In the formula, Let be the target q-axis current of the proposed control scheme.

[0048] Furthermore, in step 3, the adaptive sliding mode perturbation observer (ASMDO) is designed as follows:

[0049] At the speed of the feed system table and disturbance torque For the observed values, design the following perturbation observer:

[0050]

[0051] in, It is the observed value of the axial movement speed of the feed system's table; It is the observed value of the unknown disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current. It is a correction function used to correct velocity observations; It is the perturbation observer gain; It is a velocity observation error;

[0052] Define velocity observation error Disturbance torque observation error ,get:

[0053]

[0054] Design an integral sliding surface as follows:

[0055]

[0056] In the formula, This is the integral gain, used to adjust and analyze the intensity of the effect;

[0057] The adaptive reaching law of the design is as follows:

[0058]

[0059] In the formula, and It is a positive gain coefficient; It is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the reaching rate. Exponential coefficient Follow Dynamic changes are made so that the observer can always maintain a stable convergence rate; This is the upper limit of the perturbation of the synovial observer, satisfying , It is an adaptive perturbation suppression term. It is a constant gain coefficient;

[0060] Substituting the adaptive reaching law formula of the design into the sliding surface formula of the observer Ignoring the disturbance term in the first derivative, we obtain the control law for the adaptive sliding membrane disturbance observer, as follows:

[0061] .

[0062] Furthermore, step S4 is detailed as follows:

[0063] Design the Stribeck friction model:

[0064]

[0065] In the formula, It refers to the motor speed; It is a natural constant; It is the Stribeck frictional resistance torque. and It is the Coulomb frictional resistance torque in the positive and negative directions. and It is the maximum static friction resistance torque in both the positive and negative motion directions; and It is the equivalent viscous damping coefficient in the positive and negative motion directions; and It is the Stribeck velocity constant in the positive and negative directions of motion;

[0066] The method for identifying relevant parameters of the Stribeck friction model is as follows:

[0067] When the PMSM-driven feed system is in a state of no-load uniform motion, the magnetic torque Used only to counteract Stribeck frictional torque A servo driver is used to control the motor to move at a constant speed, and the q-axis stator current is read. Then, the magnetic torque is calculated using the host computer software. ;Magnetic moment Approximate to Stribeck frictional resistance torque Measure the speed of multiple motors Stribeck frictional resistance torque The experimental data were fitted to the Stribeck friction model using the cftool toolbox in Matlab. The least squares method was used as the fitting algorithm to identify the Stribeck friction model curve.

[0068] definition The unknown disturbance torque of the feed system other than nonlinear friction, and the friction torque Composition of disturbance torque , For its observed values, the adaptive sliding mode perturbation observer is modified as follows:

[0069]

[0070] and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is... for:

[0071] .

[0072] Furthermore, step S5 is detailed as follows:

[0073] S51. Construct VGFSTSMC and ASMDO, and determine the variables to be optimized for each controller. The variables to be optimized are determined to be sliding surfaces. Positive weighting coefficients in The base gain coefficient in VGFSTSMC and integral gain ;

[0074] S52. Determine the search range of the variable to be optimized by trial and error;

[0075] S53. Using a novel and improved particle swarm optimization algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized sequentially.

[0076] S54. Under the condition that the control system module is working normally, optimize and obtain the control parameters of VGFSTSMC and ASMDO.

[0077] Furthermore, step S53 is as follows:

[0078] S531. Initialize the basic parameters of the new improved particle swarm algorithm;

[0079] S532. Initialize the position and velocity of the particles using the improved Sine chaotic mapping formula;

[0080] S533. Select the time-weighted absolute error integral index as the fitness function of the novel improved particle swarm algorithm;

[0081] S534. Calculate the fitness value of the particles;

[0082] S535. Compare the fitness values ​​of each generation of particles and record the individual best position of each particle and the overall best position of the entire swarm.

[0083] S536. Iteratively update the particles using the velocity update formula and the improved position update formula;

[0084] S537. Determine if a particle is trapped in a local optimum;

[0085] S538. Determine if the termination condition is met: If the current iteration count has reached the maximum iteration count, the algorithm ends and outputs the parameters; otherwise, proceed to step S534.

[0086] Further, in step S532, the improved Sine chaotic mapping formula is as follows:

[0087]

[0088] In the formula, It is the first-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; It is the second-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; control parameter Let be any real number; This is the modulo operation; Iterative chaotic sequence values ​​with values ​​in the range [-1, 1].

