Hybrid control method suitable for long-stroke rapid tool servo system

Abstract

The invention discloses a hybrid control method suitable for a long-stroke rapid cutter servo system, and the method comprises the steps: obtaining a controlled object model according to the sweep frequency of an open-loop system and system identification, and constructing a closed-loop hybrid control algorithm model based on proportional integral differential control, sliding mode control and speed / acceleration feedforward control; by continuously calculating system output and control errors, parameter adjustment of a control algorithm is completed; the hybrid control algorithm model is written into PMAC hardware, step and sine response testing and control parameter optimization adjustment are completed, and high-precision machining of the long-stroke rapid tool servo system is achieved. According to the hybrid control method, the response speed and the control precision of the system can be remarkably improved, nonlinear disturbance in a complex machining task can be adapted, and a high-stability and low-inertia-force solution is provided for ultra-precision machining of a surface microarray, an optical free-form surface and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial control, and relates to a control method for a fast tool servo system, specifically to a hybrid control method applicable to a long-stroke fast tool servo system. Background Art

[0002] With the rapid development of fields such as optics, aerospace, and precision instruments, the demand for ultra-precision optical components is increasing continuously. A free-form surface refers to a non-rotationally symmetric surface with irregular contour variations, which has a greater design freedom compared to traditional spherical and aspherical surfaces. It can effectively reduce the volume of an optical system, correct geometric aberrations, and thus significantly improve the overall performance of the optical system. It is considered to be the core component of the next-generation optical system. As a high-precision machining technology, the fast tool servo technology is widely used in the machining of free-form surfaces and surface microstructures in multiple fields.

[0003] Current control strategies are generally divided into two types: model-based and feedback-based. The model-based control part relies on accurate system modeling, and avoids overshoot or oscillation by predicting future changes (such as acceleration or deceleration); the feedback-based control part adjusts the control input (such as motor torque or speed) to correct the deviation by monitoring the deviation between the system output and the target in real time, ensuring that the system performance meets the design requirements. For a long-stroke fast tool servo system, the increase in stroke leads to changes in system inertia and amplification of external disturbances. The system faces problems such as large overshoot, long adjustment time, and difficulty in tuning control algorithm parameters under high-frequency vibration. Therefore, traditional control algorithms (such as pure PID control) are difficult to meet the dual requirements of speed and accuracy of the system in a high-dynamic environment, and there is an urgent need to design an advanced control strategy that can adapt to complex dynamic characteristics to improve the response speed, accuracy, and stability of the system. Summary of the Invention

[0004] In view of the control requirements of the above long-stroke fast tool servo system in high-precision and large-stroke machining, the present invention provides a hybrid control method applicable to a long-stroke fast tool servo system.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] A hybrid control method applicable to a long-stroke fast tool servo system includes the following steps:

[0007] Step 1: Perform open-loop system frequency sweeping on the long-stroke fast tool servo system to obtain open-loop system target output and actual output data;

[0008] Step 2: Perform system identification on the obtained data, and select the state space equation Perform fitting to obtain the state - space model of the open - loop system, where: dx / dt is the rate of change of the system state vector with respect to time; x(t) is the system state vector; u(t) is the control input vector; e(t) is the error term; y(t) is the system output vector; A is the system matrix; B is the input matrix; C is the output matrix; D is the direct transmission matrix; K is the gain matrix;

[0009] Step 3: By initializing the parameters of the hybrid control method and combining with the state - space model obtained in Step 2, construct a closed - loop hybrid control algorithm model based on proportional - integral - derivative control, sliding - mode control, and velocity / acceleration feed - forward control, where:

[0010] The proportional - integral - derivative control means that by adjusting the proportional gain K p , integral gain K i and derivative gain K d , amplify the error signal, the integral of the error signal, and the derivative of the error signal respectively to generate the main control output signal where e(k) is the error signal, Δe(k) is the rate of change of the error signal, and k is the sampling time;

[0011] The sliding - mode control means that by designing the sliding - mode surface and reaching law, the system can adjust the auxiliary control output signal according to the sliding - mode state where K1, K2, K3, K4 are sliding - mode control parameters; the sliding - mode surface is the second - order sliding - mode surface S = K1e(k)+k2(Δe(k));

[0012] The velocity / acceleration feed - forward control means that by introducing the target velocity and acceleration signals, calculate the velocity / acceleration feed - forward correction signal u(k) FF =[K vff CV(k)+K aff CA(k)], where K vff is the velocity feed - forward gain, K aff is the acceleration feed - forward gain, CV(k) and CA(k) are the target velocity and target acceleration respectively;

