Control and parameter intelligent optimization method of anti-impact high-precision PMSM feed servo system

Abstract

The invention relates to the technical field of motor control, in particular to a control and parameter intelligent optimization method for an anti-impact high-precision PMSM (permanent magnet synchronous motor) feeding servo system, which comprises the following steps of: S1, establishing a physical structure and a dynamic model of a PMSM driving feeding system; s2, designing a variable gain fractional order super-spiral sliding mode controller VGFSTSMC, realizing finite time convergence of position tracking errors by dynamically adjusting and controlling gain coefficients, and inhibiting system jitter; s3, designing an adaptive sliding mode disturbance observer ASMDO, and estimating and compensating unknown disturbance in real time through adaptive gain adjustment and an integral sliding mode surface; s4, identifying a system Stribeck friction model based on a least square method, and inputting the system Stribeck friction model as a friction feedforward compensation FFC to a current loop to reduce the disturbance uncertainty of the system; s5, dynamically adjusting and optimizing control parameters of the VGFSTSMC and the ASMDO by adopting an optimization algorithm so as to minimize a root-mean-square value RMSE of a position tracking error and a maximum instantaneous error; and S6, VGFSTSMC, ASMDO and FFC are combined with an optimization algorithm, and the PMSM is driven to realize high-precision position control.

Description

Technical Field

[0001] The present invention relates to the field of motor control technology, and in particular to a control and parameter intelligent optimization method for a shock-resistant high-precision PMSM feed servo system. Background Art

[0002] Computer numerical control (CNC) machine tools are core equipment for high-end precision manufacturing. The performance of their feed systems directly impacts the upper limits of machining accuracy in key areas such as aerospace and optical devices. While the mainstream solution of permanent magnet synchronous motor (PMSM) drive combined with ball screw transmission offers high reliability, it exhibits serious flaws when responding to sudden shock disturbances. Millisecond-level mechanical shocks (such as tool breakage) excite high-frequency resonances of 200-800 Hz through the ball screw, distorting the coupled motor's back EMF and causing current runaway. Traditional PI controllers, due to response delays, are unable to suppress transient displacement deviations. Furthermore, low-speed stick-slip oscillations caused by nonlinear friction and model mismatches due to mechanical wear contribute to the continuous degradation of positioning accuracy. A highly robust control method is urgently needed that can compensate for shock disturbances in real time and simultaneously suppress interference from multiple sources 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 precise models and is sensitive to dynamic disturbances, which can easily lead to steady-state errors; although sliding mode control (SMC) is highly robust, the fixed-gain switching term can cause high-frequency chattering, exacerbating mechanical wear; improved methods such as the super-helical algorithm (STA) suppress chattering through integral terms, but can cause small oscillations near stationary targets due to gain redundancy, and it is difficult to balance the convergence speed and anti-disturbance capability; disturbance observation techniques (such as the extended state observer) have a lag in real-time estimation of compound disturbances, especially when friction suddenly changes during the startup phase, and the error accumulation is significant; friction feedforward compensation relies on high-precision modeling, but the existing segmented model is not adaptable enough to nonlinear characteristics and cannot cope with unknown external disturbances.

[0004] To address these issues, existing research has attempted to improve performance through multimodal control fusion and algorithm optimization, but limitations remain. Fuzzy adaptive control relies on expert experience to set rules and has weak generalization capabilities. While fractional-order sliding modes can improve convergence smoothness, their impact on system robustness is limited. Parameter optimization often uses standard particle swarm optimization (PSO), which is prone to local optimality and lacks deep coupling with the controller's dynamic characteristics. Furthermore, under high-speed and high-load conditions, system nonlinearities intensify, making it difficult for traditional control strategies to balance dynamic response and disturbance rejection.

[0005] Therefore, how to provide a high-precision and strong robust PMSM feed system servo control method and parameter optimization method is a problem that technical personnel in this field urgently need to solve. Summary of the Invention

[0006] The purpose of the present invention is to provide a high-precision and highly robust servo control method for a PMSM drive feed system, which solves the problems of difficult jitter suppression, delayed disturbance compensation and low parameter tuning efficiency in the prior art through multi-physics field modeling, adaptive disturbance observation and parameter optimization algorithm.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions: The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system includes the following steps: S1. Combine the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism, and the grating scale feedback position closed-loop control model to establish the physical structure and dynamic model of the PMSM drive feed system; S2. Based on the novel variable gain super-helical reaching law and fractional-order sliding mode function, a variable gain fractional-order super-helical sliding mode controller (VGFSTSMC) is designed. By dynamically adjusting the control gain coefficient, the finite time convergence of the position tracking error is achieved 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 mode surface. S4. Identify the system Stribeck friction model based on the least squares method and input it into the current loop as friction feedforward compensation (FFC) to reduce system disturbance uncertainty. S5. Dynamically tune the control parameters of VGFSTSMC and ASMDO using an optimization algorithm to minimize the root mean square value (RMSE) of the position tracking error and the maximum instantaneous error. S6. Combine VGFSTSMC, ASMDO, FFC and optimization algorithm to drive PMSM to achieve high-precision position control.