[0089] Furthermore, in step S536, the velocity update formula and the improved position update formula are as follows:

[0090]

[0091] In the formula, For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; Inertial weight; and It is the acceleration factor; and A random number within the range [0,1]; For the first Each particle undergoes The best individual particle in history after the next iteration; For the entire particle swarm to experience The optimal particle in the population after the iteration; A random number within the range [0,1]; These are random numbers that follow a Gaussian distribution. It is a variable factor;

[0092] and The formulas are as follows:

[0093]

[0094] In the formula, It follows a Gaussian distribution. Standard deviation; It is a random number within the range [-1.5, 1.5]. It is any number in the range [0,1]. The root mean square error of the fitness function; This represents the number of iterations. It was through After the nth iteration The individual historical best value of each particle; It is the average of the historical best values ​​of the current group's individuals.

[0095] Furthermore, step S537 is as follows:

[0096] If the optimal individual fitness value remains unchanged after 10% of the total number of iterations, it indicates that the particle has fallen into a local optimum. In this case, a random number in the range [0,1] is introduced in the next iteration. ;when If the particle's velocity is not updated, the particle is re-initialized using the improved Sine chaotic mapping formula, while the remaining particles are updated using the velocity update formula; otherwise, the next step is executed.

[0097] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0098] 1. This invention uses a physical structure and dynamic model that deeply integrates the dynamic model of a permanent magnet synchronous motor, the mechanical kinematic model of a ball screw, and the closed-loop control model of a grating ruler feedback position. This model can achieve collaborative modeling of electromagnetic characteristics, mechanical transmission chain dynamic characteristics, and position measurement feedback characteristics. Compared with traditional single-physics modeling methods, this method can significantly improve model accuracy, provide a more accurate dynamic benchmark for controller design and disturbance compensation, and significantly reduce tracking errors caused by model mismatch.

[0099] 2. This invention designs a variable gain fractional-order superspiral sliding mode control (VGFSTSMC), proposing a variable gain reaching law based on the hyperbolic tangent function replacing the sign function, achieving finite-time convergence of position tracking error (convergence time reduced to 1 / 3 of traditional sliding mode control). Furthermore, through a gain adaptive adjustment mechanism, it suppresses high-frequency chattering while considering dynamic response speed, solving the high-frequency oscillation problem near the stationary target position in the traditional superspiral algorithm (STA).

[0100] 3. This invention designs an Adaptive Sliding Mode Disturbance Observer (ASMDO) and a composite disturbance compensation. An integral sliding surface observer with nonlinear adaptive gain is designed, and rapid convergence of the disturbance estimation error is achieved by dynamically adjusting the exponential term. Combined with feedforward compensation based on the piecewise Stribeck friction model, a composite disturbance suppression architecture of "feedforward compensation + real-time observation" is formed, significantly reducing the compensation delay for unknown impact disturbances.

[0101] 4. This invention employs an improved Sine chaotic mapping initialization particle swarm optimization algorithm, combined with a dynamic mutation strategy, to overcome the bottleneck of traditional particle swarm optimization (PSO) algorithms easily getting trapped in local optima, effectively improving global search efficiency. By guiding the dynamic tuning of controller parameters through the ITAE index, it achieves collaborative optimization of VGFSTSMC and ASMDO parameters, reducing the workload of manual parameter tuning, and significantly enhancing the robustness of parameter combinations. Attached Figure Description

[0102] Figure 1 This is a flowchart of the intelligent optimization method for control parameters according to the present invention.

[0103] Figure 2 This is a schematic diagram of the experimental platform for the drive feed system of the present invention.

[0104] Figure 3This is a graph of the segmented Stribeck friction model of the present invention.

[0105] Figure 4 This is a schematic diagram of the composite controller structure of the present invention.

[0106] Figure 5 The reference trajectory curve is shown in the experiment for this invention.

