Ball screw driving system control method based on Gaussian kernel feed-forward compensation

Abstract

The invention provides a ball screw driving system control method based on Gaussian kernel feed-forward compensation, and belongs to the technical field of mechanical design and manufacturing. The method comprises the following steps: constructing a system model of a ball screw driving system; constructing a feedback control framework of the ball screw driving system according to the system model; on the basis of the feedback control framework, constructing a feedforward control framework of the ball screw driving system; combining the feedback control frame with the feedforward control frame to obtain a final control frame of the ball screw driving system; and controlling the ball screw driving system by using the final control frame. The dynamic response performance of the ball screw driving system can be effectively improved.

Description

Technical Field

[0001] This application relates to the technical field of mechanical design and manufacturing, and particularly relates to a control method for a ball screw drive system based on Gaussian kernel feedforward compensation. Background Art

[0002] In recent years, China has attached great importance to the technological innovation of industrial equipment, actively promoted the development of precision drive control technology, and accelerated the overall transformation and upgrading of the manufacturing industry. In the wave of the new industrial revolution, high-speed and high-precision processing equipment has become a common demand in the industrial manufacturing field, and the trajectory tracking performance of the positioning system is a key indicator determining the production quality of scientific instrument parts and industrial components.

[0003] As a core component in various mechanical processing positioning systems such as numerically controlled machine tools, 3D printers, and laser engraving machines, the motion accuracy of the ball screw largely depends on the design and optimization of the control algorithm. Therefore, reducing the tracking error of the ball screw drive system by optimizing the control algorithm not only helps improve the processing efficiency but also effectively guarantees the product accuracy, and has now become an important design optimization method.

[0004] Currently, the control of the ball screw drive system includes two parts: feedback control and feedforward control. Feedback control is mainly used to ensure the stability of the ball screw drive system and provide a certain anti-interference ability; while feedforward control plays a crucial role in improving the dynamic performance of the ball screw drive system. However, there are the following problems in the current control of the ball screw drive system:

[0005] In actual work, for a ball screw drive system with high transmission accuracy and high rigidity, due to the influence of many uncertain factors in the manufacturing and assembly processes, such as the lead error of the ball screw, preload deviation, etc., these will lead to difficulties in meeting the requirements of the workbench for high-precision motion and high-efficiency motion by using traditional dynamic modeling methods to characterize the dynamic characteristics of the ball screw drive system in actual work.

[0006] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above-mentioned related technical solutions.

[0007] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of this application, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0008] The embodiment of this application provides a control method for a ball screw drive system based on Gaussian kernel feedforward compensation, and this method includes the following steps:

[0009] Build a system model of the ball screw drive system, where each component in the system model corresponds to an equivalent parameter;

[0010] According to the system model, build a feedback control framework for the ball screw drive system. The feedback control framework includes an input end, a first indicator light, a feedback controller, a second indicator light, the ball screw drive system, and an output end connected in sequence. The output end is connected to the first indicator light;

[0011] On the basis of the feedback control framework, build a feedforward control framework for the ball screw drive system. The feedforward control framework includes setting a feedforward controller between the input end and the second indicator light, and the feedforward controller is connected in parallel with the feedback controller;

[0012] Combine the feedback control framework and the feedforward control framework to obtain the final control framework of the ball screw drive system;

[0013] Use the final control framework to control the ball screw drive system.

[0014] In an exemplary embodiment of the present application, the system model includes:

[0015] A workbench, on which a pair of support bearings are provided;

[0016] A ball screw, one end of the ball screw is mounted on one of the support bearings, and is sequentially connected to a coupling and a servo drive motor. The other end of the ball screw is mounted on the other support bearing; multiple balls are arranged in the spiral groove of the ball screw;

[0017] A lead screw nut, one end of the lead screw nut is arranged on the workbench. The other end of the lead screw nut is meshed and connected to the ball screw through multiple balls.

[0018] In an exemplary embodiment of the present application, the steps of building the system model of the ball screw drive system include:

[0019] According to all the equivalent parameters, obtain the kinetic energy and potential energy of the system model;

[0020] According to the difference between the kinetic energy and the potential energy, Coulomb friction and viscous friction, and use the Euler-Lagrange equation to describe the motion trajectory of the system model in the generalized coordinate system, and obtain the dynamic equation of the system model.

