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

Abstract

The application discloses a laser communication coarse tracking system comprehensive modeling and multi-target complementary control method, and belongs to the field of laser communication technology control. The laser communication coarse tracking system is used for control, comprising linear modeling of the coarse tracking system, combination of low frequency bands of sinusoidal sweep signals and middle and high frequency bands of pseudo-random signals to obtain system frequency response, and system transfer function obtained through Hankel matrix identification method; nonlinear modeling of the coarse tracking system, establishment of a Stribeck friction model, and design of a feedforward compensation algorithm based on the Stribeck friction model to obtain a multi-target complementary control method for controlling the coarse tracking system. The application realizes accurate identification of model order and parameters in the linear part, significantly improves low-speed tracking performance in the nonlinear part, effectively solves the contradiction between system performance and robustness, and significantly improves tracking precision and anti-interference ability.

Description

Technical Field

[0001] This invention discloses a comprehensive modeling and multi-target complementary control method for a coarse tracking system in laser communication, belonging to the field of laser communication technology control. Background Technology

[0002] Coarse tracking systems are a crucial component of aiming, acquisition, and tracking systems in laser communication, serving functions such as line-of-sight alignment, target tracking, and isolation from external interference. Coarse tracking systems typically employ a two-axis, two-frame turntable or a two-dimensional tilting mirror mechanism. Through drive control of the pitch and azimuth axes, they align the laser communication terminal with the target position, providing a fundamental guarantee for establishing a stable and persistent laser communication link. However, coarse tracking systems exhibit stronger nonlinear characteristics, such as frictional torque, load imbalance, and axis coupling, which can complicate the establishment of system models. Furthermore, coarse tracking systems are directly mounted on a moving base platform, constantly exposed to external disturbances, severely impacting their line-of-sight pointing accuracy. Therefore, it is necessary to establish accurate models for coarse tracking systems and suppress the influence of internal nonlinear characteristics and external interference to improve dynamic tracking performance.

[0003] Currently, the mainstream method for model identification is to determine model parameters using the least squares method and its improvements, assuming the model structure or order is known. However, as a complex controlled object, the flexibility and disturbances experienced by a coarse tracking system are difficult to describe with formulas, making it difficult to accurately determine the model order and resulting in low model identification accuracy. The nonlinear characteristic that plays a major role in coarse tracking systems is friction torque, whose impact on the system's dynamic and static performance is mainly reflected in the dead zone during low-speed tracking and the large error in steady state. These problems reduce the system's control accuracy. Under the classical control framework, tracking performance and disturbance suppression capability are mutually restrictive. Under the constraint of ensuring system stability, it is often necessary to make trade-offs in the design of multiple performance indicators. This design method is difficult to meet the high-performance requirements of servo control in laser communication coarse tracking systems. Summary of the Invention

[0004] The purpose of this invention is to provide a comprehensive modeling and multi-objective complementary control method for laser communication coarse tracking systems, so as to solve the problem that existing technical methods cannot meet the high-performance requirements of servo control for laser communication coarse tracking systems.

[0005] A comprehensive modeling and multi-target complementary control method for laser communication coarse tracking systems includes:

[0006] S1. Linear modeling of the coarse tracking system is performed by combining the low-frequency band of the sinusoidal sweep signal and the mid-to-high frequency band of the pseudo-random signal to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method.

[0007] S2. Nonlinear modeling of the coarse tracking system is performed, a Stribeck friction model is established, and a feedforward compensation algorithm is designed based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system.

[0008] S1 includes the following linear system state-space model:

[0009] ;

[0010] In the formula, For state variables, For input variables, For output variables, These are the parameters of the system state-space model. For a moment, For the Stribeck friction model;

[0011] Autocorrelation function of linear system and cross-correlation function They are respectively:

[0012] ;

[0013] ;

[0014] In the formula, It is the sequence length of one period of the random input signal. It is system input. It is system output. For the first That moment.

