Piezoelectric fast tilting mirror dynamic hysteresis nonlinear suppression method and control device

Abstract

The invention discloses a dynamic hysteresis nonlinearity suppression method and a dynamic hysteresis nonlinearity control device for a piezoelectric fast tilting mirror, solves the problem that the piezoelectric fast tilting mirror depends on a hysteresis model when compensating hysteresis nonlinearity, and belongs to the field of hysteresis nonlinearity compensation and control. The method comprises the steps that real-time collected input voltage x is input into a correction link, output of the correction link is input into a fast tilting mirror, and the fast tilting mirror outputs an angle y; x of different frequency points is input, a correction link coefficient is adjusted to enable x and y to be consistent in phase, the numerical value of the correction link coefficient is determined, and frequency gains and phase deviations of correction links corresponding to all the frequency points are further calculated; and determining the form of the lead phase compensator, identifying parameters in the lead phase compensator by using the frequency gains and the phase offsets corresponding to all the frequency points, replacing the correction link by using the lead phase compensator after the parameters are identified, and performing dynamic hysteresis nonlinear suppression on the piezoelectric fast tilting mirror.

Description

Technical Field

[0001] The invention relates to a method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror, and belongs to the field of hysteresis nonlinear compensation and control. Background Art

[0002] Piezoelectric ceramics are a functional material with inverse piezoelectric effect. They can convert electrical energy into mechanical energy, thereby outputting force or displacement. They are a very important driver. Due to their unique advantages such as fast response, high precision, and small size, fast-tilting mirrors driven by piezoelectric ceramics are widely used in free-space optical communications, laser processing and manufacturing, and adaptive optics. However, in actual engineering applications, the inherent hysteresis nonlinearity of piezoelectric ceramics and the peripheral driving hardware equipment together lead to dynamic hysteresis characteristics of the entire fast-tilting mirror. For this nonlinear system, a hysteresis loop with a memory effect appears between its input and output signals. The shape of the hysteresis loop is related to the frequency of the input signal, such as Figure 1 As shown in the figure, the hysteresis loop gradually widens as the input signal frequency increases. This shows that the dynamic hysteresis nonlinearity of the fast-tilt mirror reduces its deflection accuracy at all frequencies, and the impact of the hysteresis nonlinearity increases with increasing frequency.

[0003] Currently, there are two main approaches to suppressing the hysteresis nonlinearity of piezoelectric fast-tilt mirrors. The first involves using input and output data to create a hysteresis model for the hysteresis nonlinear system, then obtaining the corresponding inverse model. Finally, this inverse model is connected in series with the system to compensate for and suppress the dynamic hysteresis characteristics. In this process, various hysteresis models have been proposed, with the Preisach model, the PI model, the Bouc-Wen model, and the Maxwell model being widely used. The second approach involves directly building an inverse model of the hysteresis system. This involves swapping the input and output data and then using the aforementioned model to perform the modeling. Connecting the resulting inverse model in series with the system can compensate for the hysteresis nonlinearity. Compared to the first approach, the second is a very direct method, simplifying the design process of the hysteresis compensator. It is worth noting that both approaches utilize existing hysteresis models and require modeling of the system's dynamic hysteresis characteristics. This computationally intensive and involves numerous parameters. Both existing approaches suffer from the problem of model dependence in compensating for dynamic hysteresis in fast-tilt mirrors. Summary of the Invention

[0004] In order to overcome the problem of a piezoelectric fast-tilt mirror's reliance on a hysteresis model when compensating for hysteresis nonlinearity, the present invention provides a method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast-tilt mirror.

[0005] A method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to the present invention comprises:

[0006] S1. Build an experimental control platform for real-time acquisition of the input voltage x and output angle y of the piezoelectric fast-tilt mirror;

[0007] S2. Construct a correction link, input the real-time collected input voltage x into the correction link, and input the output of the correction link into the fast tilt mirror;

[0008] S3. Input the input voltage x at different frequency points, adjust the correction link coefficient so that the voltage x and the angle y are in phase, and determine the value of the correction link coefficient;

[0009] S4. Calculate the frequency gain and phase offset of the correction link corresponding to all frequency points based on the correction link coefficients of the determined values;

[0010] S5. Determine the form of the advanced phase compensator H(s), identify the parameters in the advanced phase compensator H(s) using the frequency gain and phase offset of the correction link corresponding to all frequency points, replace the correction link with the advanced phase compensator after the identified parameters, and perform dynamic hysteresis nonlinear suppression on the piezoelectric fast tilt mirror.