[0107] Figure 6 This is a diagram showing the experimental results of the position tracking of the present invention under impact disturbance conditions. Detailed Implementation

[0108] 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 a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0109] A permanent magnet synchronous motor (PMSM) feed servo system includes an actuator module and a control system module. The actuator module includes the PMSM, ball screw, and worktable; the control system module includes a host computer, industrial control board, and motor drive board. For example... Figure 2 As shown, the permanent magnet synchronous motor (PMSM) is rigidly connected to the ball screw via a coupling. The ball screw nut drives the worktable carrying the workpiece to move linearly along the guide rail. A grating ruler is installed parallel to the side of the worktable to detect its actual position in real time. The control system is based on the STM32F407 industrial control board. The host computer sends reference trajectory commands, and the industrial control board calculates the control quantity based on the position feedback signal of the grating ruler and outputs a PWM signal to the motor drive board. The motor drive board converts the DC power supply into three-phase AC power to drive the permanent magnet synchronous motor to rotate, forming a closed loop of "command input-drive control-position feedback".

[0110] Based on the aforementioned PMSM feed servo system, an impact disturbance device is established on the right side of the worktable. The impact disturbance device transmits the impact of the falling mass block to the worktable through a rope-pulley mechanism to simulate sudden impact interference (such as tool breakage) during machining, in order to verify the system's anti-disturbance performance.

[0111] like Figure 1 As shown, the control and parameter intelligent optimization method for a shock-resistant high-precision PMSM feed servo system includes the following steps:

[0112] S1. By combining the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism and the closed-loop control model of the grating ruler feedback position, a physical structure and dynamic model of the PMSM drive feed system is established.

[0113] S2. Based on the novel variable gain superspiral reaching law and fractional sliding mode function, a variable gain fractional superspiral sliding mode controller VGFSTSMC is designed. By dynamically adjusting the control gain coefficient, the position tracking error is converged in finite time and the system jitter is suppressed.

[0114] S3. Design an adaptive sliding mode disturbance observer (ASMDO) to estimate and compensate for unknown disturbances in real time through adaptive gain adjustment and integral sliding surface.

[0115] S4. The Stribeck friction model of the system is identified based on the least squares method and used as the input of the friction feedforward compensation FFC to the current loop to reduce the uncertainty of system disturbance.

[0116] S5. The control parameters of VGFSTSMC and ASMDO are dynamically tuned using an optimization algorithm to minimize the root mean square error (RMSE) and the maximum instantaneous error of the position tracking error.

[0117] S6. Combine VGFSTSMC, ASMDO, FFC with optimization algorithms to drive PMSM to achieve high-precision position control.

[0118] The following are the specific implementation methods for each step S1-S6.

[0119] Step S1 is as follows:

[0120] PMSM driven feed system in dq The electromagnetic torque equation in the coordinate system is expressed as:

[0121]

[0122] In the formula, It is magnetic torque; It is the torque constant; This represents the q-axis stator current.

[0123] To simplify the analysis, the elastic deformation of the motor shaft, coupling, lead screw, nut, and other components is ignored. It is assumed that the transmission chain of the PMSM drive feed system is rigid; therefore, the axial position of the worktable... equal to the mechanical angle of the motor shaft The axial equivalent displacement, the dynamic equation of the PMSM-driven feed system is expressed as:

[0124]

[0125] in, The axial movement speed of the feed system's table; This refers to the ball screw transmission ratio. For the lead screw; This is the system's equivalent moment of inertia. It is the equivalent viscous damping coefficient; This is the disturbance torque.

[0126] Because the control frequency of the PMSM-driven feed system is relatively high, the disturbance changes relatively slowly during the sampling period compared to the system state. Therefore, assuming the derivative of the equivalent disturbance torque of the motor shaft is zero, the dynamic equations of the PMSM-driven feed system are ultimately expressed as follows:

[0127]

[0128] In step S2, based on the novel variable gain superspiral reaching law and fractional sliding mode function, a variable gain fractional superspiral sliding mode controller VGFSTSMC is designed to replace the traditional position and velocity loop controller. Compared with the integer-order sliding mode surface, the fractional-order sliding mode surface adds new degrees of freedom, which can more flexibly adjust the system dynamics and reduce system jitter.

[0129] To facilitate fractional and integer differential operations, the following differential operators are used: As an operator:

[0130]

[0131] In the formula, It is a time-varying objective function, representing a physical quantity that requires fractional derivatives or integration. It is the time-dependent variable (the current moment). It is a temporary variable in integration operations and a time stamp of a past moment; C The domain representing the function used for calculus computation; , where is the fractional order, when When, it means The derivative of order, when When, it means Integrals of order, especially when When the expression is in the order of integer, it can be simplified to an integer calculus.