[0015] S1 includes setting the impulse response of the discrete linear system under zero initial state as follows: The relationship between the impulse response and the cross-correlation function is as follows:

[0016] ;

[0017] In the formula, The moment of impulse response, For the first Each impulse response time.

[0018] S1 includes obtaining the system impulse response from the relationship between the impulse response and the cross-correlation function, and constructing the Hankel matrix from the impulse response sequence. :

[0019] ;

[0020] In the formula, Hankel matrix number of rows;

[0021] Hankel matrix Singular value decomposition yields:

[0022] ;

[0023] ;

[0024] ;

[0025] In the formula, To decompose the singular values, , It is an orthogonal matrix. It is the identity matrix. It is a diagonal matrix.

[0026] S1 includes determining the system order based on the location of abrupt changes in singular values. According to the system order Hankel matrix break down:

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula, , It is a diagonal matrix. , yes The two matrix components, , yes The two matrix components;

[0031] According to Hankel's matrix The system state-space model parameters are obtained as follows:

[0032] ;

[0033] ;

[0034] In the formula, This is the intermediate matrix.

[0035] S1 includes obtaining the system transfer function through the system state-space model. Multiplicative uncertainty analysis was performed on the system to obtain the system uncertainty model. :

[0036] ;

[0037] ;

[0038] In the formula, These are the state variables in the system's state space.

[0039] S2 includes the expression for the Stribek friction model:

[0040] ;

[0041] In the formula, The Coulomb friction torque is... For the maximum static friction force, For relative velocity, For Strybeck speed, It is the macroscopic viscous friction damping coefficient. For electromagnetic torque, It is a natural constant. It is a symbolic function;

[0042] According to Newton's second law:

[0043] ;

[0044] In the formula, For the rotational inertia of the coarse tracking system, For the motor rotation angle, The second derivative of the motor rotation angle. This is the frictional torque;

[0045] When the coarse tracking system rotates at a constant speed, the frictional torque is:

[0046] ;

[0047] In the formula, The torque constant is As the driving current, the frictional torque is obtained by measuring the driving current when the coarse tracking system rotates at a constant speed.

[0048] The feedforward compensation algorithm based on the Stribeck friction model includes the following steps: [The algorithm is then applied to] the velocity signal... The input is fed into a friction compensator with a Stribek friction model and divided by the torque constant. Obtain compensation current ,at the same time The negative speed feedback signal is input to the PI controller. Obtain current signal ,Will As control input ;Will , and negative current feedback signal The current regulator is input together, then limited, and the input to the driver and motor is combined with frictional disturbance. Then sent to the coarse tracking system Then, the system output is generated;

[0049] 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. In the process, the residual signal is obtained. Then input robust controller In the process, the negative current feedback signal is obtained, and the negative current feedback signal is used as the compensation signal. ;

[0050] The negative speed feedback signal is provided by the signal after the motor. Noise is added to the signal after the motor, and a negative feedback signal is output to... Then, a negative feedback loop is output to... Previously, a negative speed feedback signal was generated.

[0051] Methods for obtaining multi-objective complementary control include equivalent robust controllers. for:

[0052] ;

[0053] for:

[0054] ;

[0055] In the formula, , The unit is yuan. Equivalent to , Equivalent to .

[0056] Solving for the equivalent robust controller Including sensitivity function Complementary sensitivity function for:

[0057] ;

[0058] ;

[0059] make of Norm less than 1:

[0060] ;

[0061] In the formula, There are three weighted functions. It is a transfer function matrix, which is adjusted using the Augw function provided by MATLAB based on the selected weighting function. Solve the problem.

[0062] Compared with the prior art, the present invention has the following beneficial effects: the present invention achieves accurate identification of model order and parameters in the linear part, significantly improves low-speed tracking performance in the nonlinear part, effectively solves the contradiction between system performance and robustness, and significantly improves tracking accuracy and anti-disturbance capability. Attached Figure Description

[0063] Figure 1 This is a flowchart of the feedforward compensation algorithm of the present invention;

[0064] Figure 2 It is the step response under PID control;

[0065] Figure 3 It is a step response under multi-objective complementary control;

[0066] Figure 4 This is the sine wave tracking effect under PID control;

[0067] Figure 5 It is a sinusoidal tracking effect under multi-target complementary control;

[0068] Figure 6 This describes the disturbance response under PID control.

