CN118192277B - Quick reflector auto-disturbance rejection controller parameter determination method for improving sparrow search - Google Patents
Quick reflector auto-disturbance rejection controller parameter determination method for improving sparrow search Download PDFInfo
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Abstract
The invention discloses a method for determining parameters of a quick reflector active disturbance rejection controller for improving sparrow search, which belongs to the technical field of disturbance rejection control and comprises the steps of adopting a system identification method to determine a transfer function of a quick reflector system driven by a voice coil motor, designing the active disturbance rejection controller according to a quick reflector model, and determining parameters based on an improved sparrow search algorithm; the active disturbance rejection controller comprises a linear extended state observer and a linear state error feedback control law; the invention can find out proper control parameters when facing different working conditions, effectively improves the parameter setting efficiency of the controller and improves the anti-interference capability and tracking precision of the quick reflector.
Description
Technical Field
The invention discloses a method for determining parameters of a fast reflector active disturbance rejection controller for improving sparrow search, and belongs to the technical field of disturbance rejection control.
Background
Wireless optical communications require aiming, acquisition and tracking (PAT) techniques to quickly acquire wireless optical communication signals, PAT systems typically employ coarse/fine composite axis techniques. The quick reflector is used as a core component for fine tracking in compound axis control, and the control precision of the quick reflector determines the tracking precision of the whole system. However, in the face of numerous uncertainty interference of the ocean, how to efficiently enable the rapid reflector not to influence the accurate output of the rapid reflector under different working conditions is a problem to be solved.
The active disturbance rejection control is an effective method for estimating and compensating uncertainty, and is characterized in that a distended state observer is utilized to estimate disturbance and design a control law to ensure the stability of a system, so that the tracking precision and the anti-disturbance capability of a quick reflector system are improved. However, the auto-disturbance-rejection controller needs more setting parameters, has higher difficulty, and most of the current auto-disturbance-rejection controllers depend on artificial and actual experiences, so that the application of the auto-disturbance-rejection technology in an actual control system is hindered to a certain extent. For this problem, intelligent algorithms may be employed to optimize the controller parameters. Compared with other traditional intelligent optimization algorithms, the sparrow search algorithm has the obvious advantages of high stability, good search precision, high convergence speed, and meanwhile, the sparrow search algorithm has the problems of easy local optimization, random optimization results and the like.
Disclosure of Invention
The invention aims to provide a quick reflector auto-disturbance-rejection controller parameter determination method for improving sparrow search, which aims to solve the problem that the auto-disturbance-rejection controller parameter is difficult to determine in the prior art.
The method for determining the parameters of the fast reflector active disturbance rejection controller for improving sparrow search comprises the steps of determining the transfer function of a fast reflector system driven by a voice coil motor by adopting a system identification method, designing the active disturbance rejection controller according to a fast reflector model, and determining the parameters based on an improved sparrow search algorithm; the active disturbance rejection controller comprises a linear extended state observer and a linear state error feedback control law;
parameter determination based on the improved sparrow search algorithm includes:
S1, constructing an adaptability function for improving a sparrow search algorithm according to a preset output angular position and an actual output angular position of a quick reflector;
s2, correlating the parameter to be set of the active disturbance rejection controller with the individual position of the sparrows and initializing the sparrow population number Maximum number of iterationsUpper and lower bounds of initial value、Determining a population as a finderPerson with vigilanceIs a ratio of (3);
s3, generating a sparrow initial population by using Chebyshev chaotic mapping;
s4, calculating and sequencing the fitness value of each sparrow individual of the sparrow population according to the fitness function, the parameter to be set and the rapid reflector system parameter obtained in real time;
S5, fusing the improved sparrow searching algorithm with a sparrow position updating formula, and carrying out iterative updating according to the improved position updating formula;
S6, after each iteration update, the target position is updated by using dynamic random disturbance according to the dynamic reverse learning and the cauchy variation strategy, so that the target position is prevented from being trapped into local optimum;
and S7, stopping updating when the iteration times reach a set value, outputting the global optimal position of the sparrow population, and finishing parameter setting of the active disturbance rejection controller.
Transfer function of a fast mirror systemComprising the following steps:
；
In the method, in the process of the invention, Is the state quantity of the fast mirror model.
