X-lms-based piezoelectric swing mirror adaptive control system and method

Abstract

The application discloses a piezoelectric swing mirror adaptive control system and method based on x-LMS, which comprises a piezoelectric swing mirror model, and further comprises an angle feedback module for acquiring the motion angle of the piezoelectric swing mirror model, a feedforward compensation module for acquiring the feedforward control voltage acting on the piezoelectric swing mirror model, an x-LMS feedback module for acquiring a feedback voltage according to a desired signal and the motion angle, and an output module for superimposing the feedforward control voltage and the feedback voltage and then applying the superimposed voltage to the piezoelectric swing mirror model. The application aims to provide a piezoelectric swing mirror adaptive control system and method based on x-LMS, which establishes a feedforward-feedback composite control strategy by taking the linear fitting of the center line of a hysteresis curve as feedforward and taking an x-LMS control algorithm as feedback, thereby reducing the control difficulty and complexity of the piezoelectric swing mirror model in the control system while ensuring the control precision and adaptability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tracking and disturbance suppression, and particularly relates to a piezoelectric swing mirror adaptive control system and method based on x-LMS. BACKGROUND

[0002] The piezoelectric swing mirror is an important device in a laser communication terminal, and generates single-axis or multi-axis micro-angle deflection by driving the expansion and contraction of the piezoelectric ceramic. The piezoelectric swing mirror control strategy is the core element for ensuring that the swing mirror effectively compensates for the residual error of the coarse tracking mechanism control and suppresses the micro-vibration of the star body transmitted to the terminal, and has a crucial influence on the tracking accuracy of the laser terminal.

[0003] The existing piezoelectric swing mirror control strategy generally adopts a feedforward-feedback compound control algorithm, that is, the piezoelectric swing mirror hysteresis inverse model or fitting model is used as feedforward to improve the control system bandwidth, and a closed-loop feedback based on a classical control algorithm or an intelligent control algorithm is used to improve the control accuracy. In the case of small amplitude motion of the swing mirror, the nonlinear part can be ignored by using a linear fitting model, and at this time, the feedback control algorithm determines the performance of the feedforward-feedback compound control algorithm. The feedback control algorithm of the piezoelectric swing mirror mostly adopts proportional-integral-derivative (PID) control and its derivative algorithm, robust control algorithm, optimal control algorithm, and sliding mode variable structure control algorithm.

[0004] The PID control algorithm does not depend on the input-output characteristic model of the object, and only needs to select the gain coefficient to make the system closed loop stable to control a class of objects to achieve the static index. However, with the increasing demand for control accuracy and speed and environmental adaptability, the traditional PID algorithm cannot meet the requirements, and a series of derivative algorithms have appeared, such as self-tuning PID and intelligent PID. However, these algorithms do not change the essence of the algorithm being independent of the model of the controlled object.

[0005] The robust control algorithm fully considers the influence of uncertain disturbances in the system during the design process, so that the system can remain stable under the influence of disturbances. However, the robust control sacrifices the control performance to ensure the robustness of the system, and the controller has a high order, which makes it difficult to implement in engineering;

[0006] Optimal control is a method of establishing an optimal control scheme for a system based on the extremum principle under certain constraint conditions, with a quadratic form of state variables and system inputs as the objective function. This method requires high accuracy of the model, and when there is modeling error or the model changes, the optimal performance cannot be achieved. In addition, the implementation of the control algorithm requires multiple state variable sensors, resulting in a complex system.

[0007] Sliding mode variable structure control is essentially a special kind of nonlinear control, which can change according to the current state in the dynamic process, force the system to move according to the predetermined "sliding mode", and has invariance when subjected to parameter perturbation and external disturbance, but its implementation still needs multiple sensors to test the state variables, and the system is complex. SUMMARY

[0008] The application aims to provide a piezoelectric swing mirror adaptive control system and method based on x-LMS, which establishes a feedforward-feedback composite control strategy by linear fitting the center line of the hysteresis curve as feedforward and x-LMS control algorithm as feedback, reduces the control difficulty and complexity of the piezoelectric swing mirror model in the premise of ensuring control accuracy and adaptability.

[0009] The application is implemented by the following technical solutions:

[0010] A piezoelectric swing mirror adaptive control system based on x-LMS, comprising a piezoelectric swing mirror model, further comprising:

[0011] An angle feedback module for acquiring the motion angle of the piezoelectric swing mirror model;

[0012] A feedforward compensation module for acquiring the feedforward control voltage acting on the piezoelectric swing mirror model;

[0013] An x-LMS feedback module for acquiring the feedback voltage according to the expected signal and the motion angle; the expected signal is the angle expected to be output by the piezoelectric swing mirror;

[0014] An output module for superimposing the feedforward control voltage and the feedback voltage and then acting on the piezoelectric swing mirror model.