[0069] Figure 7 This describes the disturbance response under multi-objective complementary control.

[0070] Figure 8 This is the control logic diagram of the feedforward compensation algorithm. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0072] A comprehensive modeling and multi-target complementary control method for laser communication coarse tracking systems includes:

[0073] S1. Linear modeling of the coarse tracking system is performed by combining the low-frequency band of the sinusoidal sweep signal and the mid-to-high frequency band of the pseudo-random signal to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method.

[0074] S2. Nonlinear modeling of the coarse tracking system is performed, a Stribeck friction model is established, and a feedforward compensation algorithm is designed based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system.

[0075] S1 includes the following linear system state-space model:

[0076] ;

[0077] In the formula, For state variables, For input variables, For output variables, These are the parameters of the system state-space model. For a moment, For the Stribeck friction model;

[0078] Autocorrelation function of linear system and cross-correlation function They are respectively:

[0079] ;

[0080] ;

[0081] In the formula, It is the sequence length of one period of the random input signal. It is system input. It is system output. For the first That moment.

[0082] S1 includes setting the impulse response of the discrete linear system under zero initial state as follows: The relationship between the impulse response and the cross-correlation function is as follows:

[0083] ;

[0084] In the formula, The moment of impulse response, For the first Each impulse response time.

[0085] S1 includes obtaining the system impulse response from the relationship between the impulse response and the cross-correlation function, and constructing the Hankel matrix from the impulse response sequence. :

[0086] ;

[0087] In the formula, Hankel matrix number of rows;

[0088] Hankel matrix Singular value decomposition yields:

[0089] ;

[0090] ;

[0091] ;

[0092] In the formula, To decompose the singular values, , It is an orthogonal matrix. It is the identity matrix. It is a diagonal matrix.

[0093] S1 includes determining the system order based on the location of abrupt changes in singular values. According to the system order Hankel matrix break down:

[0094] ;

[0095] ;

[0096] ;

[0097] In the formula, , It is a diagonal matrix. , yes The two matrix components, , yes The two matrix components;

[0098] According to Hankel's matrix The system state-space model parameters are obtained as follows:

[0099] ;

[0100] ;

[0101] In the formula, This is the intermediate matrix.

[0102] S1 includes obtaining the system transfer function through the system state-space model. Multiplicative uncertainty analysis was performed on the system to obtain the system uncertainty model. :

[0103] ;

[0104] ;

[0105] In the formula, These are the state variables in the system's state space.

[0106] S2 includes the expression for the Stribek friction model:

[0107] ;

[0108] In the formula, The Coulomb friction torque is... For the maximum static friction force, For relative velocity, For Strybeck speed, It is the macroscopic viscous friction damping coefficient. For electromagnetic torque, It is a natural constant. It is a symbolic function;

[0109] According to Newton's second law:

[0110] ;

[0111] In the formula, For the rotational inertia of the coarse tracking system, For the motor rotation angle, The second derivative of the motor rotation angle. This is the frictional torque;

[0112] When the coarse tracking system rotates at a constant speed, the frictional torque is:

[0113] ;

[0114] In the formula, The torque constant is As the driving current, the frictional torque is obtained by measuring the driving current when the coarse tracking system rotates at a constant speed.

[0115] The feedforward compensation algorithm based on the Stribeck friction model includes the following steps: [The algorithm is then applied to] the velocity signal... The input is fed into a friction compensator with a Stribek friction model and divided by the torque constant. Obtain compensation current ,at the same time The negative speed feedback signal is input to the PI controller. Obtain current signal ,Will As control input ;Will , and negative current feedback signal The current regulator is input together, then limited, and the input to the driver and motor is combined with frictional disturbance. Then sent to the coarse tracking system Then, the system output is generated;

[0116] 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. In the process, the residual signal is obtained. Then input robust controller In the process, the negative current feedback signal is obtained, and the negative current feedback signal is used as the compensation signal. ;

[0117] The negative speed feedback signal is provided by the signal after the motor. Noise is added to the signal after the motor, and a negative feedback signal is output to... Then, a negative feedback loop is output to... Previously, a negative speed feedback signal was generated.

