Comprehensive modeling and multi-target complementary control method for laser communication coarse tracking system

Abstract

The invention discloses a comprehensive modeling and multi-target complementary control method for a laser communication coarse tracking system, and belongs to the field of laser communication technology control, the laser communication coarse tracking system is used for control, and the method comprises the following steps: carrying out linear modeling on the coarse tracking system, combining a low-frequency band of a sine sweep frequency signal and a middle-high frequency band of a pseudo-random signal, obtaining a system frequency response, and obtaining a system transfer function through a Hankel matrix identification method; and performing nonlinear modeling on the coarse tracking system, establishing a Stribeck friction model, designing a feed-forward compensation algorithm based on the Stribeck friction model, and obtaining a multi-target complementary control method to control the coarse tracking system. According to the method, accurate identification of model orders and parameters is realized in the linear part, the low-speed tracking performance is remarkably improved in the nonlinear part, the contradiction between the system performance and robustness is effectively solved, and the tracking precision and the anti-interference capability are remarkably improved.

Description

Technical Field

[0001] The invention discloses a comprehensive modeling and multi-objective complementary control method for a laser communication coarse tracking system, and belongs to the field of laser communication technology control. Background Art

[0002] The coarse tracking system is an important component of the aiming, capture and tracking system in laser communications. It has the functions of line of sight alignment, target tracking and isolating the carrier from external interference. The coarse tracking system generally adopts a two-axis two-frame turntable or a two-dimensional swing mirror mechanism. By driving and controlling the pitch axis and azimuth axis, the laser communication terminal is aligned with the target position, providing a basic guarantee for establishing a stable and long-lasting laser communication link. However, the coarse tracking system has stronger nonlinear characteristics, such as friction torque, load imbalance, axis coupling, etc., which will bring difficulties to the establishment of the system model. In addition, the coarse tracking system is directly installed on the dynamic base platform and is exposed to external disturbances for a long time, which seriously affects its line of sight pointing accuracy. Therefore, it is necessary to establish an accurate model for the coarse tracking system and suppress the influence of internal nonlinear characteristics and external interference to improve the dynamic tracking performance.

[0003] The current mainstream method of model identification is to determine the model parameters through the least squares method and its improved methods, assuming that the model structure or order is known. However, as a complex controlled object, the flexibility characteristics and interference of the coarse tracking system are difficult to describe with formulas, so it is difficult to accurately determine the model order, resulting in low model identification accuracy. The nonlinear characteristic that plays a major role in the coarse tracking system is the friction torque. Its impact on the dynamic and static performance of the system is mainly reflected in the dead zone during low-speed tracking and the large error in steady state. These problems will reduce the control accuracy of the system. In the classical control framework, tracking performance and disturbance suppression capability are mutually constrained. Under the constraint of ensuring system stability, it is often necessary to compromise the design of multiple performance indicators. This design method is difficult to meet the high performance requirements of servo control for laser communication coarse tracking systems. Summary of the Invention

[0004] The purpose of the present invention is to provide a comprehensive modeling and multi-objective complementary control method for a laser communication coarse tracking system, so as to solve the problem that the existing technical methods are difficult to meet the high performance requirements of the laser communication coarse tracking system for servo control.

[0005] Comprehensive modeling and multi-objective complementary control method for laser communication coarse tracking system, including: S1. Linear modeling of the coarse tracking system is performed. The low frequency band of the sine sweep signal and the medium and high frequency bands of the pseudo-random signal are combined to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method. S2. Perform nonlinear modeling on the coarse tracking system, establish the Stribeck friction model, and design a feedforward compensation algorithm based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system.

[0006] S1 includes the linear system state space model: ; Where, is the state variable, is the input variable, is the output variable, are the system state space model parameters, For the moment, is the Stribeck friction model; Linear system autocorrelation function and cross-correlation function They are: ; ; Where, is the sequence length of one cycle of the random input signal, is the system input, is the system output, For the A moment.

[0007] S1 includes, let the impulse response of the discrete linear system under zero initial state be , the relationship between the impulse response and the cross-correlation function is: ; Where, is the impulse response time, For the impulse response moment.

[0008] S1 includes the relationship between the impulse response and the cross-correlation function to obtain the system impulse response, and construct the Hankel matrix through the impulse response sequence. : ; Where, is the Hankel matrix number of rows; Hankel matrix Perform singular value decomposition and get: ; ; ; Where, is the singular value obtained by decomposition, 、 is an orthogonal matrix, is the identity matrix, is a diagonal matrix.