[0011] Preferably, the correction link is k1+k2s, where k1 and k2 are coefficients of the proportional link and the differential link respectively, and s represents the complex frequency.

[0012] Preferably, in S4, the method for calculating the frequency gain and phase offset of the correction link corresponding to all frequency points is:

[0013] according to Obtain the frequency gain, where j represents the imaginary unit and w i Represents the angular frequency corresponding to the i-th frequency point, i=1,2,…,N, N represents the number of frequency points;

[0014] according to Get the phase shift φ(w i ).

[0015] Preferably, the leading phase compensator H(s) is:

[0016]

[0017] Among them, b m ,…,b1,b0 are the numerator coefficients to be identified, a n ,…,a1,a0 are the denominator coefficients to be identified, and the subscripts m and n are set positive integers, m>n.

[0018] Preferably, m=3, n=2.

[0019] Preferably, in S5, the method for identifying the parameters of the leading phase compensator H(s) using the frequency gain and phase offset of the correction link corresponding to all frequency points includes:

[0020] By setting s = jw i , we can get the gain of the leading phase compensator H(s) corresponding to different frequency points |H(jw i ,θ)| and phase ∠H(jw i ,θ), where θ={a0,a1,…,a n ,b0,b1,…,b m} is the parameter to be identified;

[0021] Set the optimization function to:

[0022]

[0023] According to the optimization function, the parameters θ={a0,a1,L,a n ,b0,b1,L,b m}, and then determine the leading phase compensator H(s).

[0024] The present invention also provides a control device for a piezoelectric fast-tilt mirror, comprising an advanced phase compensator, a PI feedback controller, and a feedback unit; the advanced phase compensator is implemented using the above-mentioned method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast-tilt mirror;

[0025] The voltage x is input to the leading phase compensator, and the input to the PI feedback controller is the error signal e. The output of the PI feedback controller is added to the output of the lead phase compensator and then input to the piezoelectric fast tilt mirror. The piezoelectric fast tilt mirror outputs an angle y, which is input to the feedback unit. The output of the feedback unit is K represents the proportional coefficient of the feedback unit.

[0026] The beneficial effects of the present invention are as follows: the present invention ignores the hysteresis nonlinear characteristics of the fast-tilt mirror, and from the perspective of the system phase, regards the dynamic hysteresis of the fast-tilt mirror as the phase lag of the linear system itself, and uses the advanced phase compensation theory and method to suppress the dynamic hysteresis of the system. The sinusoidal signal tracking experiment at different frequencies verifies the effectiveness of the method proposed in the present invention. It is worth noting that the present invention does not adopt any hysteresis model, but designs an advanced phase compensator for the hysteresis system. On the one hand, the method proposed in the present invention solves the problem of model dependence of the dynamic hysteresis of the fast-tilt mirror compensation; on the other hand, compared with the existing hysteresis model, the advanced phase compensator has the advantages of fewer parameters, simple structure, and simple design. In addition, the present invention completes the suppression of dynamic hysteresis characteristics from the perspective of system phase compensation, providing a different perspective in the field of hysteresis compensation and control. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is the dynamic hysteresis characteristic of the piezoelectric fast tilt mirror;

[0028] Figure 2 is a linear system without hysteresis characteristics, where (a) is the input-output relationship of the linear system at different frequencies; (b) is the input-output relationship of the linear system at different frequencies with a certain phase lag;

[0029] Figure 3 Schematic diagram of the principle of phase advance correction of piezoelectric fast tilt mirror;

[0030] Figure 4 This is the design result of the leading phase compensator in the present invention;

[0031] Figure 5 The present invention provides a method for suppressing dynamic hysteresis of a piezoelectric fast tilt mirror based on an advanced phase compensator.