[0132] Define the position error of the system noise signal and speed error ,in, It is the target location. It is the target speed. This is the actual axial position of the worktable. This is the actual speed of the workbench.

[0133] Fractional PID ( This is an extension of the traditional integer-order PID controller. Its core feature is that the orders of the integral term (I) and the derivative term (D) are extended from integers to arbitrary positive real numbers, and its sliding surface is designed. It is expressed as follows:

[0134]

[0135] In the formula, are positive weighting coefficients and ; For fractional calculus, .

[0136] This paper proposes a novel improved super-twisted arrival law with variable gain based on the Generalized Superspiral Algorithm (GSTA). The variable gain superspiral reaching law of VGFSTSMC is expressed as follows:

[0137]

[0138] In the formula, the variable gain coefficient and The expression is as follows:

[0139]

[0140] In the formula, ; The basic gain coefficient; The gain is a sensitivity parameter to the sliding surface. This is the parameter for adjusting the rate of gain change; It is a natural constant used to describe exponential decay characteristics;

[0141] and The designed variable gain coefficient varies with the sliding surface The value can be flexibly adjusted to accelerate the convergence of the feed system when it is far from the target position and reduce jitter when it is close to the target position, thus providing greater flexibility for system control.

[0142] and It is a nonlinear stable term that simultaneously satisfies Specifically, it is expressed as follows:

[0143]

[0144] In the formula, It is a sliding surface; It is a continuous variable exponential coefficient that accelerates the convergence of the system and keeps the changes in the control value smooth. It is a variable exponential adjustment parameter; It is a natural constant used to describe the coefficients of a variable exponent. Sliding mold surface The changing characteristics; The ratios of different exponential terms are used to fine-tune the integral step size, enabling VGFSTSMC to more accurately adjust the control value and seek the optimal balance between convergence speed and control accuracy; in addition, the hyperbolic tangent function is used. Replace the symbolic functions in GSTA This allows the power supply system to avoid the problem of small-amplitude high-frequency flutter near the stationary target position of GSTA, thus allowing the use of a larger gain coefficient to improve convergence speed and robustness.

[0145] For sliding surfaces The first derivative of the formula is as follows:

[0146]

[0147] Substitute the dynamic equations of the PMSM-driven feed system into the above equation and solve both sides of the equation. The derivative of order 1, after simplification, yields:

[0148]

[0149] In the formula, For disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current.

[0150] Ignoring unknown lumped disturbance torque Substituting the variable gain superspiral reaching law, we obtain the control law of the variable gain fractional superspiral sliding mode controller as follows:

[0151]

[0152] In the formula, The target q-axis current of the proposed control scheme;

[0153] Position error of system noise signal Speed ​​error and sliding surface function All are included in the fractional differential term. In this process, the memory and filtering characteristics of fractional derivatives can effectively reduce the impact of system noise, thereby suppressing system chattering and improving the position control accuracy of the feed system.

[0154] In step S3, ASMDO was proposed and designed. Based on the designed adaptive reaching law, ASMDO can quickly estimate and compensate for unknown disturbances in the PMSM-driven feed system, and effectively improve the position control accuracy and robustness.

[0155] At the speed of the feed system table and disturbance torque For the observed values, design the following perturbation observer:

[0156]

[0157] in, It is the observed value of the axial movement speed of the feed system's table; It is the observed value of the unknown disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current. It is a correction function used to correct velocity observations; It is the perturbation observer gain; It is a velocity observation error;

[0158] Define velocity observation error Disturbance torque observation error ,get:

[0159]

[0160] Design an integral sliding surface as follows:

[0161]

[0162] In the formula, This is the integral gain, used to adjust and analyze the intensity of the effect;

[0163] The adaptive reaching law of the design is as follows:

[0164]

[0165] In the formula, and It is a positive gain coefficient; It is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the reaching rate. Exponential coefficient Follow Dynamic changes are made so that the observer can always maintain a stable convergence rate; This is the upper limit of the perturbation of the synovial observer, satisfying This invention employs an adaptive method to determine the perturbation boundary. It is an adaptive perturbation suppression term. It is a constant gain coefficient.