The differential form of the fast mirror model is:
；
In the method, in the process of the invention, For the output of the system,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is a quantitative parameter of the linear expansion state observer,Is thatIs a part of the known art of the present invention,As an unknown overall disturbance, the total disturbance,In order to control the signal of the power supply,AndAs a result of the parameters being known in the art,，。
The linear extended state observer includes, setting variables：
；
In the method, in the process of the invention,For the total disturbance, let，，：
；
In the method, in the process of the invention,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
Rewriting into a matrix form:
；，，，；
In the method, in the process of the invention, 、、、Are known matrices.
The linear extended state observer is:
；
In the method, in the process of the invention, 、AndRespectively is、AndIs used for the estimation of (a),、AndIn order for the gain of the observer to be achieved,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
the linear expansion state observer is rewritten into a matrix form as follows:
；；；；
In the method, in the process of the invention, Is an observation state vector of the linear extended state observer,Is thatIs used for the purpose of determining the derivative of (c),For the observer gain matrix to be designed,In order for the observer to input,Output of the linear state observer;
The poles of the characteristic equation in the linear expansion state observer in a matrix form are all configured to the same position by utilizing a pole configuration method And (3) the following steps:
；
In the method, in the process of the invention, For the pole configuration equation,Is a three-order identity matrix,Bandwidth for observer;
Obtaining an observer gain matrix:
。
The linear state error feedback control law includes:
；
In the method, in the process of the invention, In order to control the input of the quantity,For the purpose of scaling up the coefficients of the power,For the input to the system,Is a differential amplification factor;
the control quantity input of the quick reflector system is as follows:
；
closed loop transfer function The method comprises the following steps:
；；
In the method, in the process of the invention, Is the controller bandwidth.
S5 includes that the finder update formula is as follows:
；；；；;
In the method, in the process of the invention, Is shown in the firstOn dimension (C)Only sparrow passes throughThe position at +1 iteration,Is a random number which is used to determine the random number,Is the alert value of the person in question,Representing the random numbers belonging to a normal distribution,1 For each elementThe matrix is formed by a matrix of,In order to be of the maximum dimension,Representing a security value;
the improved discoverer update formula is as follows:
；
In the method, in the process of the invention, For a globally optimal solution,In order to adapt the inertial weight factor,Is a random number.
S5 includes the following follower update formula:
；；
In the method, in the process of the invention, Representing the worst position of the current global situation,Indicating the optimal position currently occupied by the finder,Is thatIs a matrix of the (c) in the matrix,Each element of the matrix is randomly assigned with 1 or-1;
The updated follower formula after improvement is as follows:
；
In the method, in the process of the invention, In order to control the parameters of the spiral,Is a linearly varying parameter.
S5, including the following formula for updating the alerter:
；；
In the method, in the process of the invention, Is the current global optimum position and,Is a random number subject to a normal distribution with a mean value of 0 and a variance of 1,A random number is used as a control step length parameter to represent the direction of the sparrow moving position; is the minimum constant, and ensures that the denominator is not zero; For a global optimum fitness value, Is the global worst fitness value,And the fitness value of the current sparrow individual is indicated.
S6, integrating a dynamic reverse learning strategy into a sparrow search algorithm:
；
；
In the method, in the process of the invention, Is the firstA reverse solution to the optimal solution;
Introducing cauchy variation into position updates:
；
In the method, in the process of the invention, Is cauchy variation;
Alternately executing the dynamic reverse learning strategy and the cauchy variation strategy, and selecting probability The calculation formula is as follows:
。
Compared with the prior art, the invention has the following beneficial effects: the invention can find out proper control parameters when facing different working conditions, effectively improves the parameter setting efficiency of the controller and improves the anti-interference capability and tracking precision of the quick reflector.
Drawings
FIG. 1 is a block diagram of an active disturbance rejection controller;
Fig. 2 is a fast mirror control block diagram.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The method for determining the parameters of the fast reflector active disturbance rejection controller for improving sparrow search comprises the steps of determining the transfer function of a fast reflector system driven by a voice coil motor by adopting a system identification method, designing the active disturbance rejection controller according to a fast reflector model, and determining the parameters based on an improved sparrow search algorithm; the active disturbance rejection controller comprises a linear extended state observer and a linear state error feedback control law;
parameter determination based on the improved sparrow search algorithm includes:
S1, constructing an adaptability function for improving a sparrow search algorithm according to a preset output angular position and an actual output angular position of a quick reflector;
s2, correlating the parameter to be set of the active disturbance rejection controller with the individual position of the sparrows and initializing the sparrow population number Maximum number of iterationsUpper and lower bounds of initial value、Determining a population as a finderPerson with vigilanceIs a ratio of (3);
s3, generating a sparrow initial population by using Chebyshev chaotic mapping;
s4, calculating and sequencing the fitness value of each sparrow individual of the sparrow population according to the fitness function, the parameter to be set and the rapid reflector system parameter obtained in real time;
S5, fusing the improved sparrow searching algorithm with a sparrow position updating formula, and carrying out iterative updating according to the improved position updating formula;
S6, after each iteration update, the target position is updated by using dynamic random disturbance according to the dynamic reverse learning and the cauchy variation strategy, so that the target position is prevented from being trapped into local optimum;
and S7, stopping updating when the iteration times reach a set value, outputting the global optimal position of the sparrow population, and finishing parameter setting of the active disturbance rejection controller.