[0009] S1 includes determining the system order based on the location where the singular value mutation occurs , according to the system order Hankel matrix break down: ; ; ; Where, 、 is a diagonal matrix, 、 yes The two matrix components of 、 yes The two matrix components of ; According to the Hankel matrix , the system state space model parameters are obtained as: ; ; Where, is the intermediate matrix.

[0010] S1 includes the system transfer function obtained through the system state space model , perform multiplicative uncertainty analysis on the system and obtain the system uncertainty model : ; ; Where, is the state quantity of the system state space.

[0011] S2 includes the Stribeck friction model expression: ; Where, is the Coulomb friction torque, is the maximum static friction, is the relative speed, is the Stribeck speed, is the macroscopic viscous friction damping coefficient, is the electromagnetic torque, is a natural constant, is a sign function; According to Newton's second law: ; Where, is the moment of inertia of the coarse tracking system, is the motor rotation angle, is the second-order derivative of the motor angle, is the friction torque; When the coarse tracking system rotates at a constant speed, the friction torque is: ; Where, is the torque constant, The driving current is the driving current. When the coarse tracking system rotates at a constant speed, the friction torque is obtained by measuring the driving current.

[0012] The feedforward compensation algorithm based on the Stribeck friction model includes: Input to the friction compensator with the Stribeck friction model, divided by the torque constant Get compensation current ,at the same time Input to PI controller together with negative speed feedback signal Get current signal ,Will As control input ;Will 、 and negative current feedback signal Input the current regulator together, then limit it, input the driver and motor, and add friction disturbance Then sent to the coarse tracking system , and then form the system output; The negative current feedback signal is provided by the signal before the motor, and the signal before the motor is input to the system transfer function The residual signal is obtained , and then input the robust controller The negative current feedback signal is obtained and used as a compensation signal ; The negative speed feedback signal is provided by the signal after the motor, the signal after the motor is added with a noise signal, and a negative feedback signal is output to After that, the output is negatively fed back to Before, a negative speed feedback signal is formed.

[0013] The multi-objective complementary control methods include the equivalent robust controller for: ; for: ; Where, 、 is the unit element, Equivalent to , Equivalent to .

[0014] Solving the Equivalent Robust Controller Including sensitivity function and complementary sensitivity function for: ; ; make of Norm less than 1: ; Where, are three weighting functions, is the transfer function matrix, and the Augw function provided by MATLAB is used to calculate the weighting function. Solve it.

[0015] Compared with the existing technology, the present invention has the following beneficial effects: the present invention realizes the accurate identification of model order and parameters in the linear part, significantly improves the low-speed tracking performance in the nonlinear part, effectively solves the contradiction between system performance and robustness, and significantly improves tracking accuracy and anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a technical flow chart of the feedforward compensation algorithm of the present invention; Figure 2 is the step response under PID control; Figure 3 is the step response under multi-objective complementary control; Figure 4 It is the sinusoidal tracking effect under PID control; Figure 5 It is the sinusoidal tracking effect under multi-target complementary control; Figure 6 is the disturbance response under PID control; Figure 7 is the disturbance response under multi-objective complementary control; Figure 8 It is the control logic diagram of the feedforward compensation algorithm. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention are described clearly and completely below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0018] Comprehensive modeling and multi-objective complementary control method for laser communication coarse tracking system, including: S1. Linear modeling of the coarse tracking system is performed. The low frequency band of the sine sweep signal and the medium and high frequency bands of the pseudo-random signal are combined to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method. S2. Perform nonlinear modeling on the coarse tracking system, establish the Stribeck friction model, and design a feedforward compensation algorithm based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system.

[0019] S1 includes the linear system state space model: ; Where, is the state variable, is the input variable, is the output variable, are the system state space model parameters, For the moment, is the Stribeck friction model; Linear system autocorrelation function and cross-correlation function They are: ; ; Where, is the sequence length of one cycle of the random input signal, is the system input, is the system output, For the A moment.

[0020] S1 includes, let the impulse response of the discrete linear system under zero initial state be , the relationship between the impulse response and the cross-correlation function is: ; Where, is the impulse response time, For the impulse response moment.

[0021] S1 includes the relationship between the impulse response and the cross-correlation function to obtain the system impulse response, and construct the Hankel matrix through the impulse response sequence. : ; Where, is the Hankel matrix number of rows; Hankel matrix Perform singular value decomposition and get: ; ; ; Where, is the singular value obtained by decomposition, 、 is an orthogonal matrix, is the identity matrix, is a diagonal matrix.

[0022] S1 includes determining the system order based on the location where the singular value mutation occurs , according to the system order Hankel matrix break down: ; ; ; Where, 、 is a diagonal matrix, 、 yes The two matrix components of 、 yes The two matrix components of ; According to the Hankel matrix , the system state space model parameters are obtained as: ; ; Where, is the intermediate matrix.