[0021] In an exemplary embodiment of the present application, the expression of the kinetic energy of the system model is:

[0022]

[0023] Among them, E k represents the kinetic energy of the system model, J m represents the moment of inertia of the servo drive motor, represents the derivative of the rotation angle of the servo drive motor, J b represents the moment of inertia of the ball screw, represents the derivative of the rotation angle at which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, M b represents the mass of the ball screw, represents the derivative of the radial displacement of the support bearing, represents the derivative of the axial displacement of the support bearing, M t represents the mass of the workbench, represents the derivative of the displacement of the workbench in the vertical direction, represents the derivative of the displacement of the workbench in the horizontal direction;

[0024] The expression of the potential energy of the system model is:

[0025]

[0026] Among them, E p represents the potential energy of the system model, k g represents the stiffness of the coupling, θ m represents the rotation angle of the servo drive motor, θ b represents the rotation angle at which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, k s represents the contact stiffness between the ball screw and the screw nut, θ n represents the relative rotation angle of the screw nut, k e represents the axial equivalent stiffness between the ball screw and the support bearing, x b represents the axial displacement of the support bearing, k t represents the contact stiffness between the workbench and the linear guide, v represents the displacement of the workbench in the horizontal direction;

[0027] The expression of the dynamic equation of the system model is:

[0028]

[0029] Among them, represents the second derivative of the rotation angle of the servo drive motor, f vm represents the viscous friction coefficient of the servo drive motor, Q cm represents the Coulomb friction force acting on the servo drive motor during operation, τ m represents the torque output by the servo drive motor, P hrepresents the lead of the ball screw. represents the second derivative of the rotation angle at which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, f vb represents the viscous friction coefficient of the ball screw.

[0030] In an exemplary embodiment of the present application, the feedback controller adopts PID feedback control, and the expression of the PID feedback control is:

[0031]

[0032] where u fb (t) represents the output signal of the feedback controller at the t-th moment, k p represents the proportional gain of the feedback controller, e(t) represents the signal tracking error of the ball screw drive system at the t-th moment, e(t) = |y(t) - r(t)|, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, r(t) represents the reference output signal of the ball screw drive system at the t-th moment, k i represents the integral gain of the feedback controller, e(τ) represents the system error of the ball screw drive system, k d represents the derivative gain of the feedback controller.

[0033] In an exemplary embodiment of the present application, the steps of constructing the feedforward control framework of the ball screw drive system on the basis of the feedback control framework include:

[0034] Sampling datasets of the same trajectory with different amplitudes to obtain a sampling dataset;

[0035] In the dSPACE simulation software, training the inverse system of the ball screw drive system with the sampling dataset to obtain a plurality of control input signals and a plurality of actual output signals;

[0036] Superposing all the control input signals and all the actual output signals to generate an input-output dataset;

[0037] Using the sliding window method to perform offline reconstruction on the input-output dataset and introducing future information to convert the causal relationship of the ball screw drive system into a non-causal relationship to obtain a feedforward data training set;

[0038] Determine that the feedforward controller adopts Gaussian kernel feedforward control and select the Matern kernel function as the kernel function of the Gaussian kernel feedforward control;

[0039] According to the mapping relationship between the input and output of the feedforward data training set, using the Gaussian process regression model to construct the feedforward control framework of the ball screw drive system.

[0040] In an exemplary embodiment of the present application, the expression of the Matern kernel function is as follows:

[0041]

[0042] where k(x, x′) represents the covariance function between the input point x and the input point x′, l represents the hyperparameter, d(x, x′) represents the distance between the input point x and the input point x′, x represents the x-th input point, and x′ represents the x′-th input point.

[0043] In an exemplary embodiment of the present application, the expression of the ball screw drive system is as follows:

[0044] P: y(t) = g(W t , E t ) (6)

[0045] where P represents the ball screw drive system, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, g(W t , E t ) represents the state equation of the ball screw drive system at the t-th moment, W t represents all the input signals of the ball screw drive system up to the t-th moment, and E t represents all the output signals of the ball screw drive system up to the t-th moment;

[0046] The expression of the causality of the ball screw drive system is as follows:

[0047] P1: b1(t) = f1[a(t), a(t - 1), …, a(t - n c )] (7)

[0048] where P1 represents the causality of the ball screw drive system, b1(t) represents the response value of the causality of the ball screw drive system at the t-th moment, f1(·) represents the first non-linear function, and a(t - n c ) represents all the historical input signals of the ball screw drive system at the past t - n c moments;

[0049] The expression of the non-causality of the ball screw drive system is as follows:

[0050] P2: b2(t) = f2[a(t + n ac ), a(t + n ac - 1), …, a(t - n c )] (8)

[0051] Among them, P2 represents the non-causality of the ball screw drive system, b2(t) represents the response value of the non-causality of the ball screw drive system at the t-th moment, f2(·) represents the second non-linear function, a(t - n ac ) represents all future input information at the future moment of t + n ac moment, t + n ac -1 represents all future input signals at the moment of t + n ac -1 moment.

[0052] In an exemplary embodiment of the present application, the expression of the input-output data set is:

[0053] D = {X, u} (9)

[0054] Among them, D represents the input-output data set, X represents the training matrix, u represents the training objective, u = (u1, u2,..., u M ) T , u M represents the M-th training objective, M represents the number of training objectives, x N represents the N-th training sample, N represents the number of training samples, y(N - 1) represents the output corresponding to the (N - 1)-th training sample, and T represents the transpose operation.

[0055] In an exemplary embodiment of the present application, the expression of the feedforward data training set is:

[0056]

[0057] Among them, X * represents the feedforward data training set, X *,G-1 represents the (G - 1)-th reference signal, r represents the output corresponding to the reference signal, and r(G - 1) represents the output corresponding to the (G - 1)-th reference signal.

