Speed loop identification method of precise two-dimensional motion platform for controller optimization

Abstract

The invention discloses a controller optimization-oriented speed loop identification method for a precise two-dimensional motion platform. The method comprises the following steps of: 1, performing multi-band excitation by adopting a sine sweep frequency signal and acquiring a speed response; 2, performing Fourier transform on the input and output signals to obtain frequency domain features; 3, calculating amplitude-frequency characteristics and phase-frequency characteristics through a frequency-response function; and 4, fitting a high-order transfer function model containing gain, zero point and multi-pole parameters based on Bode diagram data, and finally obtaining a frequency domain identification result. Through a systematic frequency domain modeling process, the dynamic characteristics of the precise motion platform can be accurately represented, a reliable basis is provided for parameter optimization of a controller, and the method is particularly suitable for performance improvement of a high-precision motion control system, so that the problems of low control precision and poor stability of a precise two-dimensional motion platform system in the prior art are solved; and the positioning precision and stability of the precise two-dimensional motion platform system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of system identification and motion control, and more specifically, to a speed loop identification method for a precision two-dimensional motion stage for controller optimization. Background Art

[0002] With the rapid development of modern technology, the demand for high-precision motion control is increasing continuously. Especially in the fields of precision manufacturing and semiconductors, as a core component, the positioning accuracy and dynamic performance of the precision two-dimensional motion stage directly affect the processing quality and production efficiency of the system. The precision motion system integrates position detection, drive, guidance, and control technologies, and is the key to high-precision motion control.

[0003] As one of the drive elements of the motion stage, the linear motor gradually replaces the traditional rotary motor due to its advantages such as high speed and acceleration, high positioning accuracy, and unrestricted motion stroke. Therefore, the research on precision two-dimensional motion stages is a hot topic in the fields of precision machining and measurement.

[0004] Existing research shows that the linear motor has significant advantages in the engineering application of two-dimensional motion stages with its direct drive method, but it also faces many technical challenges at the electrical control level. Some controller parameters of the linear motor are difficult to be set under the guidance of theory, making it unable to meet the high positioning accuracy requirements in a short time, which affects the precision positioning performance of the motion platform.

[0005] In order to achieve the optimal control performance of the linear motor and meet the requirements of high-precision motion control, the existing technology mostly adopts the manual trial-and-error method for the problem of obtaining motor control parameters. Although certain achievements have been made in improving the control accuracy of the linear motor, in the practical application of large-stroke and high-precision motion stages, it is still difficult to meet the strict requirements of high-precision positioning, stability, etc. of the motion control system for modern precision machining and measurement. Summary of the Invention

[0006] The present invention, in order to overcome the deficiencies of the prior art, provides a speed loop identification method for a precision two-dimensional motion stage for controller optimization, in order to comprehensively characterize the amplitude-frequency, phase-frequency characteristics and multi-order dynamic response laws of its speed loop control system, and provide accurate frequency characteristic basis for the optimization of controller parameters; thereby effectively improving the speed control accuracy, dynamic response stability and anti-interference ability under complex working conditions of the precision motion stage, and supporting the breakthrough of the motion control performance of high-precision industrial equipment.

[0007] The present invention adopts the following technical solutions to achieve the above invention purpose:

[0008] The speed loop identification method for a precision two-dimensional motion stage for controller optimization of the present invention is characterized by including the following steps:

[0009] S1. Apply excitation signals \(u = \) to the precision two - dimensional motion stage for sweep - frequency testing to obtain the velocity response signal \(y=\) , where represents the \(k\) - th excitation signal at time \(t\), and \(u(t)=A\sin(\) \()\), \(A\) is the amplitude of a single excitation signal, represents the frequency, \(y(t)\) represents the velocity response signal obtained from the \(k\) - th sweep - frequency test at time \(t\), and \(y(t)=B\sin(\) +\) \()\), \(B\) represents the amplitude of a single velocity response signal, represents the phase angle, \(k = 1,2,\cdots,K\); \(K\) represents the total number of signals;

[0010] S2. Use equations (1) and (2) to perform Fourier transforms on \(u(t)\) and \(y(t)\) respectively, and correspondingly obtain the frequency - domain response of the \(k\) - th excitation signal and the frequency - domain response of the \(k\) - th velocity response signal:

