Data-driven fast reflector composite adaptive tracking control method

Abstract

The invention provides a data-driven fast reflector composite adaptive tracking control method. The data-driven fast reflector composite adaptive tracking control method comprises the following steps: S1, establishing an autoregression model of a biaxial fast reflector with external input based on multiple groups of primary functions; s2, designing an autoregression model composite parameter estimator according to the input and output data; s3, designing a nonlinear and coupling compensation controller based on an autoregression model composite parameter estimator; and S4, constructing a linear part non-minimum implementation form based on the compensation controller, and designing a model prediction controller. The method mainly aims at the difficulty caused by unknown nonlinear characteristics and double-axis coupling of the fast reflector, and can ensure that the double-axis tracking precision of the fast reflector is recovered to a model prediction control upper limit which is not influenced by coupling and nonlinearity.

Description

Technical Field

[0001] The invention belongs to the field of adaptive tracking control of fast reflectors, and in particular relates to a data-driven composite adaptive tracking control method for fast reflectors, which is mainly used for robust tracking control of dual-axis fast reflectors when motion coupling and nonlinear dynamics exist. Background Art

[0002] As a core actuating component, the fast reflector plays an important role in the precise control of the light beam and is the key to meeting the requirements of high-precision and fast-response pointing and tracking of the laser beam in laser communication applications. However, in practical applications, the fast reflector's own driver has certain nonlinear dynamics, and this dynamic exhibits complex input-output related characteristics. In addition, deviations in the fast reflector during processing and assembly will lead to its biaxial motion coupling. These problems have brought difficulties to the continuous and stable high-precision and high-dynamic beam pointing control in laser communication tasks. On the other hand, the identification of nonlinear dynamics is very difficult. The model obtained by offline data identification cannot characterize the nonlinear dynamics of the fast reflector under unknown working conditions. The controller designed based on the offline identification model limits the further improvement of control performance.

[0003] For the nonlinear model of the dual-axis fast reflector, data-driven technology can be used to estimate the dynamic characteristics of the coupling and nonlinear parts online, and the linear model predictive control technology can be realized by compensating the coupling and nonlinear dynamics. The high-speed changing reference trajectory in space missions determines that the system sampling frequency is extremely high, so it is very difficult to apply nonlinear model predictive control technology in extremely short time intervals. In addition, the general parameter estimator relies on continuous excitation conditions and cannot obtain the real dynamics when the excitation information is insufficient. The controller designed based on this will not be able to guarantee the efficient tracking of different reference trajectories by the dual-axis fast reflector. Summary of the invention

[0004] In view of the unknown coupling and nonlinear dynamic problems faced by the dual-axis rapid reflection mirror during rapid sampling, the present invention proposes a data-driven rapid reflection mirror composite adaptive tracking control method, firstly, an autoregressive model with external input of the dual-axis rapid reflection mirror is established based on multiple groups of basis functions; then, a composite parameter estimator of the autoregressive model is designed according to the input and output data; thereafter, a nonlinear and coupling compensation controller is designed based on the composite parameter estimator of the autoregressive model; thereafter, a non-minimum implementation form of the linear part is constructed based on the compensation controller and a model predictive controller is designed to ensure that the tracking accuracy of any axis of the dual-axis rapid reflection mirror is restored to the upper limit of the model predictive control that is not affected by coupling and nonlinearity, thereby improving the tracking accuracy.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A data-driven fast reflector composite adaptive tracking control method comprises the following steps:

[0007] S1: An autoregressive model with external input for a dual-axis fast reflector is established based on multiple sets of basis functions;

[0008] S2: Design composite parameter estimator of autoregressive model based on input and output data;

[0009] S3: Design of nonlinear and coupling compensation controller based on composite parameter estimator of autoregressive model;

[0010] S4: Construct a non-minimal implementation of the linear part based on the compensation controller and design a model predictive controller.

[0011] The beneficial effects of the present invention are:

[0012] 1. The method of the present invention includes an autoregressive nonlinear model with external input of a dual-axis rapid reflection mirror. Aiming at dual-axis coupling and nonlinear dynamics, the present invention constructs multiple sets of basis functions based on the historical input and output of the dual axes of the rapid reflection mirror as the state, and cooperates with the linear model to characterize the dynamic characteristics of the dual-axis rapid reflection mirror.

[0013] 2. In response to the problem of dependence on continuous excitation conditions in data-driven technology, the present invention makes full use of historical data to ensure that the online estimation of unknown parameters in the fast reflector autoregressive nonlinear model can converge to the true value. On the other hand, the convergence speed of parameter estimation is greatly improved through composite immersion and invariant adaptive control technology, and at the same time, the transient performance of the closed-loop system is improved by relying on non-deterministic criteria.