[0058] Beneficial effects:

[0059] The present application provides a control method for a ball screw drive system based on Gaussian kernel feedforward compensation, which has at least the following beneficial effects:

[0060] (1) By constructing a final control framework that combines a feedback control framework and a feedforward control framework, the present application effectively solves the problems of low accuracy and poor controllability of the traditional feedforward framework under the influence of uncertain factors, and effectively improves the dynamic response performance of the ball screw drive system;

[0061] (2) By constructing a feedback control framework, the present application can quickly track the reference signal;

[0062] (3) The present application can reduce the signal tracking error and suppress the friction interference by constructing a feedforward control framework. Description of the Drawings

[0063] The drawings herein are incorporated into and constitute a part of this specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0064] Figure 1 Schematic diagram showing the steps of a control method for a ball screw drive system based on Gaussian kernel feedforward compensation in an exemplary embodiment of the present application;

[0065] Figure 2 Schematic diagram showing the system model in an exemplary embodiment of the present application, and the equivalent parameters corresponding to all components in the system model;

[0066] Figure 3 Schematic diagram showing the structure of the feedback control framework in an exemplary embodiment of the present application;

[0067] Figure 4 Schematic diagram showing the combination of the feedback control framework and the feedforward control framework in an exemplary embodiment of the present application;

[0068] Figure 5 Schematic diagram showing the structure of the final control framework combining the PID feedback control framework and the Gaussian kernel feedforward control framework in an exemplary embodiment of the present application;

[0069] Figure 6a Schematic diagram showing the curve of signal tracking of the ball screw drive system in the simulation experiment of the present application;

[0070] Figure 6b Showing the present application Figure 6a Enlarged schematic diagram of area I;

[0071] Figure 6c Showing the present application Figure 6a Enlarged schematic diagram of area II;

[0072] Figure 6d Showing the present application Figure 6a Enlarged schematic diagram of area III;

[0073] Figure 7 Schematic diagram of error comparison using different control strategies.

[0074] In the figure, 100 is a ball screw drive system; 110 is a servo drive motor; 120 is a coupling; 130 is a support bearing; 140 is a ball screw; 150 are balls; 160 is a screw nut; 170 is a workbench. Detailed implementation manners

[0075] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more complete and comprehensive, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described can be combined in any suitable manner in one or more embodiments.

[0076] In addition, the accompanying drawings are only schematic illustrations of the present application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0077] To this end, the present example embodiment provides a control method for a ball screw drive system based on Gaussian kernel feedforward compensation, as Figure 1 shown. This method can include the following steps:

[0078] Step S101: Construct a system model of the ball screw drive system, and each component in the system model corresponds to an equivalent parameter.

[0079] Step S102: According to the system model, construct a feedback control framework for the ball screw drive system. The feedback control framework includes an input end, a first indicator light, a feedback controller, a second indicator light, the ball screw drive system, and an output end that are connected in sequence, and the output end is connected to the first indicator light.

[0080] Step S103: On the basis of the feedback control framework, construct a feedforward control framework for the ball screw drive system. The feedforward control framework includes a feedforward controller disposed between the input end and the second indicator light, and the feedforward controller is connected in parallel with the feedback controller.

[0081] Step S104: Combine the feedback control framework and the feedforward control framework to obtain the final control framework of the ball screw drive system.

[0082] Step S105: Use the final control framework to control the ball screw drive system.

[0083] The embodiment of the present application proposes a control method for a ball screw drive system based on Gaussian kernel feedforward compensation, which has at least the following beneficial effects:

[0084] (1) By constructing a final control framework that combines a feedback control framework and a feedforward control framework, the present application effectively solves the problems of low accuracy and poor controllability of the traditional feedforward framework under the influence of uncertain factors, and effectively improves the dynamic response performance of the ball screw drive system;

[0085] (2) By constructing a feedback control framework, the present application can quickly track the reference signal;

[0086] (3) By constructing a feedforward control framework, the present application can reduce the signal tracking error and suppress the friction interference.

[0087] Next, a control method for a ball screw drive system based on Gaussian kernel feedforward compensation proposed in the present exemplary embodiment will be described in more detail.

[0088] In step S101 of the present embodiment, as Figure 2 shown, a system model of the ball screw drive system 100 is constructed, and each component in the system model corresponds to an equivalent parameter. It can be seen from Figure 2 that the system model includes:

[0089] A workbench 170, on which a pair of support bearings 130 are provided;

[0090] A ball screw 140, one end of the ball screw 140 is mounted on one of the support bearings 130, and is sequentially connected to a coupling 120 and a servo drive motor 110, and the other end of the ball screw 140 is mounted on the other support bearing 130; a plurality of balls 150 are respectively arranged in the spiral groove of the ball screw 140;

[0091] A lead screw nut 160, one end of the lead screw nut 160 is arranged on the workbench 170, and the other end of the lead screw nut 160 is meshed and connected to the ball screw 140 through a plurality of balls 150.