[0023] S1 includes the system transfer function obtained through the system state space model , perform multiplicative uncertainty analysis on the system and obtain the system uncertainty model : ; ; Where, is the state quantity of the system state space.

[0024] S2 includes the Stribeck friction model expression: ; Where, is the Coulomb friction torque, is the maximum static friction, is the relative speed, is the Stribeck speed, is the macroscopic viscous friction damping coefficient, is the electromagnetic torque, is a natural constant, is a sign function; According to Newton's second law: ; Where, is the moment of inertia of the coarse tracking system, is the motor rotation angle, is the second-order derivative of the motor angle, is the friction torque; When the coarse tracking system rotates at a constant speed, the friction torque is: ; Where, is the torque constant, The driving current is the driving current. When the coarse tracking system rotates at a constant speed, the friction torque is obtained by measuring the driving current.

[0025] The feedforward compensation algorithm based on the Stribeck friction model includes: Input to the friction compensator with the Stribeck friction model, divided by the torque constant Get compensation current ,at the same time Input to PI controller together with negative speed feedback signal Get current signal ,Will As control input ;Will 、 and negative current feedback signal Input the current regulator together, then limit it, input the driver and motor, and add friction disturbance Then sent to the coarse tracking system , and then form the system output; The negative current feedback signal is provided by the signal before the motor, and the signal before the motor is input to the system transfer function The residual signal is obtained , and then input the robust controller The negative current feedback signal is obtained and used as a compensation signal ; The negative speed feedback signal is provided by the signal after the motor, the signal after the motor is added with a noise signal, and a negative feedback signal is output to After that, the output is negatively fed back to Before, a negative speed feedback signal is formed.

[0026] The multi-objective complementary control methods include the equivalent robust controller for: ; for: ; Where, 、 is the unit element, Equivalent to , Equivalent to .

[0027] Solving the Equivalent Robust Controller Including sensitivity function and complementary sensitivity function for: ; ; make of Norm less than 1: ; Where, are three weighting functions, is the transfer function matrix, and the Augw function provided by MATLAB is used to calculate the weighting function. Solve it.

[0028] The feedforward compensation algorithm technical process of the present invention is as follows Figure 1 As shown, the speed signal Input to the friction compensator with the Stribeck friction model, divided by the torque constant Get compensation current ,at the same time Together with the negative speed feedback signal, it is input into the PI controller to obtain the current signal ,Will 、 and negative current feedback signal Input the current regulator together, then limit it, input the driver and motor, and add friction disturbance Then sent to the coarse tracking system The negative current feedback signal is provided by the signal before the motor; the negative speed feedback signal is provided by the signal after the motor. The control logic of the feedforward compensation algorithm is as follows: Figure 8 As shown, the system input is set to , first enter and get As control input , then add Forming a coarse tracking system , and finally form the system output .join in The signal before input to , and get the residual signal , and then input the robust controller In the process, a negative current feedback signal is obtained, and the negative current feedback signal is used as a compensation signal. , After the signal is added , output negative feedback to Later formed as negative feedback , output negative feedback to Before, a negative speed feedback signal is formed.

[0029] The present invention combines the low frequency band of the sinusoidal sweep signal and the medium and high frequency bands of the pseudo-random sequence to obtain a new frequency response that can improve the accuracy and efficiency of the identification model. The system transfer function is obtained by the Hankel matrix identification method. In actual identification, since there are noise components in the actual or estimated impulse response sequence, when the dimension of the Hankel matrix is increased, its rank will continue to increase. If the impulse response has a high signal-to-noise ratio, it can be considered that the larger singular value is caused by the real mode and the smaller singular value is caused by noise. Therefore, the system order can be determined according to the position where the singular value has a large mutation. A Stribeck friction model is established, and a feedforward compensation algorithm is designed based on the obtained friction model. Multi-objective complementary control design is performed through the system transfer function to improve the system tracking and anti-disturbance performance. The present invention is tested in conjunction with examples. The step responses under PID control and multi-objective complementary control are as follows: Figure 2 、 Figure 3 As shown in the figure, the analysis shows that the adjustment time of PID control and multi-objective complementary control are 1.12s and 0.82s respectively, and the overshoot is 、 ; The sinusoidal tracking conditions under PID control and multi-objective complementary control are as follows: Figure 4 、 Figure 5 As shown, analysis Figure 4It can be seen that due to the influence of the accuracy of the friction model, overcompensation will occur at the speed reversal point. Figure 5 It can be seen that multi-objective complementary control can better solve this problem and improve the system control accuracy. The maximum errors of sine tracking under PID control and multi-objective complementary control are 、 ; Apply a 5Hz sinusoidal disturbance signal, the disturbance responses under PID control and multi-objective complementary control are as follows Figure 6 、 Figure 7 As shown in the figure, the analysis shows that the maximum errors under PID control and multi-objective complementary control are 、 .