[0118] Methods for obtaining multi-objective complementary control include equivalent robust controllers. for:

[0119] ;

[0120] for:

[0121] ;

[0122] In the formula, , The unit is yuan. Equivalent to , Equivalent to .

[0123] Solving for the equivalent robust controller Including sensitivity function Complementary sensitivity function for:

[0124] ;

[0125] ;

[0126] make of Norm less than 1:

[0127] ;

[0128] In the formula, There are three weighted functions. It is a transfer function matrix, which is adjusted using the Augw function provided by MATLAB based on the selected weighting function. Solve the problem.

[0129] The feedforward compensation algorithm of this invention is as follows: Figure 1 As shown, the speed signal The input is fed into a friction compensator with a Stribek friction model and divided by the torque constant. Obtain compensation current ,at the same time The negative speed feedback signal is input together with the PI controller to obtain the current signal. ,Will , and negative current feedback signal The current regulator is input together, then limited, and the input to the driver and motor is combined with frictional 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 Finally, the system output is generated. .join in The previous signal input to The residual signal is obtained. Then input robust controller In the process, a negative current feedback signal is obtained, and this negative current feedback signal is used as a compensation signal. , Subsequent signal addition Output one negative feedback path to It then forms as negative feedback. Output one negative feedback path to Previously, a negative speed feedback signal was generated.

[0130] This invention combines the low-frequency band of a sinusoidal sweep signal with the mid-to-high-frequency band of a pseudo-random sequence to obtain a new frequency response, which improves the accuracy and efficiency of the identification model. The system transfer function is obtained using the Hankel matrix identification method. In practical identification, due to noise components in the actual or estimated impulse response sequence, the rank of the Hankel matrix increases with increasing its dimension. If the impulse response has a high signal-to-noise ratio, larger singular values ​​can be considered to be caused by the true mode, and smaller singular values ​​by noise. Therefore, the system order can be determined based on the location of large abrupt changes in singular values. A Stribek friction model is established, and a feedforward compensation algorithm is designed based on the obtained friction model. Multi-objective complementary control is designed using the system transfer function to improve the system's tracking and disturbance rejection performance. This invention is illustrated with experimental examples, showing the step responses under PID control and multi-objective complementary control as follows: Figure 2 , Figure 3 As shown in the figure, the analysis reveals that the settling times for PID control and multi-objective complementary control are 1.12s and 0.82s, respectively, and the overshoots are respectively... , The sinusoidal tracking cases under PID control and multi-objective complementary control are as follows: Figure 4 , Figure 5 As shown, analysis Figure 4 It can be seen that the accuracy of the friction model affects the phenomenon of overcompensation at the velocity reversal point. Analysis 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 under PID control and multi-objective complementary control under sinusoidal tracking are respectively... , When a 5Hz sinusoidal disturbance signal is applied, the disturbance response under PID control and multi-objective complementary control are as follows: Figure 6 , Figure 7 As shown in the figure, the analysis reveals that the maximum errors under PID control and multi-objective complementary control are respectively... , .