Transfer function of a fast mirror systemComprising the following steps:
；
In the method, in the process of the invention, Is the state quantity of the fast mirror model.
The differential form of the fast mirror model is:
；
In the method, in the process of the invention, For the output of the system,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is a quantitative parameter of the linear expansion state observer,Is thatIs a part of the known art of the present invention,As an unknown overall disturbance, the total disturbance,In order to control the signal of the power supply,AndAs a result of the parameters being known in the art,，。
The linear extended state observer includes, setting variables：
；
In the method, in the process of the invention,For the total disturbance, let，，：
；
In the method, in the process of the invention,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
Rewriting into a matrix form:
；，，，；
In the method, in the process of the invention, 、、、Are known matrices.
The linear extended state observer is:
；
In the method, in the process of the invention, 、AndRespectively is、AndIs used for the estimation of (a),、AndIn order for the gain of the observer to be achieved,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
the linear expansion state observer is rewritten into a matrix form as follows:
；；；；
In the method, in the process of the invention, Is an observation state vector of the linear extended state observer,Is thatIs used for the purpose of determining the derivative of (c),For the observer gain matrix to be designed,In order for the observer to input,Output of the linear state observer;
The poles of the characteristic equation in the linear expansion state observer in a matrix form are all configured to the same position by utilizing a pole configuration method And (3) the following steps:
；
In the method, in the process of the invention, For the pole configuration equation,Is a three-order identity matrix,Bandwidth for observer;
Obtaining an observer gain matrix:
。
The linear state error feedback control law includes:
；
In the method, in the process of the invention, In order to control the input of the quantity,For the purpose of scaling up the coefficients of the power,For the input to the system,Is a differential amplification factor;
the control quantity input of the quick reflector system is as follows:
；
closed loop transfer function The method comprises the following steps:
；；
In the method, in the process of the invention, Is the controller bandwidth.
S5 includes that the finder update formula is as follows:
；；；；;
In the method, in the process of the invention, Is shown in the firstOn dimension (C)Only sparrow passes throughThe position at +1 iteration,Is a random number which is used to determine the random number,Is the alert value of the person in question,Representing the random numbers belonging to a normal distribution,1 For each elementThe matrix is formed by a matrix of,In order to be of the maximum dimension,Representing a security value;
the improved discoverer update formula is as follows:
；
In the method, in the process of the invention, For a globally optimal solution,In order to adapt the inertial weight factor,Is a random number.
S5 includes the following follower update formula:
；；
In the method, in the process of the invention, Representing the worst position of the current global situation,Indicating the optimal position currently occupied by the finder,Is thatIs a matrix of the (c) in the matrix,Each element of the matrix is randomly assigned with 1 or-1;
The updated follower formula after improvement is as follows:
；
In the method, in the process of the invention, In order to control the parameters of the spiral,Is a linearly varying parameter.
S5, including the following formula for updating the alerter:
；；
In the method, in the process of the invention, Is the current global optimum position and,Is a random number subject to a normal distribution with a mean value of 0 and a variance of 1,A random number is used as a control step length parameter to represent the direction of the sparrow moving position; is the minimum constant, and ensures that the denominator is not zero; For a global optimum fitness value, Is the global worst fitness value,And the fitness value of the current sparrow individual is indicated.
S6, integrating a dynamic reverse learning strategy into a sparrow search algorithm:
；
；
In the method, in the process of the invention, Is the firstA reverse solution to the optimal solution;
Introducing cauchy variation into position updates:
；
In the method, in the process of the invention, Is cauchy variation;
Alternately executing the dynamic reverse learning strategy and the cauchy variation strategy, and selecting probability The calculation formula is as follows:
。
The generation of the sparrow initial population by using chebyshev chaotic mapping comprises the following chebyshev chaotic mapping expression:
；
In the method, in the process of the invention, For an individual who is successful in the next moment,For the individual at the present moment in time,The iteration times;
Dynamically adaptive weights The method comprises the following steps:
；
Variable screw coefficient The method comprises the following steps:
；；；
In the method, in the process of the invention, The parameters representing the spiral period are typically population number/10.