[0092] Figure 2 It shows that each component in the system model has an equivalent parameter, at least including:

[0093] The equivalent parameter of the torque output by the servo drive motor is τ m , the equivalent parameter of the rotation angle of the servo drive motor is θ m , the equivalent parameter of the rotation angle of the torque output by the servo drive motor to drive the ball screw to rotate through the coupling is θ b , the equivalent parameter of the relative rotation angle of the lead screw nut is θ n, the equivalent parameter of the horizontal displacement of the workbench is v, and the equivalent parameter of the vertical displacement of the workbench is x t , the equivalent parameter of the stiffness of the coupling is k g , the equivalent parameter of the contact stiffness between the ball screw and the screw nut is k s , the equivalent parameter of the axial equivalent stiffness between the ball screw and the support bearing is k e , the equivalent parameter of the contact stiffness between the workbench and the linear guide is k t , the equivalent parameter of the damping value between the ball screw and the support bearing is c b , the equivalent parameter of the contact damping value between the workbench and the linear guide is c t , the equivalent parameter of the radial displacement of the support bearing is v b , the equivalent parameter of the axial displacement of the support bearing is x b .

[0094] Corresponding an equivalent parameter to each component in the system model is equivalent to simplifying the entire system model into a mass-damping-spring system. This simplification helps to improve the analysis efficiency of the system model and facilitates the integration of the control system model.

[0095] Step S101 of this embodiment may include the following sub-steps:

[0096] Sub-step S1011: Obtain the kinetic energy and potential energy of the system model according to all equivalent parameters;

[0097] Generally, the ball screw drive system can be regarded as a linear time-invariant system and obeys the law of conservation of energy.

[0098] Furthermore, the expression of the kinetic energy of the system model is:

[0099]

[0100] where E k represents the kinetic energy of the system model, J m represents the moment of inertia of the servo drive motor, represents the derivative of the rotation angle of the servo drive motor, J b represents the moment of inertia of the ball screw, represents the derivative of the rotation angle of the ball screw rotated by the torque output by the servo drive motor through the coupling, M b represents the mass of the ball screw, represents the derivative of the radial displacement of the support bearing, represents the derivative of the axial displacement of the support bearing, M t represents the mass of the workbench, represents the derivative of the vertical displacement of the workbench, Represents the derivative of the horizontal displacement of the workbench.

[0101] Furthermore, the expression for the potential energy of the system model is:

[0102]

[0103] Where, E p represents the potential energy of the system model, k g represents the stiffness of the coupling, θ m represents the rotation angle of the servo drive motor, θ b represents the rotation angle by which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, k s represents the contact stiffness between the ball screw and the screw nut, θ n represents the relative rotation angle of the screw nut, k e represents the axial equivalent stiffness between the ball screw and the support bearing, x b represents the axial displacement of the support bearing, k t represents the contact stiffness between the workbench and the linear guide, and v represents the horizontal displacement of the workbench.

[0104] In actual work, compared with load changes and structural design, v b , x b and v have a negligible impact on the ball screw drive system. Therefore, in this application, these three equivalent parameters are respectively set as: v b ≈0, x b ≈0, v≈0.

[0105] Sub-step S1012: According to the difference between the kinetic energy and potential energy of the system model, Coulomb friction and viscous friction, and using the Euler-Lagrange equation to describe the motion trajectory of the system model in the generalized coordinate system, the dynamic equation of the system model is obtained.

[0106] Given that the ball screw has a large stiffness, the rotation angle of the ball screw can be approximated as the relative rotation angle of the screw nut, that is, θ n ≈θ b . The lead of the ball screw is represented by P h To represent, therefore, the relationship between the vertical displacement x t of the workbench and the rotation angle θ b of the ball screw rotation can be expressed in the following approximate manner:

[0107]

[0108] Substituting this approximate method into formulas (1) and (2), the difference between the kinetic energy and potential energy of the ball screw drive system can be used to represent the Lagrangian L, that is, L = E k -Ep , and then substitute the formula representing L into the Euler-Lagrange equation to obtain the motion equation of the system model:

[0109]

[0110] in, represents the partial derivative.

[0111] In addition, the servo drive motor will be subjected to viscous friction Q during operation. vm and Coulomb friction force Q cm Here, the total friction force Q on the servo drive motor is m Expressed as:

[0112]

[0113] Here, sign represents the sign function.

[0114] At the same time, when the servo drive motor drives the ball screw to work, the viscous friction force Q on the ball screw is reduced. s Expressed as:

[0115]

[0116] Among them, f vm Indicates the viscous friction coefficient of the servo drive motor, f cm Indicates the Coulomb friction coefficient of the servo drive motor, f vb Indicates the viscous friction coefficient of the ball screw.