[0015] Preferably, the angle feedback module is an angle sensor.

[0016] Preferably, the feedforward control voltage is:

[0017]

[0018] Wherein, u pre (k) represents the feedforward control voltage at K time, B d represents the feedback matrix, C d represents the test matrix, Y d (k+1) represents the expected signal at k+1 time, A d represents the state matrix, X1(k) represents the state variable at K time.

[0019] Preferably, the x-LMS feedback module comprises:

[0020] an x-LMS controller state vector unit configured to update a state vector of an x-LMS controller;

[0021] a piezoelectric swing mirror model reference unit configured to update a reference signal vector of a piezoelectric swing mirror reference model according to the state vector;

[0022] an x-LMS controller weight vector unit configured to update a control weight of the x-LMS controller according to the reference signal vector, the desired signal and the motion angle;

[0023] a calculation unit configured to calculate the feedback voltage according to the state vector and the control weight.

[0024] Preferably, the reference signal vector is:

[0025]

[0026]

[0027]

[0028]

[0029] wherein, represents the reference signal vector, f(k) represents an instantaneous value of the reference signal vector at time k, represents the state vector, represents an m-th finite impulse response vector simulated by an open-loop transfer function, and N is a number of control weights of the x-LMS algorithm.

[0030] Preferably, the x-LMS controller weight vector unit comprises:

[0031] a first calculation sub-unit configured to calculate a difference between the desired signal and the motion angle;

[0032] an updating sub-unit configured to update the control weight of the x-LMS controller according to the reference signal vector and the difference.

[0033] Preferably, the control weight is:

[0034] ω(k+1) = ω(k) - 2μe(k)f(k);

[0035] wherein, ω(k+1) represents the control weight at time k+1, ω(k) represents the control weight at time k, μ is a convergence coefficient, e(k) represents the difference, and f(k) represents the instantaneous value of the reference signal vector at time k.

[0036] Preferably, the feedback voltage is:

[0037]

[0038]

[0039]

[0040] wherein s(k) represents a feedback voltage, represents a state vector, represents a weight vector.

[0041] A control method of a piezoelectric swing mirror adaptive control system based on x-LMS, comprising the following steps:

[0042] S1: obtaining a motion angle of a piezoelectric swing mirror;

[0043] S2: obtaining a feedback voltage by using an x-LMS algorithm according to a desired signal and the motion angle; the desired signal is an angle desired to be output by the piezoelectric swing mirror;

[0044] S3: superimposing a feedforward control voltage and the feedback voltage and applying the superimposed voltage to the piezoelectric swing mirror

[0045] Preferably, the S2 comprises the following sub-steps:

[0046] S21: updating a state vector of the x-LMS algorithm;

[0047] S22: updating a reference signal vector of a reference model according to the state vector;

[0048] S23: updating a control weight of the x-LMS algorithm according to the reference signal vector, the desired signal and the motion angle;

[0049] S24: calculating the feedback voltage according to the state vector and the control weight.

[0050] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0051] A feedforward-feedback composite control strategy is established by taking a linear fitting of a center line of a hysteresis curve as feedforward and taking an x-LMS control algorithm as feedback, so that the control difficulty and complexity of the piezoelectric swing mirror model are reduced under the premise of ensuring control accuracy and adaptability. BRIEF DESCRIPTION OF DRAWINGS

[0052] The accompanying drawings, which are included to provide a further understanding of the embodiments of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:

[0053] Figure 1 Fig. 1 is a structural schematic diagram of a piezoelectric swing mirror adaptive control system of the present application; and

[0054] Figure 2 Schematic diagram of the structure of the x-LMS feedback module of the present invention;

[0055] Figure 3 Schematic diagram of system response in the undisturbed step signal simulation of the present invention;

[0056] Figure 4 Schematic diagram of control voltage in the undisturbed step signal simulation of the present invention;

[0057] Figure 5 Schematic diagram of the time domain response curve in the simulation of the x-LMS feedback module of the present invention;

[0058] Figure 6 Schematic diagram of control error in the simulation of the x-LMS feedback module of the present invention;

[0059] Figure 7 Schematic diagram of the time domain curve of the system response in the step signal tracking simulation under the disturbance of the present invention;

[0060] Figure 8 Schematic diagram of control voltage in step signal tracking simulation under disturbance action of the present invention;

[0061] Figure 9 Schematic diagram of the change of 1st to 5th order weights of the x-LMS feedback module of the present invention. DETAILED DESCRIPTION

[0062] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0063] Example 1

[0064] This embodiment proposes a piezoelectric oscillating mirror adaptive control system based on x-LMS. Figure 1 As shown, it includes a piezoelectric oscillating mirror model and also includes:

[0065] Angle feedback module, used to obtain the motion angle of the piezoelectric oscillating mirror model;

[0066] In this embodiment, the movement angle of the piezoelectric oscillating mirror model is acquired by an angle sensor performing real-time detection on the piezoelectric oscillating mirror model.