[0166] Substituting the adaptive reaching law formula of the design into the sliding surface formula of the observer Ignoring the disturbance term in the first derivative, we obtain the control law for the adaptive sliding membrane disturbance observer, as follows:

[0167]

[0168] In step S4, to address the potential impact of the actual working conditions of the PMSM feed servo system and factors such as unknown wear and installation errors, a segmented Stribeck friction model was proposed and designed:

[0169]

[0170] In the formula, It refers to the motor speed; It is the natural constant, used in the exponential decay term; It is the Stribeck frictional resistance torque. and It is the Coulomb frictional resistance torque in the positive and negative directions. and It is the maximum static friction resistance torque in both the positive and negative motion directions; and It is the equivalent viscous damping coefficient in the positive and negative motion directions; and It is the Stribeck velocity constant in the positive and negative directions of motion.

[0171] The method for identifying relevant parameters of the Stribeck friction model is as follows:

[0172] When the PMSM-driven feed system is in a state of no-load uniform motion, the magnetic torque Used only to counteract Stribeck frictional torque A servo driver is used to control the motor to move at a constant speed, and the q-axis stator current is read. Then, the magnetic torque is calculated using the host computer software. ;Magnetic moment Approximate to Stribeck frictional resistance torque Measure the speed of multiple motors Stribeck frictional resistance torque The experimental data were fitted to the Stribeck friction model using the cftool toolbox in Matlab. The least squares method was used as the fitting algorithm to identify the Stribeck friction model curve, as shown below. Figure 3 As shown.

[0173] definition The unknown disturbance torque of the feed system other than nonlinear friction, and the friction torque Composition of disturbance torque , For its observed values, the adaptive sliding mode perturbation observer is modified as follows:

[0174]

[0175] and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is... for:

[0176]

[0177] Friction feedforward compensation (FFC) can effectively reduce the uncertainty of the feed system. Therefore, ASMDO and VGFSTSMC only need to suppress the modeling error of the friction model and other minor unknown disturbances, thus achieving faster convergence speed and higher position control accuracy. The combination of VGFSTSMC, ASMDO, and FFC forms a composite controller, the structure of which is as follows: Figure 4 As shown.

[0178] In step S5, the control parameters of VGFSTSMC and ASMDO are optimized sequentially by the novel improved particle swarm optimization algorithm. The specific implementation process is as follows:

[0179] S51: Construct VGFSTSMC and ASMDO, and determine the variables to be optimized for each controller. The variables to be optimized are determined to be sliding surfaces. Positive weighting coefficients in The base gain coefficient in VGFSTSMC and integral gain ;

[0180] S52: Determine the search range of the variable to be optimized by trial and error;

[0181] S53: Using a novel and improved particle swarm optimization algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized sequentially.

[0182] S54: Under normal operating conditions of the control system module, optimize and obtain the control parameters of VGFSTSMC and ASMDO.

[0183] The iterative optimization process in step S53 is as follows:

[0184] S531: Initialize the basic parameters of the new improved particle swarm algorithm;

[0185] S532: Initialize the position and velocity of the particles using the improved Sine chaotic mapping formula;

[0186] S533: Select the time-weighted absolute error integral index as the fitness function of the novel improved particle swarm algorithm;

[0187] S534: Calculate the fitness value of a particle;

[0188] S535: Compare the fitness values ​​of particles in each generation and record the individual best position of each particle and the overall best position of the entire swarm.

[0189] S536: Iteratively update particles using a velocity update formula and an improved position update formula;

[0190] S537: Determine if a particle is trapped in a local optimum;

[0191] S538: Determine if the termination condition is met: If the current iteration count has reached the maximum iteration count, the algorithm ends and outputs the parameters; otherwise, proceed to step S534.

[0192] In step S532, the Sine chaotic mapping formula is improved, and its calculation formula is as follows:

[0193]

[0194] In the formula, It is the first-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; It is the second-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; control parameter Let be any real number; This is the modulo operation; Iterative chaotic sequence values ​​with values ​​in the range [-1, 1].

[0195] In step S536, the calculation formulas for the velocity update formula and the improved position update formula are as follows:

[0196]

[0197] In the formula, For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; Inertial weight; and It is the acceleration factor; and A random number within the range [0,1]; For the first Each particle undergoes The best individual particle in history after the next iteration; For the entire particle swarm to experience The optimal particle in the population after the iteration; A random number within the range [0,1]; These are random numbers that follow a Gaussian distribution. It is a variable factor;

[0198] and The formulas are as follows:

[0199]

[0200]

[0201]

[0202] In the formula, It follows a Gaussian distribution. Standard deviation; It is a random number within the range [-1.5, 1.5]. It is any number in the range [0,1]. The root mean square error of the fitness function; This represents the number of iterations. It was through After the nth iteration The individual historical best value of each particle; It is the average of the historical best values ​​of the current group's individuals.