[0032] Figure 6 Figure 2 is a dynamic hysteresis suppression effect based on the leading phase compensator; wherein, (a) is a curve of output angle versus time when f=1 Hz, (b) is a curve of input voltage versus output angle when f=1 Hz, (c) is a curve of output angle versus time when f=100 Hz, (d) is a curve of input voltage versus output angle when f=100 Hz, (e) is a curve of output angle versus time when f=200 Hz, and (f) is a curve of input voltage versus output angle when f=200 Hz;

[0033] Figure 7 The invention provides a piezoelectric fast tilt mirror composite control method based on an advanced phase compensator;

[0034] Figure 8 It is the composite control effect based on the leading phase compensator. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0036] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0038] Prior art techniques for compensating dynamic hysteresis for piezoelectric fast-tilt mirrors require the use of existing hysteresis models and system hysteresis modeling. This embodiment proposes a method for suppressing dynamic hysteresis characteristics using a leading phase compensator. This method ignores the hysteresis nonlinearity of the fast-tilt mirror and, from the perspective of the system phase, treats the dynamic hysteresis of the fast-tilt mirror as the phase lag of the linear system itself. This method uses a leading phase compensator to suppress the system's dynamic hysteresis. This method provides leading phase compensation for the fast-tilt mirror without requiring system hysteresis modeling, and therefore does not rely on a hysteresis model.

[0039] Figure 1 The dynamic hysteresis characteristics of a piezoelectric fast-tilt mirror are demonstrated. Due to hysteresis, the nonlinear system exhibits a hysteresis loop between the input voltage and the deflection angle at 1 Hz. At 100 Hz and 200 Hz, the hysteresis nonlinearity of the fast-tilt mirror combines with the system dynamics to form dynamic hysteresis characteristics. Figure 2 A linear system without hysteresis effects is shown, from Figure 2 As can be seen in (a), the linear system has good dynamic performance at 1Hz. There is no phase lag between its input and output at the phase frequency, so the relationship between the two is a straight line. As the frequency increases to 100Hz and 200Hz, the output of this linear system gradually lags behind the input due to its own dynamic characteristics, resulting in a phase loop. When this linear system adds a fixed phase lag at each frequency point, the relationship between its input and output is as follows: Figure 2 As shown in (b). It is worth noting that Figure 2 (b) is a linear system without hysteresis characteristics, which shows a phase loop with a certain phase lag, rather than a dynamic hysteresis loop. Strictly speaking, there is an essential difference between the two. Figure 1 and Figure 2 Based on the similarity of (b), the hysteresis characteristic is approximated as a certain phase lag, and the piezoelectric fast tilt mirror is regarded as a linear system with a certain phase lag.

[0040] The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror of this embodiment includes:

[0041] Step 1: Build an experimental control platform for real-time acquisition of the input voltage x and output angle y of the piezoelectric fast-tilt mirror;

[0042] Specifically, a computer host, a fast-tilt mirror driver, and a piezoelectric fast-tilt mirror are connected to build a fast-tilt mirror experimental control platform with the ability to collect input data and output data in real time.

[0043] Step 2: Construct the correction link, input the real-time collected input voltage x into the correction link, and connect this link in series with the fast tilt mirror in the computer host, such as Figure 3 As shown, the output of the correction link is input to the fast tilt mirror;

[0044] Step 3: Input the input voltage x at different frequency points, adjust the correction link coefficient so that the voltage x and the angle y are in phase, and determine the value of the correction link coefficient; use the series proportional plus differential correction link to change the phase of this approximately linear system, such as Figure 3 As shown, s represents the complex frequency, and k1 and k2 are the coefficients of the proportional and differential components, respectively. The values of k1 and k2 are adjusted at different frequencies by observing the phase relationship between the input voltage and the output angle. To achieve phase correction of the fast-tilting mirror within the 0 to 200 Hz frequency range, different frequency points need to be divided. In the present invention, a total of 21 frequency points are divided, namely 1 Hz, 10 Hz, 20 Hz, 1, and 200 Hz. Except for 1 Hz, the remaining frequency points are separated by 10 Hz.

[0045] Input a sine signal of f = 1 Hz into the experimental platform, adjust the correction coefficients k1 and k2 so that the input voltage data X and the output angle data Y are in phase, and record the values of k1 and k2.