[0014] 3. In order to avoid observing the system state, the present invention designs a nonlinear and coupling compensation controller based on the parameter estimation value, and on this basis designs a model predictive controller relying only on the output data of the dual-axis rapid reflection mirror and the control input of the linear part, to ensure that the tracking accuracy of any axis of the dual-axis rapid reflection mirror is restored to the upper limit of the model predictive control that is not affected by coupling and nonlinearity. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flow chart of a data-driven fast reflector composite adaptive tracking control method of the present invention;

[0016] Figure 2 This is the unknown parameter estimation diagram of the fast reflector 0-5 seconds dual axis;

[0017] Figure 3 It is the fast mirror 2-2.03 seconds dual-axis output angle and reference trajectory diagram;

[0018] Figure 4 This is the dual-axis tracking error diagram of the fast reflector from 0 to 0.4 seconds. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation examples described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0020] like Figure 1 As shown, the present invention proposes a data-driven fast reflector composite adaptive tracking control method, comprising the following steps:

[0021] Step S1: Establish an autoregressive model of a dual-axis fast reflector with external input based on multiple groups of basis functions:

[0022] The autoregressive model with external input represents the output of the system as the weighted sum of historical output and historical input. Considering the nonlinear dynamic characteristics caused by the deformation of the compliant mechanism in the fast reflector, the following autoregressive model with external input is established:

[0023] ,

[0024] in, The fast reflector Axis, subscripts for all parameters All represent this parameter as The corresponding parameters of the axis, Fast reflector Moment The output angle of the shaft, Fast reflector Moment Axis control input, Any time, For fast reflector Model parameters related to axis history output, The output corresponds to The number of time steps to look back at the moment, For fast reflector Model parameters related to axis history input, The control input corresponds to The number of time steps to look back at the moment, For fast reflector axis Nonlinear and coupled dynamics at the moment To characterize the fast reflector Basis function vectors for axis nonlinearity and coupled dynamics, It is a fast reflector. The number of axis nonlinear basis function vectors, for Middle basis functions, Fast reflector The state variables at time, For fast reflector The unknown true weight vector of the axis basis function, superscript represents the transpose of a matrix, is the set of all real numbers, is the order of the model, The linear model part is represented by The zero point of determination is Assume that these zeros are all inside the unit circle;

[0025] Sinusoidal signals of different frequencies and amplitudes are input to the two axes of the fast reflector respectively, and the output angle data are recorded. The recorded input and output data are used for system identification of the linear part of the autoregressive model to determine and The specific value of .

[0026] Step S2: Design an autoregressive model composite parameter estimator based on the input and output data of each axis of the fast reflector:

[0027] The autoregressive model composite parameter estimator estimates the unknown true weight vectors of the basis functions of each axis of the fast reflector based on the autoregressive model.

[0028] First, define , is the intermediate variable, represents the filter constant, and The iterative algorithm is:

[0029] ,

[0030]

[0031] in, , , the intermediate variables satisfy , multiply both sides of the equation The adjoint matrix have to:

[0032] ,

[0033] in, , , Representative Matrix The determinant of ;

[0034] Then, define Moment Axis unknown parameter vector The initial estimated variables are , the auxiliary variables are , Moment Axis unknown parameter vector The estimated variable is , and The iterative algorithm corresponds to the design of the composite parameter estimator of the autoregressive model, which satisfies:

[0035] ;

[0036] ;

[0037] For the Constant adaptive gain of the axis, For the The constant used for normalization of the axis, , is a constant gain, , ;

[0038] in is a constant gain, , is the intermediate variable, , , , The iterative algorithm satisfies:

[0039] ,

[0040] , , is a constant gain.

[0041] Step S3: Design a nonlinear and coupling compensation controller based on the autoregressive model composite parameter estimator:

[0042] First, in order to compensate for the nonlinear and coupled dynamics in the autoregressive model, the nonlinear and coupled compensation controller is designed using the above parameter estimation, and the definition is Moment Axis unknown parameter vector The estimated error is , whose iteration satisfies:

[0043] ;

[0044] ;

[0045] in is the identity matrix, choose , , , , make All eigenvalues ​​of are less than 1, ensuring the estimation error Converges to 0;

[0046] Then, the fast reflector Moment The control input of the axis is decomposed into a linear nominal control input Compensation for nonlinearity and coupling control input , the specific form is:

[0047] ;

[0048] Since the zero points of the linear part are all within the unit circle, the nonlinear and coupling compensation controller can be expressed as:

[0049] ;

[0050] The autoregressive model in S1 is transformed into a combination of a linear model and an estimation error under the action of this controller:

[0051] .