[0203] In step S537, the method for determining whether a particle is trapped in a local optimum is as follows:

[0204] If the fitness value of the optimal individual remains unchanged after 10% of the total number of iterations, it indicates that the particle is highly likely to be trapped in a local optimum. In this case, random numbers are introduced in the next iteration. (Range in [0,1]); when If the particle's velocity is not updated, the particle is re-initialized using the improved Sine chaotic mapping formula, while the remaining particles are updated using the velocity update formula; otherwise, the next step is executed.

[0205] In step S6, VGFSTSMC is responsible for improving the system's chattering suppression capability, ASMDO is responsible for estimating and compensating for unknown disturbances in the feed system, and friction feedforward compensation (FFC) can effectively reduce the uncertainty of the feed system. VGFSTSMC, ASMDO, and FFC are combined to form a composite controller, and the proposed novel improved particle swarm optimization algorithm optimizes the parameters of the composite controller, further improving the position control performance of the feed system.

[0206] Example:

[0207] Discontinuous motion trajectories can lead to high-frequency acceleration variations and high-frequency harmonics in the torque of the permanent magnet synchronous motor, causing vibrations in the mechanical structure of the feed system. To ensure the continuity of motion of the feed system driven by the permanent magnet synchronous motor, this case uses the classic trapezoidal S-curve as the reference trajectory. This trajectory is obtained by multiple integrations of the jump, is simple to implement, requires less MCU resources, and has good continuity and smoothness.

[0208] Design as Figure 5 The trapezoidal S-curve shown has a jump amplitude of ±625 mm / s. 3 The steady-state speed is 50 mm / s, corresponding to an equivalent steady-state speed of 600 rpm for a permanent magnet synchronous motor, which is also a commonly used standard speed for CNC machine tool drive motors. The maximum acceleration of this trajectory is 125 m / s². 2 The stroke is 75 mm. To verify the position control performance of the permanent magnet synchronous motor driven feed system under high-speed conditions, the high-speed trapezoidal S-curve jump is set to ±1250 mm / s. 3 The maximum acceleration is 250 mm / s². 2 The steady-state speed is 100 mm / s, the stroke is 150 mm, and the corresponding steady-state motor speed is 1200 rpm, which is a commonly used speed for high-speed operation of CNC machine tool motors. The stage where the reference trajectory speed is 0 is defined as the positioning stage, and the rest are the motion stages.

[0209] For the composite controller, a novel and improved particle swarm optimization algorithm is used to optimize the values ​​of five parameters: positive weighting coefficients. Basic gain coefficient Integral gain .

[0210] Figure 6 The figure shows the position tracking error curve and control values ​​of the control scheme in this embodiment under the actual operating conditions of the simulated drive feed system. The maximum tracking error at the moment of sudden impact disturbance is marked on the tracking error graph and defined as the sudden impact error. The steady-state velocity of the trajectory is 50 mm / s (600 rpm). The proposed control scheme based on the novel improved particle swarm optimization algorithm (VGFSTSMC-ASMDO-FFC) has a maximum absolute error of only 6.35 μm, and mean absolute error (MA) and root mean square error (RMS) of 1.26 μm and 1.60 μm, respectively. The case data under simulated actual operating conditions effectively verify the superiority of this scheme in suppressing system jitter and improving position control accuracy under sudden impact disturbances.