[0067] A feedforward compensation module is used to obtain a feedforward control voltage acting on the piezoelectric oscillating mirror model;

[0068] Specifically, the feedforward control voltage is obtained according to the following formula:

[0069]

[0070] wherein u pre (k) represents the feedforward control voltage at time k, B d represents the feedback matrix, C d represents the test matrix, Y d (k+1) represents the expected signal at time k+1, A d represents the state matrix, X1(k) represents the state variable at time k.

[0071] an x-LMS feedback module, configured to obtain a feedback voltage according to an expected signal and a motion angle; wherein the expected signal is an angle expected to be output by the piezoelectric swing mirror;

[0072] Under normal circumstances, i.e. without the x-LMS feedback module, the discrete state equation of the piezoelectric swing mirror model is shown in formula (1):

[0073]

[0074] wherein A d is the state matrix, B d is the feedback matrix, C d is the test matrix, X1(k) and X1(k+1) are state variables of the piezoelectric swing mirror system at time k and k+1 respectively, u1(k) is the control input at time k, Y1(k) is the evaluation output at time k, and d(k) is the external disturbance at time k.

[0075] Suppose the expected output of the piezoelectric swing mirror model at time k+1 is Y d (k+1), then the feedforward control voltage of the feedforward compensation module (feedforward controller) is formula (2):

[0076]

[0077] By substituting formula (2) into formula (1), the angle output at time k+1 and the expected angle deviation E(k+1) = -d(k+1) can be obtained under the condition of ignoring modeling error, so it can be seen that the error of the feedforward compensation module is mainly caused by system disturbance in ideal conditions. Based on this, in the embodiment, the x-LMS feedback module is added to perform disturbance compensation control, so as to reduce the error caused by system disturbance. Specifically, in the embodiment, the x-LMS feedback module is shown in formula (3): Figure 2 wherein c(k) represents the actual physical characteristic model of the piezoelectric swing mirror, Figure 2 is the piezoelectric swing mirror model established as a reference, is the X-LMS controller weight vector, is the controller state vector, is the controller state vector, is the reference model output vector, d(k) is the desired signal, y(k) is the actual output signal of the piezoelectric swing mirror, e(k) is the control error, including:

[0078] an x-LMS controller state vector unit for updating the state vector of the x-LMS controller;

[0079] Specifically, the controller state vector in the embodiment is updated as follows: as shown in the following formula:

[0080]

[0081] wherein N is the number of x-LMS controller weights, and the vector updating rule is to insert the detection variable instantaneous value into the first position of the state vector, and to eliminate the last position of the state vector, wherein the detection variable instantaneous value is the output displacement detection instantaneous value.

[0082] a piezoelectric swing mirror model reference unit for updating the reference signal vector of the piezoelectric swing mirror reference model according to the state vector;

[0083] Specifically, it is assumed that the open-loop transfer function G(s) between the x-LMS control output and the feedback loop in the embodiment can be simulated as an m-order finite impulse response vector

[0084]

[0085] The actual output of the piezoelectric swing mirror model is equal to the convolution of the x-LMS controller output and the finite impulse response vector:

[0086]

[0087] wherein as shown in formula (4):

[0088]

[0089] In the formula:

[0090]

[0091]

[0092] At this time, the actual output of the piezoelectric swing mirror model can be expressed as:

[0093]

[0094] In the formula is the reference signal vector:

[0095]

[0096] In the formula For the parameter identification vector in the modeling process, the instantaneous value of the reference signal vector f(k) at the current moment has the following identity relationship with the transfer function of the oscillating mirror system:

[0097]

[0098] That is, f(k) can be obtained by solving the transfer function response of the swing mirror system with the state vector input.