[0117] Therefore, the dynamic equation of the system model can be expressed as:

[0118]

[0119] in, Represents the second-order derivative of the rotation angle of the servo drive motor, f vm The viscous friction coefficient of the servo drive motor, Q cm Indicates the Coulomb friction force on the servo drive motor when it is in working state, τ m Indicates the torque output by the servo drive motor, P h Indicates the lead of the ball screw, It represents the second derivative of the rotation angle of the ball screw driven by the torque output by the servo drive motor through the coupling, f vb Indicates the viscous friction coefficient of the ball screw.

[0120] In step S102 of this embodiment, a feedback control framework of the ball screw drive system is constructed based on the system model.

[0121] In this embodiment, as Figure 3 shown, the feedback control framework includes an input end, a first indicator light, a feedback controller, a second indicator light, a ball screw drive system, and an output end that are connected in sequence, and the output end is connected to the first indicator light.

[0122] Further, on the premise of clarifying the dynamic equation of the system model, this application introduces PID (Proportional Integral Differential) feedback control. By reducing the error between the actual output signal and the reference output signal of the controlled object, the precise control goal of making the actual output signal and the reference output signal of the controlled object completely coincide is achieved.

[0123] The expression of the PID feedback control adopted in this embodiment is:

[0124]

[0125] where u fb (t) represents the output signal of the feedback controller at the t-th moment, k p represents the proportional gain of the feedback controller, e(t) represents the signal tracking error of the ball screw drive system at the t-th moment, e(t) = |y(t) - r(t)|, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, r(t) represents the reference output signal of the ball screw drive system at the t-th moment, k i represents the integral gain of the feedback controller, e(τ) represents the system error of the ball screw drive system, k d represents the differential gain of the feedback controller.

[0126] It can be seen from step S102 that the PID feedback control framework operates with the signal tracking error of the ball screw drive system as the control input. When there is a deviation between the output signal and the reference signal, the feedback controller will control the output quantity to reduce the tracking error. Therefore, the PID feedback control inevitably has a certain time lag. Therefore, in high-speed and high-precision application scenarios, relying solely on PID feedback control is difficult to meet the expected control requirements.

[0127] In step S103 of this embodiment, as Figure 4 shown, on the basis of the feedback control framework, a feedforward control framework of the ball screw drive system is constructed.

[0128] In practical applications, during the manufacturing and assembly processes of ball screw drive systems with high transmission accuracy and high rigidity, they are affected by uncertain factors, making it difficult for traditional dynamic modeling methods to accurately describe their dynamic characteristics, and thus unable to meet the requirements of the drive workbench for high-precision and high-efficiency motion. Aiming at the uncertainty of manufacturing or assembly parameters, the drive reference trajectory and the actual output trajectory are used as single-input and single-output for Gaussian model training, and the inverse system parameters of the ball screw drive system are parameterized as a non-causal nonlinear finite impulse response system. Based on this, a nonlinear inverse system model control framework based on Gaussian kernel feedforward control is constructed, effectively solving the limitations of low accuracy and poor controllability of traditional feedforward control frameworks under uncertain conditions.

[0129] In this embodiment, based on PID feedback control, a feedforward controller is set between the input end and the second indicator light, and the feedforward controller is connected in parallel with the feedback controller.

[0130] Step S103 of this embodiment may include the following sub-steps:

[0131] Sub-step S1031: Sample the data sets with different amplitudes for the same trajectory to obtain a sampled data set.

[0132] Furthermore, in order to obtain the feedforward data training set of the ball screw drive system, the ball screw drive system needs to be trained first. The training trajectory is R = {q1, q2, …, q n}, where R is a set of different amplitudes for the same input trajectory, q1 is the first input trajectory with different amplitudes, and q n is the nth input trajectory with different amplitudes. Sample the training trajectory i times to obtain [q(0), … q(Z i -1)] T , where Z i represents the number of samples for the i-th sampling, and a sampled data set is obtained.

[0133] The purpose of sampling the training trajectory is to use this rich data for training to improve the prediction accuracy of the feedforward signal and compensate for the uncertainty of the ball screw drive system.

[0134] Sub-step S1032: In the dSPACE simulation software, use the sampled data set to train the inverse system of the ball screw drive system to obtain a plurality of control input signals and a plurality of actual output signals.

[0135] Furthermore, as Figure 5 shown, when the training trajectory in the sampled data set is input into the dSPACE simulation software for operation, a set of control input signals is obtained: o i = [o(1), … o(Z i )] T, the set of actual output signals: j i = [j(1), … j(Z i )] T .

[0136] Sub-step S1033: Superimpose all control input signals and all actual output signals to generate an input-output data set.

[0137] Furthermore, superimpose all control input signals and all actual output signals generated by the loop to obtain:

[0138]

[0139] Represent the above two formulas using the data set Q = {O, J}. To satisfy the non-causality of the ball screw drive system, the system model needs to be formatted to be able to receive future information. Define the input of the feedforward control framework as X and the output, i.e., the training target, as u, to obtain the input-output data set D = {X, u}.

[0140] Sub-step S1034: Use the sliding window method to perform offline reconstruction on the input-output data set, introduce future information, and convert the causality of the ball screw drive system into non-causality to obtain a feedforward data training set.