[0052] Step S4: Based on the nonlinear and coupling compensation controller, a non-minimum implementation form of the linear part is constructed and a model predictive controller is designed. The specific design steps are as follows:

[0053] First, a cost function with limited prediction time is designed for the linear part after the autoregressive model transformation:

[0054] ,

[0055] in For fast reflector The linear nominal control input sequence for the axis to be optimized, is the prediction step length, for Time fast mirror Axial Forward Prediction The output angle at the moment, for Time fast mirror Axial Forward Prediction The reference trajectory at each moment, , for Time fast mirror Axial Forward Prediction The linear nominal control input at each moment, for Time fast mirror Axial Forward Prediction The linear nominal control input increment at each moment;

[0056] Then, according to the linear part transformed by the autoregressive model in S3 Design the following non-minimal implementation state space:

[0057] ,

[0058] in, for Time fast mirror The state of the non-minimal realization of the linear part of the axis model, for Time fast mirror Model output of the non-minimum realization of the linear part of the axis model, parameters , , for:

[0059] ,

[0060] ,

[0061] ;

[0062] After that, in order to solve the optimal linear nominal control input sequence, the following linear dynamic programming problem is designed:

[0063]

[0064] satisfy: ,

[0065] ,

[0066] ,

[0067] ;

[0068] in, yes Time fast mirror Forward prediction of the non-minimal implementation form of the linear part of the axis model The state of a moment, yes Time fast mirror The state of the non-minimal realization of the linear part of the axis model, yes Time fast mirror Forward prediction of the non-minimal implementation form of the linear part of the axis model The state at a moment;

[0069] The optimal solution to the above problem is expressed in the following compact form:

[0070] ,

[0071] in, is the decision vector, represents its optimal value,

[0072] ,

[0073] ,

[0074] ,

[0075] , ,

[0076] ,

[0077] ;

[0078] is the vector formed by the reference trajectory of the i-th axis of the fast reflector from time k+1 to k+N, is a parameter Nth power, due to is a positive definite matrix, we have ,but Time fast mirror The axis model predictive controller is ,in represent The first row, therefore, Time fast mirror The control input of the axis is .

[0079] Example:

[0080] (1) Simulation settings:

[0081] In the present invention, the simulation step size is set to 0.0001s (i.e., the sampling frequency is 10kHz), the total simulation time is 5s, and the model order is , the number of zero points is 2;

[0082] In the actual model of the first axis of the actual fast reflection mirror, , , , , , , ,definition , ;

[0083] In the actual model of the second axis, , , , , , , , ;

[0084] The adaptive part parameters are , , , , , , , , , , , , , .

[0085] (2) Sine and composite signal tracking test:

[0086] First, a sine wave signal with an input amplitude of 10μrad and a frequency of 100Hz is used as the reference trajectory signal for the 1-axis quasi-tracking, and a composite signal composed of sine signals with an amplitude of 7μrad and a frequency of 200Hz, an amplitude of 5μrad and a frequency of 300Hz, and an amplitude of 6μrad and a frequency of 10Hz is used as the reference trajectory signal for the 2-axis quasi-tracking. The initial state of the system is . Carry out simulation and record the changes in the estimation of unknown parameters of the fast reflector's dual axes, the output angle and the tracking error within 5 seconds. Figure 2 Estimation of unknown parameters of the fast mirror 0-5 s dual axis. Figure 3 The fast mirror outputs the rotation angle and reference trajectory in two axes in 2-2.03 seconds. Figure 4 The fast reflector has a dual-axis tracking error of 0-0.4 seconds, and the final steady-state tracking error of 1 axis does not exceed μrad, the final steady-state tracking error of the 2 axes does not exceed μrad.

[0087] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A data-driven fast mirror composite adaptive tracking control method, characterized in that: The following steps are involved: S1. Establishing an autoregressive model of a dual-axis fast reflector with external input based on multiple sets of basis functions; S2, designing an autoregressive model composite parameter estimator according to the input and output data of each axis of the fast reflector; S3. Design of nonlinear and coupling compensation controller based on composite parameter estimator of autoregressive model; S4. Construct a non-minimum implementation of the linear part based on the compensation controller and design a model predictive controller.