[0099] The x-LMS controller weight vector unit is used to update the control weight of the x-LMS controller according to the reference signal vector, the desired signal, and the motion angle. Specifically, the x-LMS controller weight vector unit in this embodiment includes:

[0100] A first calculation subunit, configured to calculate a difference between an expected signal and a motion angle;

[0101] Update subunit, used to update the control weights of the x-LMS controller based on the reference signal vector and the difference

[0102] A calculation unit is used to calculate the feedback voltage according to the state vector and the control weight, that is:

[0103] ω(k+1)=ω(k)-2μe(k)f(k);

[0104] Where ω(k+1) represents the control weight at time k+1, ω(k) represents the control weight at time k, μ is the partial negative gradient added to the weight coefficient to improve system performance, which is the so-called convergence coefficient, e(k) represents the difference, and f(k) represents the instantaneous value of the reference signal vector at time k. The first value is solved by formula (1).

[0105] The output module is used to superimpose the feedforward control voltage and the feedback voltage and apply them to the piezoelectric oscillating mirror model.

[0106] As can be seen from equations (1) to (10), the present application makes up for the defects in the aforementioned prior art, such as the control algorithm being separated from the piezoelectric oscillating mirror transfer model, the difficulty in algorithm engineering implementation, and the complexity of the system.

[0107] Moreover, the control system proposed in this application can make full use of the piezoelectric pendulum mirror transfer model, and the control parameters can be adaptively adjusted as the external environment changes, with high control accuracy and adaptability; the control equation is a combination of multiplication and addition operations, given in discrete form, does not contain high-order differential equations, and is easy to implement in engineering; there is no need to detect multiple state variables, avoiding the increase in system complexity caused by the multivariable detection system.

[0108] Example 2

[0109] The embodiment is based on the embodiment 1, and proposes a control method of a piezoelectric swing mirror adaptive control system based on x-LMS, comprising the following steps:

[0110] S1: obtaining the motion angle of the piezoelectric swing mirror;

[0111] S2: obtaining the feedback voltage according to the x-LMS algorithm based on the expected signal and the motion angle; the expected signal is the angle expected to be output by the piezoelectric swing mirror;

[0112] Specifically, it comprises:

[0113] S21: updating the state vector of the x-LMS algorithm;

[0114] S22: updating the reference signal vector of the reference model according to the state vector;

[0115] S23: updating the control weight value of the x-LMS algorithm according to the reference signal vector, the expected signal and the motion angle;

[0116] S24: calculating the feedback voltage according to the state vector and the control weight value.

[0117] S3: superimposing the feedforward control voltage and the feedback voltage and then applying them to the piezoelectric swing mirror.

[0118] Embodiment 3

[0119] In this embodiment, the effectiveness of the piezoelectric swing mirror adaptive control system or method proposed in embodiments 1 and 2 is verified. Specifically:

[0120] According to formulas (1)-(9), a simulation model is established in Matlab / Simulink;

[0121] The transfer function of the piezoelectric swing mirror model is:

[0122]

[0123] Figure 3 and Figure 4 The response result of the step signal tracking response of the system under the condition that the external disturbance is zero is shown in FIGS. 1-3, and the expected signal is 10 μrad at 1 s. As shown in FIGS. 1-3, Figure 3 and Figure 4 It can be seen that under the action of the step signal, the system output can tend to be stable in a short time, the overshoot is 0, and the steady-state error is less than 2 μrad.

[0124] Figure 5 and Figure 6 The composite signal tracking simulation verification result under the condition of no disturbance is shown in FIGS. 4-6, and the expected signal components are shown in Table 1:

[0125] Table 1 Expected signal components

[0126] Serial number Frequency (Hz) Amplitude (μrad) 1 1 100 2 50 10 3 100 20 4 150 15 5 200 10

[0127] Depend on Figure 5 and Figure 6 The simulation results shown in the figure show that in the initial stage of the controller, since the initial values ​​of the weights are all zero, there is a large error in the output. As the training progresses, the controller weights are adaptively adjusted, the control error gradually decreases, and the desired signal can be effectively tracked. The tracking error decreases rapidly, and the phase error is less than 0.2%. This proves that under the action of the constructed control system, the piezoelectric pendulum mirror can effectively track the desired signal within a large frequency range.