[0008] Furthermore, step S1 is specifically as follows: PMSM drive feed system dq The electromagnetic torque equation in the coordinate system is expressed as:

[0009] Where, is the magnetic moment; is the torque constant; is the q-axis stator current; Ignoring the elastic deformation of the motor shaft, coupling, screw, nut and other components, assuming that the transmission chain of the PMSM drive feed system is a rigid transmission, the axial position of the worktable Equal to the motor shaft mechanical angle The axial equivalent displacement of the PMSM drive feed system is expressed as follows:

[0010] in, is the axial moving speed of the feed system worktable; is the ball screw transmission ratio, is the screw lead; is the equivalent moment of inertia of the system; is the equivalent viscous damping coefficient; is the disturbance torque; Assuming that the derivative of the equivalent interference torque of the motor shaft is zero, the dynamic equation of the PMSM drive feed system is finally expressed as: .

[0011] Furthermore, in step S2, a variable gain fractional-order super-spiral sliding mode controller VGFSTSMC is designed as follows: Using differential operators: , Where, is the time-varying objective function, which represents the physical quantity that requires fractional derivative or integral operations. is the time variable representing the current moment, It is a temporary variable in the integral operation and a time marker of the past moment; C represents the domain of the calculus function; , is the fractional order; Define the position error of the system noise signal and speed error ,in, is the target location, is the target speed, is the actual axial position of the table, is the actual speed of the workbench; Design of Fractional-Order PID Sliding Mode Surface It is expressed as follows:

[0012] Where, is a positive weight coefficient and ; is the fractional calculus order, ; The variable gain superhelical reaching law of VGFSTSMC is expressed as follows:

[0013] In the formula, the variable gain coefficient and The expression is as follows:

[0014] Where, ; is the basic gain coefficient; is the sensitivity parameter of the gain to the sliding surface, is the gain change rate adjustment parameter; is a natural constant; and is a nonlinear stability term, and satisfies , specifically expressed as follows:

[0015] Where, is the sliding surface; It is a continuously variable exponential coefficient that accelerates the convergence of the system and keeps the change of the control value smooth; is the variable exponential adjustment parameter; is a natural constant; Used to adjust the ratio of different exponential terms to fine-tune the integration step size; Sliding surface The formula for the first-order derivative is as follows:

[0016] Substitute the dynamic equation of the PMSM drive feed system into the above equation and solve both sides of the equation ( ) order derivative, we can get:

[0017] Where, is the disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; Ignore the unknown lumped disturbance torque , by introducing the variable gain super-helical reaching law, the control law of the variable gain fractional-order super-helical sliding mode controller is obtained as follows:

[0018] Where, is the target q-axis current of the proposed control scheme.

[0019] Furthermore, in step 3, the adaptive sliding mode disturbance observer ASMDO is designed as follows: The speed of the feed system table and disturbance torque For the observed value, the following disturbance observer is designed:

[0020] in, is the observed value of the axial speed of the worktable of the feed system; is the observed value of the unknown disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; is the correction function used to correct the velocity observation value; is the disturbance observer gain; is the velocity observation error; Define velocity observation error , disturbance torque observation error ,get:

[0021] Design of integral sliding surface as follows:

[0022] Where, It is the integral gain, used to adjust and analyze the action intensity; The designed adaptive reaching law is as follows:

[0023] Where, and is the positive gain coefficient; is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the approach rate. ; Exponential coefficient Follow Dynamic changes so that the observer always maintains a stable convergence rate; is the upper limit of disturbance of the synovial observer, satisfying , is the adaptive disturbance rejection term, is the constant gain coefficient; Substitute the designed adaptive reaching law formula into the observer sliding surface formula Ignoring the disturbance term in the first-order derivative of , we can obtain the adaptive synovial disturbance observer control law, which is as follows: .

[0024] Furthermore, step S4 is specifically as follows: Design the Stribeck friction model:

[0025] Where, is the motor speed; is a natural constant; is the Stribeck friction torque, and is the Coulomb friction torque in the positive and negative directions, and is the maximum static friction resistance torque in the positive and negative directions of motion; and is the equivalent viscous damping coefficient in the positive and negative directions of motion; and is the Stribeck velocity constant in the positive and negative directions of motion; The method for identifying the relevant parameters of the Stribeck friction model is as follows: When the PMSM drive feed system is in a no-load uniform motion state, the magnetic torque Only used to offset Stribeck friction torque , use the servo drive to control the motor to move at a constant speed and read the q-axis stator current , and then calculate the magnetic torque through the host computer software ;Magnetic moment Approximate Stribeck friction torque , measure the speed of multiple motors Stribeck friction torque under , the experimental data were fitted to the Stribcek friction model using Matlab's cftool toolbox. The fitting algorithm used the least squares method to identify the Stribeck friction model curve; definition is the unknown disturbance torque other than the nonlinear friction of the feed system, and is related to the friction torque Constituent disturbance torque , For its observed value, the adaptive sliding mode disturbance observer is modified as:

[0026] and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is for: .