[0030] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Comprehensive modeling and multi-objective complementary control method of laser communication coarse tracking system, characterized by: include: S1. Linear modeling of the coarse tracking system is performed. The low frequency band of the sine sweep signal and the medium and high frequency bands of the pseudo-random signal are combined to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method. S2. Perform nonlinear modeling on the coarse tracking system, establish the Stribeck friction model, and design a feedforward compensation algorithm based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system.

2. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 1 is characterized in that: S1 includes the linear system state space model: ； Where, is the state variable, is the input variable, is the output variable, are the system state space model parameters, For the moment, is the Stribeck friction model; Linear system autocorrelation function and cross-correlation function They are: ； ； Where, is the sequence length of one cycle of the random input signal, is the system input, is the system output, For the A moment.

3. The comprehensive modeling and multi-objective complementary control method for a laser communication coarse tracking system according to claim 2 is characterized in that: S1 includes, let the impulse response of the discrete linear system under zero initial state be , the relationship between the impulse response and the cross-correlation function is: ； Where, is the impulse response time, For the impulse response moment.

4. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 3 is characterized in that: S1 includes the relationship between the impulse response and the cross-correlation function to obtain the system impulse response, and construct the Hankel matrix through the impulse response sequence. : ； Where, is the Hankel matrix number of rows; Hankel matrix Perform singular value decomposition and get: ； ； ； Where, is the singular value obtained by decomposition, 、 is an orthogonal matrix, is the identity matrix, is a diagonal matrix.

5. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 4 is characterized in that: S1 includes determining the system order based on the location where the singular value mutation occurs , according to the system order Hankel matrix break down: ； ； ； Where, 、 is a diagonal matrix, 、 yes The two matrix components of 、 yes The two matrix components of ; According to the Hankel matrix , the system state space model parameters are obtained as: ； ； Where, is the intermediate matrix.

6. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 5 is characterized in that: S1 includes the system transfer function obtained through the system state space model , perform multiplicative uncertainty analysis on the system and obtain the system uncertainty model : ； ； Where, is the state quantity of the system state space.

7. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 6 is characterized in that: S2 includes the Stribeck friction model expression: ； Where, is the Coulomb friction torque, is the maximum static friction, is the relative speed, is the Stribeck speed, is the macroscopic viscous friction damping coefficient, is the electromagnetic torque, is a natural constant, is a sign function; According to Newton's second law: ； Where, is the moment of inertia of the coarse tracking system, is the motor rotation angle, is the second-order derivative of the motor angle, is the friction torque; When the coarse tracking system rotates at a constant speed, the friction torque is: ； Where, is the torque constant, The driving current is the driving current. When the coarse tracking system rotates at a constant speed, the friction torque is obtained by measuring the driving current.

8. The comprehensive modeling and multi-objective complementary control method for a laser communication coarse tracking system according to claim 7 is characterized in that: The feedforward compensation algorithm based on the Stribeck friction model includes: Input to the friction compensator with the Stribeck friction model, divided by the torque constant Get compensation current ,at the same time Input to PI controller together with negative speed feedback signal Get current signal ,Will As control input ;Will 、 and negative current feedback signal Input the current regulator together, then limit it, input the driver and motor, and add friction disturbance Then sent to the coarse tracking system , and then form the system output; The negative current feedback signal is provided by the signal before the motor, and the signal before the motor is input to the system transfer function The residual signal is obtained , and then input the robust controller The negative current feedback signal is obtained and used as a compensation signal ; The negative speed feedback signal is provided by the signal after the motor, the signal after the motor is added with a noise signal, and a negative feedback signal is output to After that, the output is negatively fed back to Before, a negative speed feedback signal is formed.

9. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 8 is characterized in that: The multi-objective complementary control methods include the equivalent robust controller for: ； for: ； Where, 、 is the unit element, Equivalent to , Equivalent to .

10. The laser communication coarse tracking system comprehensive modeling and multi-objective complementary control method according to claim 9 is characterized in that: Solving the Equivalent Robust Controller Including sensitivity function and complementary sensitivity function for: ； ； make of Norm less than 1: ； Where, are three weighting functions, is the transfer function matrix, and the Augw function provided by MATLAB is used to calculate the weighting function. Solve it.

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