[0128] In order to verify the anti-disturbance performance of the control system, the disturbances applied to the foundation are set to be 20μrad, 200Hz sine, 10μrad, 100Hz sine and a 20μrad step signal with an amplitude of 3s. The expected signal is set to a 10μrad step at 1s. The simulation results are as follows: Figure 7 and Figure 8 As shown by Figure 7 and Figure 8 As can be seen, initially, the controller weights are zero, making it unable to suppress disturbances. Within the range of 0s to 0.1s, some weights are updated, and the system response follows the disturbance. Furthermore, because the weights of the fine aiming controller and the oscillating mirror controller have not yet reached steady state, the oscillating mirror's own second-order underdamped oscillations dominate, resulting in a significant overshoot in the initial response. However, as training progresses, the disturbance is quickly suppressed, and the system output is able to track the desired angle. Under the influence of a step disturbance at 3s, the angle response deviation jumps, decays within 0.1s, and reaches steady state. The steady-state deviation is less than 2μrad, meeting the control accuracy requirements. Figure 8 It shows that in the case of small disturbance, the control voltage of the piezoelectric oscillating mirror has no large step.

[0129] Figure 9 The figure shows the adaptive changes of the 1st to 5th order weights during the control process. It can be seen that in the initial situation, the system deviation changes dramatically and the weight changes greatly. As the system deviation decreases, the weight change rate decreases and gradually stabilizes. After the weight reaches the steady-state value, the system achieves the goal of following the expected instructions and resisting disturbances.

[0130] In summary, the piezoelectric pendulum mirror adaptive control system and method based on x-LMS proposed in this application can effectively drive the pendulum mirror to track control instructions, and can realize disturbance compensation by adaptively adjusting the controller weights. The system stability is greatly improved, ensuring that the piezoelectric pendulum mirror can achieve high-precision output in a disturbed environment.

[0131] The above detailed description of the specific embodiments of the present application has been given to understand the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A piezoelectric oscillating mirror adaptive control system based on x-LMS, including a piezoelectric oscillating mirror model, characterized in that: Also comprising: an angle feedback module, configured to acquire a motion angle of the piezoelectric swing mirror model; a feedforward compensation module, configured to acquire a feedforward control voltage acting on the piezoelectric swing mirror model; the feedforward control voltage is: ； wherein, represents a feedforward control voltage at time k, represents a feedback matrix, represents a test matrix, represents a desired signal at time k+1, represents a state matrix, represents a state variable at time k; an x-LMS feedback module, configured to acquire a feedback voltage according to a desired signal and the motion angle; the desired signal is an angle desired to be output by the piezoelectric swing mirror; the x-LMS feedback module comprises: an x-LMS controller state vector unit, configured to update a state vector of an x-LMS controller; a piezoelectric swing mirror model reference unit, configured to update a reference signal vector of a piezoelectric swing mirror reference model according to the state vector; an x-LMS controller weight vector unit, configured to update a control weight of the x-LMS controller according to the reference signal vector, the desired signal and the motion angle; the reference signal vector is: ； ； ； ； wherein, denotes a reference signal vector, denotes an instantaneous value of the reference signal vector at time k, denotes a state vector, denotes an mth finite impulse response vector modeled by an open loop transfer function, N is a number of control weights of the x-LMS algorithm; a calculation unit, configured to calculate the feedback voltage according to the state vector and the control weight; the x-LMS controller weight vector unit comprises: a first calculation subunit, configured to calculate a difference between the desired signal and the motion angle; an updating subunit, configured to update the control weight of the x-LMS controller according to the reference signal vector and the difference; the control weight is: ； wherein, denotes the control weight at time k+1, denotes the control weight at time k, is a convergence factor, denotes the difference, denotes the instantaneous value of the reference signal vector at time k; the feedback voltage is: ； ； ； wherein, denotes the feedback voltage, denotes the state vector, denotes the weight vector; an output module, configured to superimpose the feedforward control voltage and the feedback voltage and then act on the piezoelectric swing mirror model.

2. The x-LMS based adaptive control system for piezoelectric mirror according to claim 1, wherein, The angle feedback module is an angle sensor.

3. The control method of the x-LMS-based adaptive control system of a piezoelectric swing mirror according to claim 1 or 2, characterized in that, The method comprises the following steps: S1: acquiring a motion angle of a piezoelectric swing mirror; S2: acquiring a feedback voltage by using an x-LMS algorithm according to a desired signal and the motion angle; the desired signal is an angle desired to be output by the piezoelectric swing mirror; S3: superimposing a feedforward control voltage and the feedback voltage and then acting on the piezoelectric swing mirror.

4. The x-LMS based adaptive control method of piezoelectric swing mirror according to claim 3, characterized in that, The S2 comprises the following substeps: S21: updating a state vector of the x-LMS algorithm; S22: updating a reference signal vector of a reference model according to the state vector; S23: updating a control weight of the x-LMS algorithm according to the reference signal vector, the desired signal and the motion angle; S24: calculating the feedback voltage according to the state vector and the control weight.

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