[0027] Furthermore, step S5 is specifically as follows: S51, construct VGFSTSMC and ASMDO, and determine the variables to be optimized for each controller, and the variables to be optimized are determined as sliding surface The positive weight coefficient in , the basic gain coefficient in VGFSTSMC and integral gain ; S52. Determine the search range of the variable to be optimized by trial and error; S53. Using the new improved particle swarm algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized in turn; S54. Under the condition that the control system module operates normally, the control parameters of VGFSTSMC and ASMDO are optimized.

[0028] Furthermore, step S53 is specifically 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 chaos mapping formula; S533, selecting the time-weighted absolute error integral index as the fitness function of the new improved particle swarm algorithm; S534, calculating the fitness value of the particle; S535. Compare the fitness values ​​of particles of each generation and record the individual optimal position of the particle and the optimal position of the entire group; S536. Iteratively update the particles using the velocity update formula and the improved position update formula; S537, judging whether the particle falls into a local optimum; S538. Determine whether the end condition is met: if the current number of iterations has reached the maximum number of iterations, the algorithm ends and outputs the parameters; otherwise, execute step S534.

[0029] Furthermore, in step S532, the improved Sine chaotic mapping formula is as follows:

[0030] Where, It is the first iteration variable in the chaotic map, and its initial value is The value range of is [0,1]; is the second iteration variable in the chaotic map, and its initial value The value range of the control parameter is [0,1]. is any real number; is the remainder operation; is the iterative chaotic sequence value in the range of [-1,1].

[0031] Furthermore, in step S536, the speed update formula and the improved position update formula are as follows:

[0032] Where, For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; is the inertia weight; and is the acceleration factor; and is a random number in [0,1]; For the The particles are experiencing The individual historical best particle experienced after iterations; For the entire particle group The best particle in the group after iterations; is a random number in the range [0,1]; is a random number that obeys Gaussian distribution; is the variation factor; and The formulas are as follows:

[0033] Where, It follows a Gaussian distribution The standard deviation of is a random number in the range [-1.5,1.5]; is any number in the range [0,1]; is the root mean square error of the fitness function; is the number of iterations; It is through After the iteration The individual historical optimal value of each particle; is the average of the individual historical optimal values ​​of the current group.

[0034] Furthermore, step S537 is specifically as follows: After the number of iterations of the particle reaches 10% of the total number of iterations, if the optimal individual fitness value still does not change, it means that the particle is trapped in the local optimum. In the next iteration, a random number in the range of [0,1] is introduced. ;when When , the particle uses the improved Sine chaos mapping formula to reinitialize its velocity, and the other particles still use the velocity update formula to update their velocities; otherwise, proceed to the next step.

[0035] Compared with the prior art, the present invention has the following beneficial effects: 1. The present 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 scale feedback position. It can achieve collaborative modeling of electromagnetic characteristics, mechanical transmission chain dynamic characteristics, and position measurement feedback characteristics. Compared with traditional single physical field modeling methods, it can greatly improve model accuracy, provide a more accurate dynamic benchmark for controller design and disturbance compensation, and significantly reduce tracking errors caused by model mismatch.

[0036] 2. This paper designs a variable-gain fractional-order super-spiral sliding mode control (VGFSTSMC) and proposes a variable-gain convergence law based on replacing the sign function with a hyperbolic tangent function. This method achieves finite-time convergence of the position tracking error (convergence time is reduced to one-third that of traditional sliding mode control). Furthermore, through an adaptive gain adjustment mechanism, it suppresses high-frequency chattering while maintaining dynamic response speed, thus resolving the high-frequency oscillation problem of the traditional super-spiral algorithm (STA) near a stationary target position.

[0037] 3. This paper designs an adaptive sliding mode disturbance observer (ASMDO) and composite disturbance compensation. It also employs an integral sliding mode surface observer with nonlinear adaptive gain. By dynamically adjusting the exponential term, it achieves rapid convergence of the disturbance estimation error. Combined with feedforward compensation based on a piecewise Stribeck friction model, this creates a composite disturbance suppression architecture of "feedforward compensation + real-time observation," significantly reducing the compensation delay for unknown impact disturbances.

[0038] 4. This invention uses an improved Sine chaotic map to initialize the particle swarm optimization algorithm, combined with a dynamic mutation strategy, to overcome the bottleneck of traditional particle swarm optimization (PSO) algorithms that are prone to falling into local optimality, effectively improving global search efficiency. By guiding the dynamic tuning of controller parameters through the ITAE indicator, this method achieves coordinated optimization of VGFSTSMC and ASMDO parameters, reducing the manual tuning workload and significantly enhancing the robustness of the parameter combination. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1This is a flow chart of the control parameter intelligent optimization method of the present invention.