[0211] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for intelligent optimization of control and parameters of a high-precision, impact-resistant PMSM feed servo system, characterized in that, Includes the following steps: S1. By combining the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism and the closed-loop control model of the grating ruler feedback position, a physical structure and dynamic model of the PMSM drive feed system is established. S2. Based on the novel variable gain superspiral reaching law and fractional sliding mode function, a variable gain fractional superspiral sliding mode controller VGFSTSMC is designed. By dynamically adjusting the control gain coefficient, the position tracking error is converged in finite time and the system jitter is suppressed. S3. Design an adaptive sliding mode disturbance observer (ASMDO) to estimate and compensate for unknown disturbances in real time through adaptive gain adjustment and integral sliding surface. S4. The Stribeck friction model of the system is identified based on the least squares method and used as the input of the friction feedforward compensation FFC to the current loop to reduce the uncertainty of system disturbance. S5. The control parameters of VGFSTSMC and ASMDO are dynamically tuned using an optimization algorithm to minimize the root mean square error (RMSE) and the maximum instantaneous error of the position tracking error. S6. Combine VGFSTSMC, ASMDO, FFC with optimization algorithms to drive PMSM to achieve high-precision position control; Step S1 is as follows: The electromagnetic torque equation of the PMSM-driven feed system in the dq coordinate system is expressed as: ， In the formula, It is magnetic torque; It is the torque constant; This refers to the q-axis stator current. Ignoring the elastic deformation of the motor shaft, coupling, lead screw, nut, and other components, and assuming that the transmission chain of the PMSM drive feed system is rigid, the axial position of the worktable... equal to the mechanical angle of the motor shaft The axial equivalent displacement, the dynamic equation of the PMSM-driven feed system is expressed as: ， in, The axial movement speed of the feed system's table; This refers to the ball screw transmission ratio. For the lead screw; This is the system's equivalent moment of inertia. It is the equivalent viscous damping coefficient; For disturbance torque; Assuming the derivative of the equivalent disturbance torque of the motor shaft is zero, the final dynamic equation of the PMSM drive feed system is expressed as: ， In step 3, the adaptive sliding mode perturbation observer (ASMDO) is designed as follows: At the speed of the feed system table and disturbance torque For the observed values, design the following perturbation observer: ， in, It is the observed value of the axial movement speed of the feed system's table; It is the observed value of the unknown disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current. It is a correction function used to correct velocity observations; It is the perturbation observer gain; It is a velocity observation error; Define velocity observation error Disturbance torque observation error ,get: ， Design an integral sliding surface as follows: ， In the formula, This is the integral gain, used to adjust and analyze the intensity of the effect; The adaptive reaching law of the design is as follows: ， In the formula, and It is a positive gain coefficient; It is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the reaching rate. Exponential coefficient Follow Dynamic changes are made so that the observer can always maintain a stable convergence rate; This is the upper limit of the perturbation of the synovial observer, satisfying , It is an adaptive perturbation suppression term. It is a constant gain coefficient; Substituting the adaptive reaching law formula of the design into the sliding surface formula of the observer Ignoring the disturbance term in the first derivative, we obtain the control law for the adaptive sliding membrane disturbance observer, as follows: ， Step S4 is as follows: Design the Stribeck friction model: ， In the formula, It refers to the motor speed; It is a natural constant; It is the Stribeck frictional resistance torque. and It is the Coulomb frictional resistance torque in the positive and negative directions. and It is the maximum static friction resistance torque in both the positive and negative motion directions; and It is the equivalent viscous damping coefficient in the positive and negative motion directions; and It is the Stribeck velocity constant in the positive and negative directions of motion; The method for identifying relevant parameters of the Stribeck friction model is as follows: When the PMSM-driven feed system is in a state of no-load uniform motion, the magnetic torque Used only to counteract Stribeck frictional torque A servo driver is used to control the motor to move at a constant speed, and the q-axis stator current is read. Then, the magnetic torque is calculated using the host computer software. ;Magnetic moment Approximate to Stribeck frictional resistance torque Measure the speed of multiple motors Stribeck frictional resistance torque The experimental data were fitted to the Stribeck friction model using the cftool toolbox in Matlab. The least squares method was used as the fitting algorithm to identify the Stribeck friction model curve. definition The unknown disturbance torque of the feed system other than nonlinear friction, and the friction torque Composition of disturbance torque , For its observed values, the adaptive sliding mode perturbation observer is modified as follows: ， and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is... for: 。 2. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 1, characterized in that, In step S2, the design of the variable gain fractional-order superspiral sliding mode controller VGFSTSMC is as follows: Using differential operators: ， in, It is a time-varying objective function, representing a physical quantity that requires fractional derivatives or integration. It is the time independent variable representing the current moment. It is a temporary variable in the integration operation, and is a time marker of a past moment; C represents the domain of the calculus calculation function; , which is the fractional order; Define the position error of the system noise signal and speed error ,in, It is the target location. It is the target speed. This is the actual axial position of the worktable. This is the actual speed of the workbench; Design a fractional-order PID sliding surface It is expressed as follows: ， In the formula, are positive weighting coefficients and ; For fractional calculus, ; The variable gain superspiral reaching law of VGFSTSMC is expressed as follows: ， In the formula, the variable gain coefficient and The expression is as follows: ， In the formula, ; The basic gain coefficient; The gain is a sensitivity parameter to the sliding surface. This is the parameter for adjusting the rate of gain change; It is a natural constant; and It is a nonlinear stable term that simultaneously satisfies Specifically, it is expressed as follows: ， ， In the formula, It is a sliding surface; It is a continuous variable exponential coefficient, which accelerates the convergence of the system and keeps the changes in the control value smooth; It is a variable exponential adjustment parameter; It is a natural constant; Used to adjust the ratio of different exponential terms to fine-tune the integration step size; For sliding surfaces The first derivative of the formula is as follows: ， Substitute the dynamic equations of the PMSM-driven feed system into the above equation and solve both sides of the equation. The derivative of order 1, after simplification, yields: ， In the formula, For disturbance torque; This refers to the ball screw transmission ratio. For the lead screw; The moment of inertia of the motor shaft; Let be the torque constant, representing the electromagnetic torque generated per ampere of q-axis current; This refers to the q-axis stator current. Ignoring unknown lumped disturbance torque Substituting the variable gain superspiral reaching law, we obtain the control law of the variable gain fractional superspiral sliding mode controller as follows: ， In the formula, Let be the target q-axis current of the proposed control scheme.

3. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 1, characterized in that, Step S5 is as follows: S51. Construct VGFSTSMC and ASMDO, and determine the variables to be optimized for each controller. The variables to be optimized are determined to be sliding surfaces. Positive weighting coefficients in The base gain coefficient in VGFSTSMC and integral gain ; S52. Determine the search range of the variable to be optimized by trial and error; S53. Using a novel and improved particle swarm optimization algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized sequentially. S54. Under the condition that the control system module is working normally, optimize and obtain the control parameters of VGFSTSMC and ASMDO.

4. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 3, characterized in that, Step S53 is as follows: S531. Initialize the basic parameters of the new improved particle swarm algorithm; S532. Initialize the position and velocity of the particles using the improved Sine chaotic mapping formula; S533. Select the time-weighted absolute error integral index as the fitness function of the novel improved particle swarm algorithm; S534. Calculate the fitness value of the particles; S535. Compare the fitness values ​​of each generation of particles and record the individual best position of each particle and the overall best position of the entire swarm. S536. Iteratively update the particles using the velocity update formula and the improved position update formula; S537. Determine if a particle is trapped in a local optimum; S538. Determine if the termination condition is met: If the current iteration count has reached the maximum iteration count, the algorithm ends and outputs the parameters; otherwise, proceed to step S534.

5. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 4, characterized in that, In step S532, the improved Sine chaotic mapping formula is as follows: ， In the formula, It is the first-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; It is the second-path iteration variable in the chaotic mapping, and its initial value is... The value range is [0,1]; control parameter Let be any real number; This is the modulo operation; Iterative chaotic sequence values ​​with values ​​in the range [-1, 1].

6. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 4, characterized in that, In step S536, the velocity update formula and the improved position update formula are as follows: ， ， In the formula, For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; For the first The particle in the first The velocity vector at the next iteration For the first The particle in the first The position vector at the next iteration; Inertial weight; and It is the acceleration factor; and A random number within the range [0,1]; For the first Each particle undergoes The best individual particle in history after the next iteration; For the entire particle swarm to experience The optimal particle in the population after the iteration; A random number within the range [0,1]; These are random numbers that follow a Gaussian distribution. It is a variable factor; and The formulas are as follows: ， ， ， In the formula, It follows a Gaussian distribution. Standard deviation; It is a random number within the range [-1.5, 1.5]. It is any number in the range [0,1]. The root mean square error of the fitness function; This represents the number of iterations. It was through After the nth iteration The individual historical best value of each particle; It is the average of the historical best values ​​of the current group's individuals.

7. The control and parameter intelligent optimization method for the impact-resistant high-precision PMSM feed servo system according to claim 4, characterized in that, Step S537 is as follows: If the optimal individual fitness value remains unchanged after 10% of the total number of iterations, it indicates that the particle has fallen into a local optimum. In this case, a random number in the range [0,1] is introduced in the next iteration. ;when If the particle's velocity is not updated, the particle is re-initialized using the improved Sine chaotic mapping formula, while the remaining particles are updated using the velocity update formula; otherwise, the next step is executed.

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