[0046] Using the formula w = 2πf, calculate the angular frequency w corresponding to f = 1 Hz.

[0047] Step 4: Calculate the frequency gain and phase offset of the correction link corresponding to all frequency points based on the correction link coefficients of the determined values. Specifically, the calculation formulas for the amplitude-frequency characteristics and phase-frequency characteristics of the correction link at different frequency points are as follows:

[0048] (1) Amplitude-frequency characteristics of the correction link:

[0049]

[0050] (2) Phase-frequency characteristics of the correction link:

[0051]

[0052] Among them, |G(jw i )| represents the frequency gain at different frequency points, φ(w i ) represents the phase shift at different frequency points, j and w are the imaginary unit and angular frequency respectively.

[0053] Substitute k1, k2, and w into formula (1) and formula (2), calculate the gain |G(jw1)| and phase offset φ(w1) of the correction link at the 1Hz frequency point, and record |G(jw1)| and φ(w1). Change the frequency point in sequence until the gain data of all frequency points are obtained Γ={|G(jw1)|、|G(jw2)|、|G(jw3)|、L、|G(jw 21)|} and phase data

[0054] Step 5. Determine the form of the advanced phase compensator H(s), identify the parameters in the advanced phase compensator H(s) using the frequency gain and phase offset of the correction link corresponding to all frequency points, replace the correction link with the advanced phase compensator after the identified parameters, and perform dynamic hysteresis nonlinear suppression on the piezoelectric fast-tilt mirror.

[0055] Specifically, the form of the leading phase compensator is selected as where b m ,L,b1,b0 are the numerator coefficients, a n , L, a1, a0 are denominator coefficients. In the present invention, m = 3, n = 2 are selected.

[0056] By setting s = jω, we can obtain the gain of H(s) to be identified |H(jw i ,θ)| and phase ∠H(jw i ,θ), where θ={a0,a1,L,a n ,b0,b1,L,b m} is the parameter to be identified.

[0057] Setting the optimization function

[0058] Substitute the obtained gain data Γ into the optimization function L, that is, |G(jw1)|=|H data (jw1)|, |G(jw2)|=|H data (jw2)|、L|G(jw N )|=|H data (jw N )|. Substitute the acquired phase data Ψ into the optimization function L, that is, After the data is substituted, the parameters θ={a0,a1,L,a n ,b0,b1,L,b m}, and then determine the leading phase compensator H(s).

[0059] When the input signal is x(t), the output signal of the leading phase compensator H(s) is r(t), which satisfies the relationship R(s) = X(s)H(s). Here symbol represents the Laplace transform.

[0060] The designed advanced phase compensator is connected in series with the fast tilt mirror, such as Figure 5 shown.

[0061] Based on the advanced phase compensator obtained by the above method, in order to further improve the control accuracy of the piezoelectric fast-tilt mirror system, the control device of the piezoelectric fast-tilt mirror in this embodiment includes an advanced phase compensator, a PI feedback controller and a feedback unit;

[0062] The voltage x is input to the leading phase compensator, and the input to the PI feedback controller is the error signal e. The output of the PI feedback controller is added to the output of the lead phase compensator and then input to the piezoelectric fast tilt mirror to form a composite control of the piezoelectric fast tilt mirror. The piezoelectric fast tilt mirror outputs an angle y. The feedback unit converts the angle y into a voltage signal, which can be expressed as an input K represents the proportional coefficient of the feedback unit, y is the input of the feedback unit, is the output of the feedback unit. Error signal is input into the PI controller.

[0063] Figure 6 This paper demonstrates the effectiveness of the advanced phase compensator in suppressing dynamic hysteresis. It can be seen that the advanced phase compensator can effectively adjust the system's phase, ensuring that the input and output phases of the rapidly tilting mirror hysteresis system remain essentially consistent, while also effectively suppressing the system's dynamic hysteresis. It is worth noting that while the phase compensation is effective, there is a certain amplitude error. The present invention further combines the advanced phase compensator with feedback control to correct the amplitude. Figure 8 The composite control effect based on the leading phase compensator is demonstrated. It can be seen that the system output is basically consistent with the expected value, which fully verifies the effectiveness of the method of the present invention.