[0040] Figure 2 This is the principle diagram of the experimental platform of the drive feeding system of the present invention.

[0041] Figure 3 It is a segmented Stribeck friction model curve diagram of the present invention.

[0042] Figure 4 This is a structural principle diagram of the composite controller of the present invention.

[0043] Figure 5 This is a reference trajectory curve diagram for the experiment conducted in the present invention.

[0044] Figure 6 This is a diagram of the position tracking experiment results of the present invention under impact disturbance conditions. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0046] The permanent magnet synchronous motor (PMSM) feed servo system includes an actuator module and a control system module; the actuator module includes a permanent magnet synchronous motor (PMSM), a ball screw and a workbench; the control system module includes a host computer, an industrial control board and a motor drive board. Figure 2 As shown in the figure, a permanent magnet synchronous motor (PMSM) is rigidly connected to a ball screw through a coupling. The 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 a reference trajectory command. 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 driver board. The motor driver 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".

[0047] Based on the above-mentioned PMSM feed servo system, an impact disturbance device was established on the right side of the workbench. The impact disturbance device transmits the falling impact of the mass block to the workbench through a rope-pulley mechanism, simulating sudden impact interference during processing (such as tool breakage) to verify the system's anti-disturbance performance.

[0048] like Figure 1As shown, the control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system includes the following steps: S1. Combine the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism, and the grating scale feedback position closed-loop control model to establish the physical structure and dynamic model of the PMSM drive feed system; S2. Based on the novel variable gain super-helical reaching law and fractional-order sliding mode function, a variable gain fractional-order super-helical sliding mode controller (VGFSTSMC) is designed. By dynamically adjusting the control gain coefficient, the finite time convergence of the position tracking error is achieved 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 mode surface. S4. Identify the system Stribeck friction model based on the least squares method and input it into the current loop as friction feedforward compensation (FFC) to reduce system disturbance uncertainty. S5. Dynamically tune the control parameters of VGFSTSMC and ASMDO using an optimization algorithm to minimize the root mean square value (RMSE) of the position tracking error and the maximum instantaneous error. S6. Combine VGFSTSMC, ASMDO, FFC and optimization algorithm to drive PMSM to achieve high-precision position control.

[0049] The following is a specific implementation of each step S1-S6.

[0050] Step S1 is specifically as follows: PMSM drive feed system dq The electromagnetic torque equation in the coordinate system is expressed as:

[0051] Where, is the magnetic moment; is the torque constant; is the q-axis stator current.

[0052] To simplify the analysis, the elastic deformation of the motor shaft, coupling, screw, nut and other components is ignored. Assuming that the transmission chain of the PMSM drive feed system is a rigid transmission, the axial position of the worktable is Equal to the motor shaft mechanical angle The axial equivalent displacement of the PMSM drive feed system is expressed as follows:

[0053] in, is the axial moving speed of the feed system worktable; is the ball screw transmission ratio, is the screw lead; is the equivalent moment of inertia of the system; is the equivalent viscous damping coefficient; is the disturbance torque.

[0054] Since the control frequency of the PMSM-driven feeding system is high, the disturbance changes relatively slowly during the sampling period compared to the system state. Therefore, assuming that the derivative of the equivalent disturbance torque of the motor shaft is equal to zero, the dynamic equation of the PMSM-driven feeding system is finally expressed as follows:

[0055] In step S2, a variable gain fractional-order superhelical sliding mode controller (VGFSTSMC) is designed based on the novel variable gain superhelical reaching law and fractional-order sliding mode function 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.

[0056] In order to facilitate fractional and integer order differential operations, the following differential operators are used: As an operator:

[0057] Where, is the time-varying objective function, which represents the physical quantity that requires fractional derivative or integral operations. is the time variable (the current moment), It is a temporary variable in the integral operation and a time marker of the past moment; C represents the domain of the calculus function; , is the fractional order, when When The differential of the order, when When Integrals of order, in particular, when , the formula can be simplified to integer-order calculus.

[0058] Define the position error of the system noise signal and speed error ,in, is the target location, is the target speed, is the actual axial position of the table, is the actual speed of the table.

[0059] Fractional-order PID ( ) is a generalization of the traditional integer-order PID controller. Its core feature is to extend the order of the integral term (I) and the differential term (D) from integers to any positive real number, and to design its sliding surface It is expressed as follows:

[0060] Where, is a positive weight coefficient and ; is the fractional calculus order, .

[0061] Here we propose a novel improved supertwist arrival law with variable gain based on the generalized supertwist algorithm (GSTA). The variable gain supertwist reaching law of VGFSTSMC is expressed as follows:

[0062] In the formula, the variable gain coefficient and The expression is as follows:

[0063] Where, ; is the basic gain coefficient; is the sensitivity parameter of the gain to the sliding surface, is the gain change rate adjustment parameter; is a natural constant used to describe exponential decay characteristics; and The designed variable gain coefficient follows the sliding surface The value of can be flexibly adjusted to accelerate the convergence of the feed system when it is far away from the target position and reduce jitter when it is close to the target position, providing higher flexibility for system control.