[0013] Step 4: Calculate the output control signal u(k)=u(k) SMC +u(k) PID +u(k) FF , input u(k) into the long - stroke quick - tool system, calculate the actual output displacement signal x(k) according to the state - space equation, and feedback this signal back to the controller;

[0014] Step 5: Calculate the difference between the system input and output to obtain the control error e(k) of the system, and output the control law through the hybrid control method to complete the closed - loop control of the system:

[0015] e(k) = x r (k) - x(k)

[0016] where x r is the input target displacement signal;

[0017] Step 6: Optimize and adjust the parameters in the hybrid control method according to the control error to complete the parameter tuning of the control method;

[0018] Step 7: Write the established closed-loop hybrid control algorithm model into the controller PMAC hardware to complete the hardware construction of the hybrid control method;

[0019] Step 8: Complete the initialization of the control method parameters in the controller PMAC hardware according to the parameters adjusted in Step 6;

[0020] Step 9: Complete the step response and sine response tests of the actual system, and further optimize the parameters of the control method according to the test results to complete the parameter adjustment of the long-stroke fast tool servo system.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. The hybrid control method of the present invention combines the advantages of proportional integral derivative, feedforward control and sliding mode control. It realizes the precise compensation of the dynamic characteristics of the system through proportional integral derivative control and feedforward control, effectively reducing the influence of inertial force on the system stability; uses sliding mode control to further compensate for the overshoot of the system to ensure high-precision motion of the system within the millimeter-level stroke range.

[0023] 2. The hybrid control method of the present invention can not only significantly improve the response speed and control accuracy of the system, but also adapt to the non-linear disturbances in complex machining tasks, providing a solution with high stability and low inertial force for ultra-precision machining such as surface microarrays and optical free-form surfaces.

[0024] 3. The hybrid control method of the present invention has significant practicality and broad application prospects, and can meet the stringent requirements of the ultra-precision machining field for high-precision and long-stroke control. Description of the Drawings

[0025] Figure 1 is the flowchart of the hybrid control method applicable to the long-stroke fast tool servo system;

[0026] Figure 2 is the control block diagram of the hybrid control method applicable to the long-stroke fast tool servo system;

[0027] Figure 3 is the actual schematic diagram of the control system implementation case of the hybrid control algorithm for controlling the long-stroke fast tool servo mechanism;

[0028] Figure 4 is the step response curve of 1mm for the hybrid control algorithm;

[0029] Figure 5 is the sine response curve of the hybrid control algorithm and PID control with 0.43mm and 50Hz as the input signal. Specific implementation manners

[0030] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0031] The present invention provides a hybrid control method applicable to a long-stroke fast tool servo system. The controlled object model is obtained according to the open-loop system frequency sweep and system identification, and a closed-loop hybrid control algorithm model based on proportional-integral-derivative control, sliding mode control, and velocity / acceleration feedforward control is constructed; by continuously calculating the system output and control error, the control algorithm parameters are adjusted; the hybrid control algorithm model is written into the PMAC hardware to complete the step and sine response tests and optimize the control parameters, so as to achieve high-precision machining of the long-stroke fast tool servo system. As Figure 1 shown, the specific steps are as follows:

[0032] Step 1: Use the sine frequency sweep function of the PMAC controller to perform an open-loop frequency sweep on the long-stroke fast tool servo system by setting parameters such as amplitude, start frequency, end frequency, and sweep time, and obtain the data of the target output voltage and actual output displacement of the open-loop system.

[0033] Step 2: Use the system identification toolbox in Matlab to perform system identification on the obtained data, and select the state space equation for fitting to obtain the state space model of the open-loop system, where: dx / dt is the change rate of the system state vector with time; x(t) is the system state vector; u(t) is the control input vector; e(t) is the error term; y(t) is the system output vector; A is the system matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; K is the gain matrix.

[0034] Step 3: According to Figure 2 it can be seen that the hybrid control method consists of three parts: proportional-integral-derivative control, sliding mode control, and velocity / acceleration feedforward control. By initializing the parameters of the hybrid control method and combining the state space model of the long-stroke fast tool system obtained in Step 2, a Simulink model of the hybrid control method is constructed.