[0011] (1)

[0012] (2)

[0013] In equations (1) and (2), \(j\) represents the imaginary unit, represents the frequency of the \(k\) - th excitation signal; \(j\) represents the component at the \(k\) - th frequency;

[0014] S3. Use equation (3) to obtain the \(k\) - th frequency response function :

[0015] (3)

[0016] S4. Use equation (4) to obtain the \(k\) - th amplitude - frequency characteristic of the precision two - dimensional motion stage:

[0017] (4)

[0018] In equation (3), represents the absolute value;

[0019] S5. Use equation (5) to obtain the \(k\) - th phase - frequency characteristic \(\varphi(\) ):

[0020] (5)

[0021] S6. Draw the Bode plot of the precision two-dimensional motion stage according to Equations (4) and (5), and fit the high-order transfer function model shown in Equation (6) according to the Bode plot:

[0022] (6)

[0023] In Equation (6), is the gain of the precision two-dimensional motion stage, is the zero time constant, are the time constants of the first pole, the second pole, and the third pole respectively, and s is the integral in the time domain;

[0024] S7. Let s = jω, where ω represents the angular frequency and ω = , so as to obtain the frequency-domain identification result of the precision two-dimensional motion stage using Equation (7) :

[0025] (7).

[0026] An electronic device according to the present invention includes a memory and a processor, characterized in that the memory is used to store a program for supporting the processor to execute the speed loop identification method, and the processor is configured to execute the program stored in the memory.

[0027] A computer-readable storage medium according to the present invention, characterized in that a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the speed loop identification method when run by a processor.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] 1. The present invention identifies the speed loop of the precision two-dimensional motion stage, simplifies the complexity of the model, improves the efficiency of optimizing the controller parameters, and thus improves the performance of the two-dimensional motion stage such as positioning accuracy and stability. The present invention can meet the requirements of high-precision applications such as precision machining and semiconductor manufacturing for motion control systems, and has a wide range of application prospects.

[0030] 2. The present invention adopts a swept-frequency test method combining multi-frequency sine signals, covering a wide frequency band range from low frequency to high frequency, and solves the defect that the traditional manual trial-and-error method can only obtain local response data in a limited frequency band. Compared with single-frequency excitation, this method can comprehensively stimulate the dynamic characteristics of the precision two-dimensional motion stage in the full frequency domain, thus significantly improving the completeness and accuracy of subsequent model identification, and laying a data foundation for wide-band controller optimization.

[0031] 3. The present invention converts the time-domain signal into a frequency-domain response through Fourier transform, and combines the quantitative calculations of the frequency response function, amplitude-frequency characteristic, and phase-frequency characteristic, breaking through the technical barriers that traditional time-domain analysis is difficult to separate noise interference and cannot accurately extract the phase lag characteristic. This technical means can accurately quantify the gain attenuation and phase shift laws of the system at different frequencies, thus effectively solving the problems of low parameter tuning efficiency and poor robustness caused by the manual trial-and-error method relying on empirical judgment.

[0032] 4. The present invention fits a high-order transfer function model containing zeros and third-order poles through Bode plot data, innovatively modeling the system dynamic characteristics, and breaking through the technical limitations that the simplified second-order model in the prior art cannot characterize the complex non-linear dynamics of the linear motor drive system (such as resonance, friction hysteresis, etc.). This model can accurately describe the multi-physical field coupling effects such as mechanical resonance and electromagnetic coupling within a wide frequency band, thereby providing a high-fidelity mathematical model that matches the actual working conditions for controller design.