[0064] and is a nonlinear stability term, and satisfies , specifically expressed as follows:

[0065] Where, is the sliding surface; is a continuously variable exponential coefficient that accelerates the convergence of the system and keeps the change of the control value smooth; is the variable exponential adjustment parameter; Is a natural constant used to describe the coefficient of a variable exponent Following the sliding surface The changing characteristics of Used to adjust the ratio of different exponential terms to fine-tune the integration step size, so that VGFSTSMC can adjust the control value more accurately and seek the best balance between convergence speed and control accuracy; in addition, the hyperbolic tangent function is used Replace the symbolic function in GSTA , which enables the feeding system to avoid the problem of small-amplitude high-frequency chattering near the stationary target position of the GSTA, thereby allowing the use of a larger gain coefficient to improve the convergence speed and robustness.

[0066] Sliding surface The formula for the first-order derivative is as follows:

[0067] Substitute the dynamic equation of the PMSM drive feed system into the above equation and solve both sides of the equation ( ) order derivative, we can get:

[0068] Where, is the disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; Ignore the unknown lumped disturbance torque , by introducing the variable gain super-helical reaching law, the control law of the variable gain fractional-order super-helical sliding mode controller is obtained as follows:

[0069] Where, is the target q-axis current of the proposed control scheme; Position error of system noise signal , speed error and sliding surface function are all included in the fractional differential terms In the proposed method, the memory and filtering characteristics of fractional-order differentials can effectively weaken the influence of system noise, thereby suppressing system chattering and improving the position control accuracy of the feed system.

[0070] In step S3, an ASMDO is proposed and designed. Based on the designed adaptive reaching law, the ASMDO can quickly estimate and compensate for unknown disturbances in the PMSM-driven feed system and effectively improve the position control accuracy and robustness.

[0071] The speed of the feed system table and disturbance torque For the observed value, the following disturbance observer is designed:

[0072] in, is the observed value of the axial speed of the worktable of the feed system; is the observed value of the unknown disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; is the correction function used to correct the velocity observation value; is the disturbance observer gain; is the velocity observation error; Define velocity observation error , disturbance torque observation error ,get:

[0073] Design of integral sliding surface as follows:

[0074] Where, It is the integral gain, used to adjust and analyze the action intensity; The designed adaptive reaching law is as follows:

[0075] Where, and is the positive gain coefficient; is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the approach rate. ; Exponential coefficient Follow Dynamic changes so that the observer always maintains a stable convergence rate; is the upper limit of disturbance of the synovial observer, satisfying ; The present invention adopts an adaptive method to determine the disturbance boundary, is the adaptive disturbance rejection term, is the constant gain coefficient.

[0076] Substitute the designed adaptive reaching law formula into the observer sliding surface formula Ignoring the disturbance term in the first-order derivative of , we can obtain the adaptive synovial disturbance observer control law, which is as follows:

[0077] In step S4, in order 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 is proposed and designed:

[0078] Where, is the motor speed; is a natural constant used for the exponential decay term; is the Stribeck friction torque, and is the Coulomb friction torque in the positive and negative directions, and is the maximum static friction resistance torque in the positive and negative directions of motion; and is the equivalent viscous damping coefficient in the positive and negative directions of motion; and is the Stribeck velocity constant in the positive and negative directions of motion.

[0079] The method for identifying the relevant parameters of the Stribeck friction model is as follows: When the PMSM drive feed system is in a no-load uniform motion state, the magnetic torque Only used to offset Stribeck friction torque , use the servo drive to control the motor to move at a constant speed and read the q-axis stator current , and then calculate the magnetic torque through the host computer software ;Magnetic moment Approximate Stribeck friction torque , measure the speed of multiple motors Stribeck friction torque under , the experimental data were fitted to the Stribeck friction model using Matlab's cftool toolbox. The fitting algorithm used the least squares method to identify the Stribeck friction model curve, as shown in Figure 3 shown.

[0080] definition is the unknown disturbance torque other than the nonlinear friction of the feed system, and is related to the friction torque Constituent disturbance torque , For its observed value, the adaptive sliding mode disturbance observer is modified as:

[0081] and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is for:

[0082] Friction feedforward compensation (FFC) can effectively reduce the uncertainty of the feed system. ASMDO and VGFSTSMC only need to suppress the modeling error of the friction model and other small amounts of unknown disturbances, thereby achieving faster convergence speed and higher position control accuracy. VGFSTSMC, ASMDO, and FFC are combined to form a composite controller. The structure of the composite controller is as follows: Figure 4 shown.