[0035] According to the signal period of the system, the value of the target signal in the first period is input into the hybrid control method. The output signal is subtracted from the target signal, and the difference is input into the hybrid control method to complete the closed-loop control of the system.

[0036] Step 4: Proportional-Integral-Derivative (PID) control is a classic control algorithm that uses the error signal, the integral, and the derivative of the error signal to form a control law:

[0037]

[0038] where K p 、K i 、K d are the proportional, derivative, and integral gains respectively, e(k) is the error signal, Δe(k) is the rate of change of the error signal, and k is the sampling time. According to the above formula, the main control signal u(k) is calculated by the proportional-integral-derivative algorithm PID .

[0039] Step 5: Sliding Mode Control (SMC) is a non-linear and discontinuous control algorithm that can adjust the control law in real time according to the state of the controlled object and has the advantage of being insensitive to parameter changes and disturbances. Since the long-stroke fast tool servo system is prone to overshoot under high-frequency vibration, the present invention innovatively adds sliding mode control, and the overshoot of the system is effectively controlled by the sliding mode control, reducing the overshoot of the step response to zero.

[0040] The key to sliding mode control lies in the design of the sliding mode surface, the reaching law, and the control law. The present invention designs a second-order sliding mode surface S = K1e(k) + K2(Δe(k)), and designs the sliding mode control law in the form of a power series |e(k)|)), where K1, K2, K3, and K4 are all sliding mode control parameters. According to the above formula, the auxiliary control output signal u(k) is calculated by the sliding mode control algorithm SMC .

[0041] Step 6: Since the non-linearity of the sliding mode control will prolong the adjustment time of the system and cause system chattering, the present invention proposes a control algorithm structure of speed / acceleration feedforward assisted sliding mode. The speed / acceleration feedforward control law u(k) FF = [K vff CV(k) + K aff CV(k)], where K vff is the speed feedforward gain, K aff is the acceleration feedforward gain, and CV(k) and CA(k) are the target speed and target acceleration respectively. Appropriate K affThe value can reduce the inertial error of the system, especially for the FTS system where the inertial force is proportional to the square of the frequency. According to the above formula, the feedforward correction signal u(k) is calculated by the velocity / acceleration feedforward control algorithm FF .

[0042] Step 7: As Figure 2 shown, the total output of the controller is equal to the superposition of three control outputs, that is, the final control signal u(k) = u(k) SMC + u(k) PID + u(k) FF . The controller output signal u(k) is input into the long-stroke fast tool system, and the output displacement signal x is calculated according to the above state space equation. This signal is fed back to the controller through the grating scale measurement

[0043] Step 8: The control error of the system is obtained by continuously calculating the difference between the input and output of the system. The error calculation formula: e(k) = x r (k) - x(k), where x r is the input target displacement signal, and x is the above output displacement signal. Optimize and adjust the parameters in the control algorithm according to the system error calculated above to complete the parameter tuning of the control algorithm

[0044] Step 9: Based on the established Simulink hybrid control algorithm model, use the custom algorithm function in the multi-axis motion controller PMAC to write the hybrid control method into the motion controller hardware in the form of a C language structure to complete the hardware construction of the hybrid control method

[0045] Step 10: Initialize the control method parameters in the PMAC controller hardware according to the parameters adjusted in Step 8

[0046] Step 11: Use the PMAC controller to complete the step response and sine response tests of the actual system. Further optimize the parameters of the control method according to the test results (such as rise time, adjustment time, overshoot, steady-state error, phase error, etc.) to complete the parameter adjustment of the long-stroke fast tool servo system

[0047] Figure 3 is the actual schematic diagram of the control system implementation case of the hybrid control algorithm for controlling the long-stroke fast tool servo mechanism. The hybrid control algorithm is directly written into the motion controller, and the operation of the mechanism is controlled by the difference between the feedback signal of the grating scale received and the set target position

[0048] Figure 4 is the 1mm step response curve of the hybrid control algorithm. As Figure 4 can be seen, the system has no overshoot, and the adjustment time is 0.0134s

[0049] Figure 5 is the sine response curve of the hybrid control algorithm and PID control under the input signal of 0.43mm and 50Hz. It can be seen from Figure 5 that the following error of the hybrid control algorithm is 0.871%, which is significantly lower than the following error of 3.153% of the PID control algorithm.

[0050] Compared with the prior art, the hybrid control method proposed by the present invention has the following advantages:

[0051] 1. By establishing the system identification and control algorithm model, the problem of difficult parameter tuning of the fast tool servo system in engineering is solved, and the system tuning speed is improved.