2. A data-driven fast mirror composite adaptive tracking control method according to claim 1, characterized in that: The S1 includes: Considering the nonlinear dynamic characteristics caused by the deformation of the compliant mechanism in the fast reflector, the following autoregressive model with external input is established: ， in, The fast reflector Axis, subscripts for all parameters All represent this parameter as The corresponding parameters of the axis, Fast reflector Moment The output angle of the shaft, Fast reflector Moment Axis control input, Any time, For fast reflector Model parameters related to axis history output, The output corresponds to The number of time steps to look back at the moment, For fast reflector Model parameters related to axis history input, The control input corresponds to The number of time steps to look back at the moment, For fast reflector axis Nonlinear and coupled dynamics at the moment To characterize the fast reflector Basis function vectors for axis nonlinearity and coupled dynamics, It is a fast reflector. The number of axis nonlinear basis function vectors, for Middle basis functions, Fast reflector The state variables at time, For fast reflector The unknown true weight vector of the axis basis function, superscript represents the transpose of a matrix, is the set of all real numbers, is the order of the model, The linear model part is represented by The zero point of determination is Assume that these zeros are all inside the unit circle; Sinusoidal signals of different frequencies and amplitudes are input to the two axes of the fast reflector respectively, and the output angle data are recorded. The recorded input and output data are used for system identification of the linear part of the autoregressive model to determine and The specific value of .

3. A data-driven fast mirror composite adaptive tracking control method according to claim 2, characterized in that: The S2 includes: First, define , is the intermediate variable, represents the filter constant, and The iterative algorithm is: ， ； in, , , the intermediate variables satisfy , multiply both sides of the equation The adjoint matrix have to: ， in, , , Representative Matrix The determinant of ; Then, define Moment Axis unknown parameter vector The initial estimated variables are , the auxiliary variables are , Moment Axis unknown parameter vector The estimated variable is , and The iterative algorithms satisfy: ； ； For the Constant adaptive gain of the axis, For the The constant used for normalization of the axis, , is a constant gain, , ; in is a constant gain, , is the intermediate variable, , , , The iterative algorithm satisfies: ， , , is a constant gain.

4. A data-driven fast mirror composite adaptive tracking control method according to claim 3, characterized in that: The S3 includes: First, to compensate for nonlinearities such as coupling, a compensation controller is designed using the above parameter estimation, defining Moment Axis unknown parameter vector The estimated error is , whose iteration satisfies: ； ； in is the identity matrix, choose , , , , make The eigenvalue of is less than 1, ensuring the estimation error Converges to 0; Then, the fast reflector Moment The control input of the axis is decomposed into a linear nominal control input Compensation for nonlinearity and coupling control input , the specific form is: ； Since the zero points of the linear part are all within the unit circle, the nonlinear and coupling compensation control input The analytical expression of is: ； The autoregressive model in S1 is transformed into a combination of a linear model and an estimation error under the action of the compensation controller: 。 5. A data-driven fast mirror composite adaptive tracking control method according to claim 4, characterized in that: The S4 includes: First, a cost function with limited prediction time is designed for the linear part after the autoregressive model transformation: ， in For fast reflector The linear nominal control input sequence for the axis to be optimized, is the prediction step length, for Time fast mirror Axial Forward Prediction The output angle at the moment, for Time fast mirror Axial Forward Prediction The reference trajectory at each moment, No. A constant penalty factor for the axis, for Time fast mirror Axial Forward Prediction The linear nominal control input at each moment, for Time fast mirror Axial Forward Prediction The linear nominal control input increment at each moment; Then, the following non-minimum implementation state space is designed based on the linear part transformed from the autoregressive model in S3: ， in, for Time fast mirror The state of the non-minimal realization of the linear part of the axis model, for Time fast mirror Model output of the non-minimum realization of the linear part of the axis model, parameters , , for: ， ， ； After that, in order to solve the optimal linear nominal control input sequence, the following linear dynamic programming problem is designed: ； satisfy: ， ， ， ； in, yes Time fast mirror Forward prediction of the non-minimal implementation form of the linear part of the axis model The state of a moment, yes Time fast mirror The state of the non-minimal realization of the linear part of the axis model, yes Time fast mirror Forward prediction of the non-minimal implementation form of the linear part of the axis model The state at a moment; The optimal solution to the above problem is expressed in the following compact form: ， in, is the decision vector, represents its optimal value, ， ， ， ， , ， ； Is to Time fast mirror The vector formed by the reference trajectory of the axis, is a parameter of power, due to is a positive definite matrix, we have ,but Time fast mirror The optimal linear nominal control input of the axis is ,in represent The first row, therefore, Time fast mirror The control input of the axis is .

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