[0033] 5. The present invention establishes a direct mapping relationship between the frequency response characteristics and the frequency-domain correction parameters of the controller by converting the transfer function model into a frequency-domain expression. Compared with the traditional trial-and-error method that can only achieve static parameter adjustment, this method can dynamically optimize the PID parameters or the feed-forward compensation coefficient according to the frequency-domain indicators such as phase margin and gain margin, thereby significantly improving the anti-interference ability and tracking accuracy of the moving stage under complex working conditions such as high-speed commutation and sudden load changes, and solving the industry problem that it is difficult to theoretically set the control parameters of the linear motor in the background technology. Description of the Drawings

[0034] Figure 1 is the control block diagram of the precision two-dimensional moving stage;

[0035] Figure 2 is the frequency characteristic curve diagram of the moving stage;

[0036] Figure 3 is the control scheme block diagram of the precision two-dimensional moving stage;

[0037] Figure 4 is the PDFF adjustment structure diagram. Detailed Embodiments

[0038] In this embodiment, a speed loop identification method for a precision two-dimensional motion stage optimized for a controller aims to construct a high-precision frequency-domain dynamic model of the precision two-dimensional motion stage. At the same time, speed response data is obtained through swept-frequency testing of multi-frequency excitation signals, and a system transfer function model is constructed by combining frequency-domain analysis to deeply analyze the nonlinear dynamic behavior of the system within a wide frequency band. The mechanical structure of this method adopts a stacked layout, and both the X-axis and Y-axis are driven by linear motors; at the same time, a grating sensor is configured to measure the displacement information of the motion stage in two axial directions in real time. The control system is connected to the signals of the linear motor and the grating sensor, and its core lies in the speed loop identification method. This method inputs a sine excitation signal into the servo system, gradually obtains the frequency characteristics and transfer function model of the motion stage system, and optimizes the parameters of the PDFF controller, namely the integral gain, proportional gain, and feedforward gain, accordingly, and finally realizes closed-loop control to ensure high-precision positioning of the motion stage during high-speed movement and acceleration. The speed loop identification method includes the following steps:

[0039] The precision two-dimensional motion stage described in this example is as Figure 1 shown, and it consists of a motion stage body G(s), a feedback controller C(s), a mechanical guide P, a grating scale H(s), a driver, and a trajectory generator R(t); the motion stage body is arranged on the mechanical guide and performs linear motion along the mechanical guide, and the displacement is measured by the grating scale; the output of the trajectory generator R(t) is the reference input r(t), the output of the feedback controller is the current u, and the output of the motion stage G(s) is the actual position y; the error value e between the reference input r(t) and the actual output y is input to the feedback controller C(s), and the output value u of the feedback controller is input to the motion stage G(s).

[0040] S1. The servo system uses excitation signals u = with different frequencies to perform swept-frequency testing on the precision two-dimensional motion stage, and obtains the speed response signal y = , where represents the k-th excitation signal at time t, and (t) = Asin( ), A is the amplitude of a single excitation signal, represents 's frequency, (t) represents the speed response signal obtained from the k-th swept-frequency test at time t, and (t) = B sin( + ), B represents the amplitude of a single speed response signal, represents 's phase angle, k = 1, 2,..., K; K represents the total number of signals;

[0041] By collecting these input and output signals, a sample data set can be constructed to obtain the displacement and velocity information of the moving stage during movement, and based on this, the velocity response curve of the moving stage can be plotted.

[0042] S2. Respectively use Equation (1) and Equation (2) to (t) and (t) for Fourier transform, and correspondingly obtain the frequency-domain response of the k-th excitation signal and the frequency-domain response of the k-th velocity response signal:

[0043] (1)

[0044] (2)

[0045] In Equation (1) and Equation (2), j represents the imaginary unit, represents the frequency of the k-th excitation signal; j represents the component at the k-th frequency;

[0046] Collect the displacement response data of the moving stage at different frequencies, and then generate the amplitude-frequency characteristic curve and phase-frequency characteristic curve, as Figure 2 shown.

[0047] S3. Use Equation (3) to obtain the k-th frequency response function :

[0048] (3)

[0049] S4. Use Equation (4) to obtain the k-th amplitude-frequency characteristic of the precision two-dimensional moving stage:

[0050] (4)

[0051] In Equation (3), represents the absolute value.

[0052] S5. Use Equation (5) to obtain the k-th phase-frequency characteristic ϕ( ) of the precision two-dimensional moving stage:

[0053] (5)

[0054] Figure 2 is the system block diagram of the moving stage velocity loop, and this transfer function model can be expressed as:

[0055]

[0056] Among them, r(t) represents the reference input, that is, the desired speed of the motor; C(s) is the transfer function of the controller, which is the transfer function of the PDFF controller; G(s) is the transfer function of the controlled object (two-dimensional motion stage), that is, the transfer function from the motor current to the motor speed; H(s) is the transfer function of the feedback; y(t) is the output, that is, the actual speed output of the motor; u is the input of the controlled object, corresponding to the current of the motor.