[0141] Sub-step S1035: Determine that the feedforward controller adopts Gaussian kernel feedforward control and select the Matern kernel function as the kernel function of the Gaussian kernel feedforward control.

[0142] Furthermore, the expression of the Matern kernel function is:

[0143]

[0144] Among them, k(x, x′) represents the covariance function between the input point x and the input point x′, l represents the hyperparameter, d(x, x′) represents the distance between the input point x and the input point x′, x represents the x-th input point, and x′ represents the x′-th input point. The input points here refer to the signals or data that need to be received in the system model, and are usually used to calculate the output or affect the behavior of the system model.

[0145] The Matern kernel function generates functions that change from very rough to very smooth by controlling the hyperparameters, thereby reflecting that the greatest advantage of the Matern kernel function lies in its strong flexibility. In this embodiment, the Matern kernel function when γ = 3 / 2 is preferably selected. At this time, the Matern kernel function has better robustness in the face of noise or changes in the data and can effectively control and predict the ball screw drive system.

[0146] Sub-step S1036: According to the mapping relationship between the input and output of the feedforward data training set, use the Gaussian process regression model to construct the feedforward control framework of the ball screw drive system.

[0147] Furthermore, the expression of the ball screw drive system is:

[0148] P: y(t) = g(W t , E t ) (6)

[0149] where P represents the ball screw drive system, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, g(W t , E t ) represents the state equation of the ball screw drive system at the t-th moment, W t represents all the input signals of the ball screw drive system up to the t-th moment, and E t represents all the output signals of the ball screw drive system up to the t-th moment.

[0150] Furthermore, the expression of the causality of the ball screw drive system is:

[0151] P1: b1(t) = f1[a(t), a(t - 1), …, a(t - n c )] (7)

[0152] where P1 represents the causality of the ball screw drive system, b1(t) represents the response value of the causality of the ball screw drive system at the t-th moment, f1(·) represents the first nonlinear function, and a(t - n c ) represents all the historical input signals of the ball screw drive system at the past t - n c moments;

[0153] Furthermore, the expression of the non-causality of the ball screw drive system is:

[0154] P2: b2(t) = f2[a(t + n ac ), a(t + n ac - 1), …, a(t - n c )] (8)

[0155] where P2 represents the non-causality of the ball screw drive system, b2(t) represents the response value of the non-causality of the ball screw drive system at the t-th moment, f2(·) represents the second nonlinear function, a(t - n ac ) represents all the future input information at the future t + n ac moments, t + n ac - 1 represents the future t + n acAll future input signals at time - 1.

[0156] Here, non - causality includes both all historical input signals and all future input signals.

[0157] Furthermore, the expression of the input - output data set is:

[0158] D = {X, u} (9)

[0159] Where D represents the input - output data set, X represents the training matrix, u represents the training target, u=(u1, u2, …, u M ) T , u M represents the M - th training target, M represents the number of training targets, x N represents the N - th training sample, N represents the number of training samples, y(N - 1) represents the output corresponding to the N - 1 - th training sample, and T represents the transpose operation.

[0160] Furthermore, the expression of the feed - forward data set is:

[0161]

[0162] Where X * represents the feed - forward data training set, which can be regarded as a set of reference signals, X *,G-1 represents the (G - 1) - th reference signal, r represents the output corresponding to the reference signal, and r(G - 1) represents the output corresponding to the (G - 1) - th reference signal.

[0163] Furthermore, after hyperparameter optimization and adjustment, the mapping relationship between the training matrix X and the training target u can be obtained, which is the model of the feed - forward control framework of the ball - screw drive system. The training data and the prediction data are jointly distributed (f, f(X * ))), f(X * ) represents the feed - forward signal of the ball - screw drive system, that is, Gaussian kernel feed - forward control is realized.

[0164] In step S104 of this embodiment, as Figure 5 shown, the feedback control framework and the feed - forward control framework are combined to obtain the final position control framework of the ball - screw drive system.

[0165] In this embodiment, the feedback control framework is PID feedback control; the feed - forward control framework is Gaussian kernel feed - forward control.

[0166] In step S105 of this embodiment, the ball - screw drive system is controlled using the final position framework.

[0167] To verify the beneficial effects of a control method for a ball screw drive system based on Gaussian kernel feedforward compensation proposed in this application, the following simulation experiments are carried out.

[0168] The experimental equipment used in this simulation experiment consists of two parts, namely a servo drive (model: SOLOISTCP0-IO) and a servo motor (model: BMS60-A-D25-E2500H-BK1, torque constant: 0.14 Nm / A) developed by AEROTECH, and a rotary encoder with 2500 lines and 4-fold frequency resolution (10,000 pulse signals per revolution) is used to connect to the DS3002 incremental encoder board of dSPACE for real-time detection of the rotation angle of the servo motor.