[0052] 2. The innovative introduction of sliding mode control solves the problem of large overshoot of the fast tool servo system under high-frequency vibration, has strong anti-interference ability, and has a good control effect on nonlinear systems.

[0053] 3. The combination of sliding mode control and velocity / acceleration feedforward improves the dynamic response speed of the system, providing a new design for the rapid working stroke adjustment of the fast tool servo system.

[0054] 4. The combination of proportional integral derivative, velocity / acceleration feedforward control and sliding mode control significantly improves the response speed and control accuracy of the system, and effectively overcomes the cutting force interference in the actual machining of the long-stroke fast tool servo system.

[0055] 5. The present invention provides a solution with high stability and rapidity for ultra-precision machining such as surface microarrays and optical free-form surfaces.

Claims

1. A hybrid control method applicable to a long-stroke fast tool servo system, characterized in that The method includes the following steps: Step 1: Perform open-loop system frequency sweeping on the long-stroke fast tool servo system to obtain the open-loop system target output and actual output data; Step 2: Conduct system identification on the acquired data and select the state-space equation for fitting to obtain the state-space model of the open-loop system, where: dx / dt is the rate of change of the system state vector with respect to time; x(t) is the system state vector; u(t) is the control input vector; e(t) is the error term; y(t) is the system output vector; A is the system matrix; B is the input matrix; C is the output matrix; D is the direct transmission matrix; K is the gain matrix; Step 3: By initializing the parameters of the hybrid control method and combining the state-space model obtained in Step 2, construct a closed-loop hybrid control algorithm model based on proportional-integral-derivative control, sliding mode control, and velocity / acceleration feedforward control; Step 4: Calculate the output control signal \(u(k)=u(k)\) SMC +u(k) PID +u(k) FF , \(u(k)\) SMC is the auxiliary control output signal, \(u(k)\) PID is the main control output signal, \(u(k)\) FF is the speed / acceleration feedforward correction signal. Input \(u(k)\) into the long-stroke quick tool servo system, calculate the actual output displacement signal \(x(k)\) according to the state space equation, and feedback this signal back to the controller; Step 5: Calculate the difference between the system input and output to obtain the control error e(k) of the system, and output the control law through the hybrid control method to complete the closed-loop control of the system: e(k) = x r (k) - x(k) where x r is the target displacement signal input; Step 6: Optimize and adjust the parameters in the hybrid control method according to the control error to complete the parameter tuning of the control method; Step 7: Write the constructed closed-loop hybrid control algorithm model into the controller PMAC hardware to complete the hardware construction of the hybrid control method; Step 8: Complete the initialization of the control method parameters in the controller PMAC hardware according to the parameters adjusted in Step 6; Step 9: Complete the step response and sine response tests of the actual system, further optimize the parameters of the control method according to the test results, and complete the parameter adjustment of the long-stroke fast tool servo system.

2. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 1, characterized in that In the said Step 1, the long-stroke fast tool servo system is subjected to open-loop frequency sweeping by setting the amplitude, starting frequency, ending frequency, and scanning time.

3. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 1, wherein In the said step 3, the proportional-integral-derivative control means that by adjusting the proportional gain K p , the integral gain K i and the derivative gain K d , the error signal, the integral of the error signal and the derivative of the error signal are amplified respectively to generate the main control output signal where e(k) is the error signal, Δe(k) is the rate of change of the error signal, and k is the sampling time.

4. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 1, wherein In the said step 3, the sliding mode control means that by designing the sliding mode surface and the reaching law, the system can adjust the auxiliary control output signal according to the sliding mode state wherein, K1, K2, K3, and K4 are sliding mode control parameters.

5. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 4, characterized in that The sliding mode surface is a second-order sliding mode surface S = K1e(k) + K2(Δe(k)).

6. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 1, wherein In the said step 3, the speed / acceleration feedforward control means that by introducing the target speed and acceleration signals, the speed / acceleration feedforward correction signal u(k) is calculated FF =[K vff CV(k)+K aff CA(k)], where K vff is the speed feedforward gain, K aff is the acceleration feedforward gain, and CV(k) and CA(k) are the target speed and target acceleration respectively.

7. The hybrid control method applicable to a long-stroke fast tool servo system according to claim 1, characterized in that In the said Step 9, the test results include rise time, settling time, overshoot, steady-state error, and phase error.

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