[0083] In step S5, the control parameters of VGFSTSMC and ASMDO are optimized in turn by the novel improved particle swarm optimization algorithm. The specific implementation process 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 as sliding surface The positive weight coefficient in , the basic gain coefficient in VGFSTSMC and integral gain ; S52: Determine the search range of the variable to be optimized by trial and error; S53: Using the new improved particle swarm algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized in turn; S54: Under the condition that the control system module operates normally, the control parameters of VGFSTSMC and ASMDO are optimized.

[0084] The iterative optimization process in step S53 is as follows: S531: Initialize the basic parameters of the new improved particle swarm algorithm; S532: Initialize the position and velocity of particles using the improved Sine chaos mapping formula; S533: Select the time-weighted absolute error integral index as the fitness function of the new improved particle swarm algorithm; S534: Calculate the fitness value of the particle; S535: Compare the fitness values ​​of particles in each generation and record the individual optimal position of the particle and the optimal position of the entire group; S536: Use the velocity update formula and the improved position update formula to iteratively update the particles; S537: Determine whether the particle is trapped in a local optimum; S538: Determine whether the end condition is met: If the current number of iterations has reached the maximum number of iterations, the algorithm ends and outputs the parameters; otherwise, execute step S534.

[0085] In step S532, the Sine chaotic mapping formula is improved, and its calculation formula is:

[0086] Where, It is the first iteration variable in the chaotic map, and its initial value is The value range of is [0,1]; is the second iteration variable in the chaotic map, and its initial value The value range of the control parameter is [0,1]. is any real number; is the remainder operation; is the iterative chaotic sequence value in the range of [-1,1].

[0087] In step S536, the speed update formula and the improved position update formula are calculated as follows:

[0088] Where, For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; is the inertia weight; and is the acceleration factor; and is a random number in [0,1]; For the The particles are experiencing The individual historical best particle experienced after iterations; For the entire particle group The best particle in the group after iterations; is a random number in the range [0,1]; is a random number that obeys Gaussian distribution; is the variation factor; and The formulas are as follows:

[0089]

[0090]

[0091] Where, It follows a Gaussian distribution The standard deviation of is a random number in the range [-1.5,1.5]; is any number in the range [0,1]; is the root mean square error of the fitness function; is the number of iterations; It is through After the iteration The individual historical optimal value of each particle; is the average of the individual historical optimal values ​​of the current group.

[0092] In step S537, the method for determining whether the particle is trapped in a local optimum is as follows: After the number of iterations of the particle reaches 10% of the total number of iterations, if the optimal individual fitness value still does not change, it means that the particle is very likely to fall into the local optimum. In the next iteration, a random number is introduced. (range is [0,1]); when When , the particle uses the improved Sine chaos mapping formula to reinitialize its velocity, and the other particles still use the velocity update formula to update their velocities; otherwise, proceed to the next step.

[0093] 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 new improved particle swarm optimization algorithm optimizes the composite controller parameters to further improve the position control performance of the feed system. Example:

[0094] Discontinuous motion trajectories can lead to high-frequency acceleration variations and high-frequency harmonics in the permanent magnet synchronous motor's torque, causing vibration in the feed system's mechanical structure. To ensure the continuity of the permanent magnet synchronous motor-driven feed system's motion, this case uses a classic trapezoidal S-curve as the reference trajectory. This trajectory, derived through multiple integrations of the jumps, is simple to implement, consumes minimal MCU resources, and offers excellent continuity and smoothness.

[0095] 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, and the equivalent steady-state speed of the permanent magnet synchronous motor is 600 rpm, which is also the commonly used standard speed of CNC machine tool drive motors. The maximum acceleration of this trajectory is 125 m / s 2 , the stroke is 75 mm. In order to verify the position control performance of the permanent magnet synchronous motor driven feed system under high-speed working conditions, the high-speed trapezoidal S curve jump is set to ±1250 mm / s 3 , maximum acceleration is 250mm / s 2 , with a steady-state speed of 100 mm / s and a travel of 150 mm, corresponding to a steady-state motor speed of 1200 rpm, a common speed for high-speed CNC machine tool motors. The phase where the reference trajectory speed is 0 is defined as the positioning phase, and the rest as the motion phase.

[0096] For the composite controller, a new improved particle swarm optimization algorithm is used to optimize the values ​​of 5 parameters: Positive weight coefficient ; Basic gain coefficient ; Integral gain .

[0097] Figure 6 The following are the position tracking error curves and control values ​​of the control scheme of this embodiment under the actual working conditions of the simulated drive feed system. The maximum tracking error at the moment of sudden impact interference is marked in the tracking error graph and is defined as the sudden impact error. The steady-state speed of the trajectory is 50 mm / s (600 rpm). The maximum absolute error of the proposed control scheme (VGFSTSMC-ASMDO-FFC) based on the new improved particle swarm optimization algorithm is only 6.35 μm, and the mean absolute error (MA) and root mean square error (RMS) are 1.26 μm and 1.60 μm, respectively. The case data under simulated actual working conditions effectively verified the superiority of the scheme in suppressing system jitter and improving position control accuracy under sudden impact interference.