[0064] In response to the common model dependence problem in the prior art when compensating for dynamic hysteresis of piezoelectric fast-tilt mirrors, namely the limitation of needing to construct an accurate hysteresis model and perform system modeling, the present invention proposes a method for suppressing dynamic hysteresis characteristics based on an advance phase compensator. Unlike the prior art path, the present invention completely abandons the traditional hysteresis modeling method and instead realizes dynamic hysteresis compensation by designing an advance phase compensator, which has the following significant advantages: (1) It solves the problem of traditional methods' strong dependence on the hysteresis model and avoids the compensation error caused by model mismatch; (2) Compared with complex hysteresis models, the advance phase compensator has the characteristics of fewer parameters, simple structure, and convenient design; (3) It realizes dynamic hysteresis suppression from the perspective of system phase compensation, providing a different technical path for the precise control of fast-tilt mirrors.

[0065] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror, characterized in that: include: S1. Build an experimental control platform for real-time acquisition of the input voltage x and output angle y of the piezoelectric fast-tilt mirror; S2. Construct a correction link, input the real-time collected input voltage x into the correction link, and input the output of the correction link into the fast tilt mirror; S3. Input the input voltage x at different frequency points, adjust the correction link coefficient so that the voltage x and the angle y are in phase, and determine the value of the correction link coefficient; S4. Calculate the frequency gain and phase offset of the correction link corresponding to all frequency points based on the correction link coefficients of the determined values; S5. Determine the form of the advanced phase compensator H(s), identify the parameters in the advanced phase compensator H(s) using the frequency gain and phase offset of the correction link corresponding to all frequency points, replace the correction link with the advanced phase compensator after the identified parameters, and perform dynamic hysteresis nonlinear suppression on the piezoelectric fast tilt mirror.

2. The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to claim 1, characterized in that: The correction link is k1+k2s, where k1 and k2 are the coefficients of the proportional link and the differential link respectively, and s represents the complex frequency.

3. The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to claim 1, characterized in that: In S4, the method for calculating the frequency gain and phase offset of the correction link corresponding to all frequency points is: according to Get the frequency gain |G(jw i )|, where j represents the imaginary unit, w i Represents the angular frequency corresponding to the i-th frequency point, i=1,2,…,N, N represents the number of frequency points; according to Get the phase shift φ(w i ).

4. The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to claim 1, characterized in that: The leading phase compensator H(s) is: Among them, b m ,…,b1,b0 are the numerator coefficients to be identified, a n ,…,a1,a0 are the denominator coefficients to be identified, and the subscripts m and n are set positive integers, m>n.

5. The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to claim 4, characterized in that: m=3, n=2.

6. The method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to claim 4, characterized in that: In S5, the method for identifying the parameters of the leading phase compensator H(s) using the frequency gain and phase offset of the correction link corresponding to all frequency points includes: By setting s = jw i , we can get the gain of the leading phase compensator H(s) corresponding to different frequency points |H(jw i ,θ)| and phase ∠H(jw i ,θ), where θ={a0,a1,…,a n ,b0,b1,…,b m } is the parameter to be identified; Set the optimization function to: According to the optimization function, the parameters θ={a0,a1,L,a n ,b0,b1,L,b m }, and then determine the leading phase compensator H(s).

7. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to any one of claims 1 to 6 are implemented.

8. A device for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes the computer program to implement the steps of the method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror according to any one of claims 1 to 6.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast tilt mirror as claimed in any one of claims 1 to 6 are implemented.

10. A control device for a piezoelectric fast-tilt mirror, comprising an advanced phase compensator, a PI feedback controller, and a feedback unit; the advanced phase compensator is obtained based on the method for suppressing dynamic hysteresis nonlinearity of a piezoelectric fast-tilt mirror according to any one of claims 1 to 6; The voltage x is input to the leading phase compensator, and the input to the PI feedback controller is the error signal e. The output of the PI feedback controller is added to the output of the lead phase compensator and then input to the piezoelectric fast tilt mirror. The piezoelectric fast tilt mirror outputs an angle y, which is input to the feedback unit. The output of the feedback unit is K represents the proportional coefficient of the feedback unit.

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