[0131] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions 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. A comprehensive modeling and multi-target complementary control method for laser communication coarse tracking systems, characterized in that, include: S1. Linear modeling of the coarse tracking system is performed by combining the low-frequency band of the sinusoidal sweep signal and the mid-to-high frequency band of the pseudo-random signal to obtain the system frequency response. The system transfer function is obtained by the Hankel matrix identification method. S2. Nonlinear modeling of the coarse tracking system is performed, a Stribeck friction model is established, and a feedforward compensation algorithm is designed based on the Stribeck friction model to obtain a multi-objective complementary control method to control the coarse tracking system. S1 includes obtaining the system transfer function through the system state-space model. Multiplicative uncertainty analysis was performed on the system to obtain the system uncertainty model. : ； ； In the formula, These are the state variables in the system's state space; S2 includes the expression for the Stribek friction model: ； In the formula, The Coulomb friction torque is... For maximum static friction, For relative velocity, For Strybeck speed, It is the macroscopic viscous friction damping coefficient. For electromagnetic torque, It is a natural constant. It is a symbolic function; According to Newton's second law: ； In the formula, For the rotational inertia of the coarse tracking system, For the motor rotation angle, The second derivative of the motor rotation angle. This is the frictional torque; When the coarse tracking system rotates at a constant speed, the frictional torque is: ； In the formula, The torque constant is As the driving current, the frictional torque is obtained by measuring the driving current when the coarse tracking system rotates at a constant speed. The feedforward compensation algorithm based on the Stribeck friction model includes the following steps: [The algorithm is then applied to] the velocity signal... The input is fed into a friction compensator with a Stribek friction model and divided by the torque constant. Obtain compensation current ,at the same time The negative speed feedback signal is input to the PI controller. Obtain current signal ,Will As control input ;Will , and negative current feedback signal The current regulator is input together, then limited, and the input to the driver and motor is combined with frictional disturbance. Then sent to the coarse tracking system Then, the system output is generated; 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. In the process, the residual signal is obtained. Then input robust controller In the process, the negative current feedback signal is obtained, and the negative current feedback signal is used as the compensation signal. ; The negative speed feedback signal is provided by the signal after the motor. Noise is added to the signal after the motor, and a negative feedback signal is output to... Then, a negative feedback loop is output to... Previously, a negative speed feedback signal was generated; Methods for obtaining multi-objective complementary control include equivalent robust controllers. for: ； for: ； In the formula, , The unit is yuan. Equivalent to , Equivalent to ; Solving for the equivalent robust controller Including sensitivity function Complementary sensitivity function for: ； ； make of Norm less than 1: ； In the formula, There are three weighted functions. It is a transfer function matrix, which is adjusted using the Augw function provided by MATLAB based on the selected weighting function. Solve the problem.

2. The method for integrated modeling and multi-target complementary control of a laser communication coarse tracking system according to claim 1, characterized in that, S1 includes the following linear system state-space model: ； In the formula, For state variables, For input variables, For output variables, These are the parameters of the system state-space model. For a moment, For the Stribeck friction model; Autocorrelation function of linear system and cross-correlation function They are respectively: ； ； In the formula, It is the sequence length of one period of the random input signal. It is system input. It is system output. For the first That moment.

3. The method for integrated modeling and multi-target complementary control of a laser communication coarse tracking system according to claim 2, characterized in that, S1 includes setting the impulse response of the discrete linear system under zero initial state as follows: The relationship between the impulse response and the cross-correlation function is as follows: ； In the formula, The moment of impulse response, For the first Each impulse response time.

4. The method for integrated modeling and multi-target complementary control of a laser communication coarse tracking system according to claim 3, characterized in that, S1 includes obtaining the system impulse response from the relationship between the impulse response and the cross-correlation function, and constructing the Hankel matrix from the impulse response sequence. : ； In the formula, Hankel matrix number of rows; Hankel matrix Singular value decomposition yields: ； ； ； In the formula, To decompose the singular values, , It is an orthogonal matrix. It is the identity matrix. It is a diagonal matrix.

5. The method for integrated modeling and multi-target complementary control of a laser communication coarse tracking system according to claim 4, characterized in that, S1 includes determining the system order based on the location of abrupt changes in singular values. According to the system order Hankel matrix break down: ； ； ； In the formula, , It is a diagonal matrix. , yes The two matrix components, , yes The two matrix components; According to Hankel's matrix The system state-space model parameters are obtained as follows: ； ； In the formula, This is the intermediate matrix.

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