[0057] S6. Draw the Bode diagram of the precision two-dimensional motion stage according to Equations (4) and (5), and fit the high-order transfer function model shown in Equation (6) according to the Bode diagram:

[0058] (6)

[0059] In Equation (6), is the gain of the precision two-dimensional motion stage, is the zero time constant, are the time constants of the first pole, the second pole, and the third pole respectively, and s is the integral in the time domain.

[0060] S7. Let s = jω, where ω represents the angular frequency and ω = , so as to obtain the frequency-domain identification result of the precision two-dimensional motion stage by using Equation (7) :

[0061] (7).

[0062] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0063] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium. When the computer program is run by a processor, it executes the steps of the above method.

[0064] Experiment:

[0065] Figure 3 In [], the motion stage controller is designed by using a PDFF controller: By using a PDFF controller, precise control of the motion stage is achieved by adjusting the proportional gain, integral gain, and feedforward gain. Among them, the feedforward gain is used to compensate for the dynamic lag error in the acceleration stage of the motion stage, the integral gain is used to eliminate the steady-state error, and the proportional gain is used to adjust the system response speed.

[0066] The PDFF control equivalent model is as Figure 4 shown as:

[0067]

[0068] In the formula, is the current, is the reference speed, is the feedback speed, is the integral gain, is the proportional gain, is the feed-forward gain.

[0069] The feedforward gain is mainly used to compensate for the dynamic lag error generated by the motion platform during the acceleration phase, the integral gain is used to eliminate the system steady-state error, and the proportional gain is used to adjust the system response speed to ensure fast response and stable control of the system.

[0070] In the above scheme, the feedforward gain is mainly used to compensate for the dynamic lag error generated by the motion platform during the acceleration phase, the integral gain is used to eliminate the system steady-state error, and the proportional gain is used to adjust the system response speed to ensure fast response and stable control of the system.

[0071] The optimized controller parameters are applied to the actual system to achieve closed-loop control, so that the precision two-dimensional motion table can complete the target trajectory motion stably, quickly and accurately, meeting the motion control needs of high-demand applications such as modern precision machining and measurement.

Claims

1. A velocity loop identification method for a precision two-dimensional motion stage for controller optimization, characterized in that: The following steps are involved: S1, using different frequency excitation signals u= Perform a frequency sweep test on the precision two-dimensional motion stage to obtain the velocity response signal y= ,in, represents the kth excitation signal at time t, and (t)=Asin( ), A is the amplitude of a single excitation signal, express The frequency, (t) represents the speed response signal obtained by the kth frequency sweep test at time t, and (t) = B sin( + ), B represents the amplitude of a single velocity response signal, express The phase angle, k=1,2,…,K; K represents the total number of signals; S2, using formula (1) and formula (2) respectively (t) and (t) Perform Fourier transform and obtain the frequency domain response of the kth excitation signal And the frequency domain response of the kth speed response signal : (1) (2) In formula (1) and formula (2), j represents an imaginary unit, represents the frequency of the kth excitation signal; j represents the component at the kth frequency; S3. Use formula (3) to get the kth frequency response function : (3) S4. Use formula (4) to obtain the kth amplitude-frequency characteristic of the precision two-dimensional motion stage: : (4) In formula (3), Indicates absolute value; S5. Using formula (5), we can get the kth phase-frequency characteristic φ( ): (5) S6. Draw the Bode diagram of the precision two-dimensional motion stage according to equations (4) and (5), and fit the high-order transfer function model shown in equation (6) according to the Bode diagram: (6) In formula (6), is the gain of the precision two-dimensional motion stage, is the zero time constant, The time constants of the first, second, and third poles respectively, and s is the integral in the time domain; S7, let s = jω, ω represents the angular frequency, and ω = , and then use formula (7) to get the frequency domain identification result of the precision two-dimensional motion stage : (7)。 2. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the speed loop identification method according to claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the speed loop identification method according to claim 1 are executed.

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