[0098] The above description of the embodiments is intended to facilitate understanding and application of the present invention by those skilled in the art. It is apparent that 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 requiring creative effort. Therefore, the present invention is not limited to the above embodiments. Any improvements or modifications made by those skilled in the art based on the disclosure of the present invention should fall within the scope of protection of the present invention.

Claims

1. A control and parameter intelligent optimization method for a shock-resistant high-precision PMSM feed servo system, characterized in that: The following steps are involved: S1. Combine the dynamic model of the permanent magnet synchronous motor, the mechanical kinematic model of the ball screw transmission mechanism, and the grating scale feedback position closed-loop control model to establish the physical structure and dynamic model of the PMSM drive feed system; S2. Based on the novel variable gain super-helical reaching law and fractional-order sliding mode function, a variable gain fractional-order super-helical sliding mode controller (VGFSTSMC) is designed. By dynamically adjusting the control gain coefficient, the finite time convergence of the position tracking error is achieved 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 mode surface. S4. Identify the system Stribeck friction model based on the least squares method and input it into the current loop as friction feedforward compensation (FFC) to reduce system disturbance uncertainty. S5. Dynamically tune the control parameters of VGFSTSMC and ASMDO using an optimization algorithm to minimize the root mean square value (RMSE) of the position tracking error and the maximum instantaneous error. S6. Combine VGFSTSMC, ASMDO, FFC and optimization algorithm to drive PMSM to achieve high-precision position control.

2. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 1 is characterized in that: Step S1 is specifically as follows: PMSM drive feed system dq The electromagnetic torque equation in the coordinate system is expressed as: ， Where, is the magnetic moment; is the torque constant; is the q-axis stator current; Ignoring the elastic deformation of the motor shaft, coupling, screw, nut and other components, assuming that the transmission chain of the PMSM drive feed system is a rigid transmission, the axial position of the worktable Equal to the motor shaft mechanical angle The axial equivalent displacement of the PMSM drive feed system is expressed as follows: ， in, is the axial moving speed of the feed system worktable; is the ball screw transmission ratio, is the screw lead; is the equivalent moment of inertia of the system; is the equivalent viscous damping coefficient; is the disturbance torque; Assuming that the derivative of the equivalent interference torque of the motor shaft is zero, the dynamic equation of the PMSM drive feed system is finally expressed as: 。 3. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 2 is characterized in that: In step S2, the variable gain fractional-order super-spiral sliding mode controller VGFSTSMC is designed as follows: Using differential operators: ， in, is the time-varying objective function, which represents the physical quantity that requires fractional derivative or integral operations. is the time variable representing the current moment, It is a temporary variable in the integral operation and a time marker of the past moment; C represents the domain of the calculus function; , is the fractional order; Define the position error of the system noise signal and speed error ,in, is the target location, is the target speed, is the actual axial position of the table, is the actual speed of the workbench; Design of Fractional-Order PID Sliding Mode Surface It is expressed as follows: ， Where, is a positive weight coefficient and ; is the fractional calculus order, ; The variable gain superhelical reaching law of VGFSTSMC is expressed as follows: ， In the formula, the variable gain coefficient and The expression is as follows: ， Where, ; is the basic gain coefficient; is the sensitivity parameter of the gain to the sliding surface, is the gain change rate adjustment parameter; is a natural constant; and is a nonlinear stability term, and satisfies , specifically expressed as follows: ， ， Where, is the sliding surface; It is a continuously variable exponential coefficient that accelerates the convergence of the system and keeps the change of the control value smooth; is the variable exponential adjustment parameter; is a natural constant; Used to adjust the ratio of different exponential terms to fine-tune the integration step size; Sliding surface The formula for the first-order derivative is as follows: ， Substitute the dynamic equation of the PMSM drive feed system into the above equation and solve both sides of the equation ( ) order derivative, we can get: ， Where, is the disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; Ignore the unknown lumped disturbance torque , by introducing the variable gain super-helical reaching law, the control law of the variable gain fractional-order super-helical sliding mode controller is obtained as follows: ， Where, is the target q-axis current of the proposed control scheme.

4. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 3 is characterized in that: In step 3, the adaptive sliding mode disturbance observer ASMDO is designed as follows: The speed of the feed system table and disturbance torque For the observed value, the following disturbance observer is designed: ， in, is the observed value of the axial speed of the worktable of the feed system; is the observed value of the unknown disturbance torque; is the ball screw transmission ratio, is the screw lead; is the motor shaft moment of inertia; is the torque constant, which represents the electromagnetic torque generated per ampere of q-axis current; is the q-axis stator current; is the correction function used to correct the velocity observation value; is the disturbance observer gain; is the velocity observation error; Define velocity observation error , disturbance torque observation error ,get: ， Design of integral sliding surface as follows: ， Where, It is the integral gain, used to adjust and analyze the action intensity; The designed adaptive reaching law is as follows: ， Where, and is the positive gain coefficient; is an exponential coefficient used to dynamically adjust the nonlinear characteristics of the approach rate. ; Exponential coefficient Follow Dynamic changes so that the observer always maintains a stable convergence rate; is the upper limit of disturbance of the synovial observer, satisfying , is the adaptive disturbance rejection term, is the constant gain coefficient; Substitute the designed adaptive reaching law formula into the observer sliding surface formula Ignoring the disturbance term in the first-order derivative of , we can obtain the adaptive synovial disturbance observer control law, which is as follows: 。 5. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 4 is characterized in that: Step S4 is specifically as follows: Design the Stribeck friction model: ， Where, is the motor speed; is a natural constant; is the Stribeck friction torque, and is the Coulomb friction torque in the positive and negative directions, and is the maximum static friction resistance torque in the positive and negative directions of motion; and is the equivalent viscous damping coefficient in the positive and negative directions of motion; and is the Stribeck velocity constant in the positive and negative directions of motion; The method for identifying the relevant parameters of the Stribeck friction model is as follows: When the PMSM drive feed system is in a no-load uniform motion state, the magnetic torque Only used to offset Stribeck friction torque , use the servo drive to control the motor to move at a constant speed and read the q-axis stator current , and then calculate the magnetic torque through the host computer software ;Magnetic moment Approximate Stribeck friction torque , measure the speed of multiple motors Stribeck friction torque under , the experimental data were fitted to the Stribcek friction model using Matlab's cftool toolbox. The fitting algorithm used the least squares method to identify the Stribeck friction model curve; definition is the unknown disturbance torque other than the nonlinear friction of the feed system, and is related to the friction torque Constituent disturbance torque , For its observed value, the adaptive sliding mode disturbance observer is modified as: ， and Compensation is performed in the current loop, and the target q-axis current of the proposed control scheme is for: 。 6. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 5 is characterized in that: Step S5 is specifically as follows: S51, construct VGFSTSMC and ASMDO, and determine the variables to be optimized for each controller, and the variables to be optimized are determined as sliding surface The positive weight coefficient in , the basic gain coefficient in VGFSTSMC and integral gain ; S52. Determine the search range of the variable to be optimized by trial and error; S53. Using the new improved particle swarm algorithm, the control parameters of VGFSTSMC and ASMDO are iteratively optimized in turn; S54. Under the condition that the control system module operates normally, the control parameters of VGFSTSMC and ASMDO are optimized.

7. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 6 is characterized in that: Step S53 is specifically 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 chaos mapping formula; S533, selecting the time-weighted absolute error integral index as the fitness function of the new improved particle swarm algorithm; S534, calculating the fitness value of the particle; S535. Compare the fitness values ​​of particles of each generation and record the individual optimal position of the particle and the optimal position of the entire group; S536. Iteratively update the particles using the velocity update formula and the improved position update formula; S537, judging whether the particle falls into a local optimum; S538. Determine whether the end condition is met: if the current number of iterations has reached the maximum number of iterations, the algorithm ends and outputs the parameters; otherwise, execute step S534.

8. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 7 is characterized in that: In step S532, the improved Sine chaotic mapping formula is as follows: ， Where, It is the first iteration variable in the chaotic map, and its initial value is The value range of is [0,1]; is the second iteration variable in the chaotic map, and its initial value The value range of the control parameter is [0,1]. is any real number; is the remainder operation; is the iterative chaotic sequence value in the range of [-1,1].

9. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 7 is characterized in that: In step S536, the speed update formula and the improved position update formula are as follows: ， Where, For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; For the The particle in The velocity vector at the iteration, For the The particle in The position vector at the iteration; is the inertia weight; and is the acceleration factor; and is a random number in [0,1]; For the The particles are experiencing The individual historical best particle experienced after iterations; For the entire particle group The best particle in the group after iterations; is a random number in the range [0,1]; is a random number that obeys Gaussian distribution; is the variation factor; and The formulas are as follows: ， Where, It follows a Gaussian distribution The standard deviation of is a random number in the range [-1.5,1.5]; is any number in the range [0,1]; is the root mean square error of the fitness function; is the number of iterations; It is through After the iteration The individual historical optimal value of each particle; is the average of the individual historical optimal values ​​of the current group.

10. The control and parameter intelligent optimization method of the shock-resistant high-precision PMSM feed servo system according to claim 7, characterized in that: Step S537 is specifically as follows: After the number of iterations of the particle reaches 10% of the total number of iterations, if the optimal individual fitness value still does not change, it means that the particle is trapped in the local optimum. In the next iteration, a random number in the range of [0,1] is introduced. ;when When , the particle uses the improved Sine chaos mapping formula to reinitialize its velocity, and the other particles still use the velocity update formula to update their velocities; otherwise, proceed to the next step.

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