[0169] Since the control input signal of the control method proposed in this application is essentially torque, the control mode of the servo drive is set to torque mode, and the torque command (analog voltage range -10~+10v) sent by the DS2103 digital-to-analog conversion board is received in real time. In addition, a ball screw motion workbench (model: PRO115SLE-200-TT1-BS1-M2-3-E4-LI1-CP1-PL1, maximum stroke: 400 mm, maximum lead: 5 mm) produced by AEROTECH is selected as the research object in this simulation experiment, and an incremental read head and grating ruler developed by RENISHAW are equipped as the end position detection device (model: TI-0040A20A-0FQP27, resolution: 0.5 μm). To ensure the smoothness of the reference signal in the start / stop stage of the workbench, a reference position trajectory r(t)=2sin(5πt - π / 2)+2 and a reference velocity trajectory r′(t)=10πsin(5πt) with a period of 0.4 s are adopted. Generally, the motion of the workbench in the start / stop stage has little effect on the actual machining accuracy, so the trajectory tracking effects in these two stages are not within the scope of discussion. In addition, the above control systems are all calculated with a fixed step size, and the operation period is set to 0.1 ms.

[0170] As Figure 6a 、 Figure 6b 、 Figure 6c and Figure 6d shown, PID refers to PID feedback control, GR refers to the combination of PID feedback control and Gaussian kernel feedforward control, and r refers to the output corresponding to the reference signal. Figure 6a is the signal tracking result obtained. Figure 6b and Figure 6c The regions in are the signal tracking results of the workbench at the commutation point in the system model. Figure 6dIt is the signal tracking result of the forward movement in Region III. From this, it can be seen that compared with the trajectory tracking result of the PID method, the trajectory tracking result of the GR method is closer to the reference trajectory. This indicates that the tracking error generated by GR is smaller than that generated by PID. This shows that the method proposed in this application is superior to the traditional PID control, and the Gaussian kernel feedforward can effectively improve the dynamic response performance of the system model.

[0171] As Figure 7 shown, Figure 7 in (a) and (b) regions in [reference document] are the error comparison effects of the ball screw workbench at the commutation position. From this, it can be known that introducing the Gaussian kernel feedforward compensation reduces the commutation error in Region I from 0.01 mm to 0.006 mm, and reduces the commutation error in Region II from 0.008 mm to 0.006 mm.

[0172] In summary, the Gaussian kernel feedforward control strategy proposed by the present invention, as well as the method based on input-output data, trains the system model and directly generates the feedforward signal of the system, solves the problem of the decline in signal tracking performance caused by uncertain factors, and thus improves the tracking and positioning accuracy of the ball screw drive system.

[0173] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present application, "a plurality" means two or more unless otherwise specifically defined.

[0174] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0175] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present application.

[0176] Other embodiments of the present application will be readily contemplated by those skilled in the art in view of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include known common general knowledge or conventional technical means in the technical field not disclosed in the present application.

Claims

1. A control method for a ball screw drive system based on Gaussian kernel feedforward compensation, characterized in that, The method includes the following steps: Construct a system model of the ball screw drive system, where each component in the system model corresponds to an equivalent parameter; Based on the system model, construct a feedback control framework for the ball screw drive system. The feedback control framework includes an input end, a first indicator light, a feedback controller, a second indicator light, the ball screw drive system, and an output end connected in sequence. The output end is connected to the first indicator light; On the basis of the feedback control framework, construct a feedforward control framework for the ball screw drive system. The feedforward control framework includes arranging a feedforward controller between the input end and the second indicator light, and the feedforward controller is connected in parallel with the feedback controller; Combine the feedback control framework and the feedforward control framework to obtain the final control framework of the ball screw drive system; Use the final control framework to control the ball screw drive system.

2. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 1, wherein The system model includes: A workbench with a pair of support bearings arranged thereon; A ball screw, one end of which is mounted on one of the support bearings and is connected to a coupling and a servo drive motor in sequence, and the other end of the ball screw is mounted on the other support bearing; multiple balls are arranged in the spiral groove of the ball screw; A lead screw nut, one end of which is arranged on the workbench, and the other end of which is meshed and connected to the ball screw through multiple balls.

3. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 2, wherein The steps of constructing the system model of the ball screw drive system include: Obtain the kinetic energy and potential energy of the system model according to all the equivalent parameters; According to the difference between the kinetic energy and the potential energy, Coulomb friction and viscous friction, and use the Euler-Lagrange equation to describe the motion trajectory of the system model in the generalized coordinate system to obtain the dynamic equation of the system model.

4. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 3, characterized in that, The expression of the kinetic energy of the system model is: Among them, E k represents the kinetic energy of the system model, J m represents the moment of inertia of the servo drive motor, represents the derivative of the rotation angle of the servo drive motor, J b represents the moment of inertia of the ball screw, represents the derivative of the rotation angle at which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, M b represents the mass of the ball screw, represents the derivative of the radial displacement of the support bearing, represents the derivative of the axial displacement of the support bearing, M t represents the mass of the workbench, represents the derivative of the displacement of the workbench in the vertical direction, represents the derivative of the displacement of the workbench in the horizontal direction; The expression of the potential energy of the system model is: Among them, F p represents the potential energy of the system model, k g represents the stiffness of the coupling, θ m represents the rotation angle of the servo drive motor, θ b represents the rotation angle at which the torque output by the servo drive motor drives the ball screw to rotate through the coupling, k s represents the contact stiffness between the ball screw and the screw nut, θ n represents the relative rotation angle of the screw nut, k e represents the axial equivalent stiffness between the ball screw and the support bearing, x b represents the axial displacement of the support bearing, k t represents the contact stiffness between the workbench and the linear guide, and v represents the displacement of the workbench in the horizontal direction; The expression of the dynamic equation of the system model is: Among them, represents the second derivative of the rotation angle of the servo drive motor, f vm represents the viscous friction coefficient of the servo drive motor, Q cm represents the Coulomb friction force acting on the servo drive motor in the working state, τ m represents the torque output by the servo drive motor, P h represents the lead of the ball screw, represents the second derivative of the rotation angle of the ball screw rotated by the torque output by the servo drive motor through the coupling, f vb represents the viscous friction coefficient of the ball screw.

5. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 1, characterized in that The feedback controller adopts PID feedback control, and the expression of the PID feedback control is: where, u fb (t) represents the output signal of the feedback controller at the t-th moment, k p represents the proportional gain of the feedback controller, e(t) represents the signal tracking error of the ball screw drive system at the t-th moment, e(t) = |y(t) - r(t)|, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, r(t) represents the reference output signal of the ball screw drive system at the t-th moment, k i represents the integral gain of the feedback controller, e(τ) represents the system error of the ball screw drive system, k d represents the derivative gain of the feedback controller.

6. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 1, characterized in that The steps of constructing the feedforward control framework of the ball screw drive system on the basis of the feedback control framework include: Sample a data set with the same trajectory but different amplitudes to obtain a sampled data set; In the dSPACE simulation software, use the sampled data set to train the inverse system of the ball screw drive system to obtain multiple control input signals and multiple actual output signals; Superimpose all the control input signals and all the actual output signals to generate an input-output data set; Use the sliding window method to perform offline reconstruction on the input-output data set and introduce future information to convert the causal relationship of the ball screw drive system into a non-causal relationship to obtain a feedforward data training set; Determine that the feedforward controller adopts Gaussian kernel feedforward control and select the Matern kernel function as the kernel function of the Gaussian kernel feedforward control; According to the mapping relationship between the input and output of the feedforward data training set, a feedforward control framework of the ball screw drive system is constructed by using a Gaussian process regression model.

7. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 6, characterized in that, The expression of the Matern kernel function is: Among them, k(x, x ′ ) represents the covariance function between the input point x and the input point x ′ , l represents the hyperparameter, d(x, x ′ ) represents the distance between the input point x and the input point x ′ , x represents the x-th input point, and x ′ represents the x ′ -th input point.

8. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 6, characterized in that, The expression of the ball screw drive system is: P: y(t) = g(W t , E t ) (6) Among them, P represents the ball screw drive system, y(t) represents the actual output signal of the ball screw drive system at the t-th moment, and g(W t , E t ) represents the state equation of the ball screw drive system at the t-th moment, W t represents all input signals of the ball screw drive system up to the t-th moment, and E t represents all output signals of the ball screw drive system up to the t-th moment; The expression of the causal relationship of the ball screw drive system is: P1: b1(t) = f1[a(t), a(t - 1), …, a(t - n c )] (7) Among them, P1 represents the causality of the ball screw drive system, b1(t) represents the response value of the causality of the ball screw drive system at the t-th moment, f1(·) represents the first nonlinear function, and a(t - n c ) represents all historical input signals of the ball screw drive system in the past t - n c moments; The expression of the non-causal relationship of the ball screw drive system is: P2: b2(t) = f2[a(t + n ac ), a(t + n ac - 1), …, a(t - n c )] (8) Among them, P2 represents the non-causality of the ball screw drive system, b2(t) represents the response value of the non-causality of the ball screw drive system at the t-th moment, f2(·) represents the second non-linear function, a(t + n ac ) represents all future input signals at the future time t + n ac , and t + n ac -1 represents all future input signals at the future time t + n ac -1.

9. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 8, wherein The expression of the input-output data set is: D = {X, u} (9) Among them, D represents the input-output data set, and X represents the training matrix. u represents the training objective, u = (u1, u2, …, u M ) T , where u M represents the Mth training objective, M represents the number of training objectives, x N represents the Nth training sample, N represents the number of training samples, y(N - 1) represents the output corresponding to the (N - 1)th training sample, and T represents the transpose operation.

10. The control method of the ball screw drive system based on Gaussian kernel feedforward compensation according to claim 9, characterized in that, The expression of the feedforward data training set is: Among them, X * represents the feedforward data training set, and X *,G-1 represents the (G-1)th reference signal, r represents the output corresponding to the reference signal, and r(G-1) represents the output corresponding to the (G-1)th reference signal.

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