Dynamic reverse learning is based on reverse learning, so that the symmetrical area of the search space is enlarged, and the development capability of an algorithm is improved;
the reverse learning strategy and dynamic reverse learning strategy expressions are as follows:
；
；
In the method, in the process of the invention, ，Respectively an upper boundary and a lower boundary; Is defined as Is used in the number of the opposite of (a),Is defined asDynamic opposite numbers of (2); is a random number; ；
the cauchy variation is derived from a cauchy distribution and expressed as follows:
The fitness function in S4 is specifically as follows:
；
In the method, in the process of the invention, Is the difference between the input and output of the system,In order to control the amount of the liquid,AndIs the weight.
Figure 1 is a block diagram of an active disturbance rejection controller,For the reference input to be made,For the output of the system,In order to control the signal of the power supply,Is a linear extended state observer parameter,AndThe linear extended state observer estimates the angular position, the differential angular velocity of the angular position, and the total disturbance. In FIG. 2, the sparrow search algorithm parameter adjuster is modified to take into account the inputControl amountAnd system outputAs input, the bandwidth of the parameter controller to be setAnd observer bandwidthAnd (3) performing iterative optimization according to the fitness function in association with the individual position of the sparrow to obtain optimized parameters to act on the active disturbance rejection controller.
In order to compare the optimizing performance of different algorithms, the effectiveness of an improvement method of an Improved Sparrow Search Algorithm (ISSA) is detected, and six reference test functions are selected for simulation test. Wherein,The method is a unimodal function and is used for testing the convergence speed and convergence accuracy of the algorithm.Is a multimodal function used to evaluate the global search and mining capabilities of the algorithm. The functional names, expressions, search ranges and theoretical optimal solutions of the benchmark functions are shown in tables 1 and 2.
Table 1 unimodal benchmark functions
；
TABLE 2 multimodal benchmark functions
；
And selecting a Sparrow Search Algorithm (SSA), a particle swarm algorithm (PSO), a Whale Optimization Algorithm (WOA) and an artificial bee colony Algorithm (ABC) to carry out comparison experiments with ISSA algorithm. And setting the population quantity of all algorithms to 30, setting the maximum iteration number to 500, setting the dimension to 30, and respectively recording the optimal value, the average value and the standard deviation of the optimization result to verify the exploration performance of the algorithms and evaluate the accuracy and the stability of the algorithms. The experimental results are shown in tables 3 and 4.
Table 3 unimodal benchmark function optimization results
；
TABLE 4 multimodal benchmark function optimization results
。
The amplitude is 0.05%) Sinusoidal signals with frequencies of 30Hz and 50Hz are taken as examples, and the amplitude of the sinusoidal signals is 0.01%) Noise interference at a frequency of 100Hz, verifies SSA and ISSA's ability to optimize for controller parameters. ADRC tracking effect graphs under SSA and ISSA algorithms are respectively shown under two frequencies, and ISSA-ADRC has better tracking effect compared with SSA-ADRC, so that tracking error is obviously reduced.
The above embodiments are only for illustrating the technical aspects of the present invention, not for limiting the same, and although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may be modified or some or all of the technical features may be replaced with other technical solutions, which do not depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. The method is characterized by comprising the steps of determining a transfer function of a voice coil motor driven quick reflector system by adopting a system identification method, designing an automatic disturbance rejection controller according to a quick reflector model, and determining parameters based on an improved sparrow search algorithm; the active disturbance rejection controller comprises a linear extended state observer and a linear state error feedback control law;
parameter determination based on the improved sparrow search algorithm includes:
S1, constructing an adaptability function for improving a sparrow search algorithm according to a preset output angular position and an actual output angular position of a quick reflector;
s2, correlating the parameter to be set of the active disturbance rejection controller with the individual position of the sparrows and initializing the sparrow population number Maximum number of iterationsUpper and lower bounds of initial value、Determining a population as a finderPerson with vigilanceIs a ratio of (3);
s3, generating a sparrow initial population by using Chebyshev chaotic mapping;
s4, calculating and sequencing the fitness value of each sparrow individual of the sparrow population according to the fitness function, the parameter to be set and the rapid reflector system parameter obtained in real time;
S5, fusing the improved sparrow searching algorithm with a sparrow position updating formula, and carrying out iterative updating according to the improved position updating formula;
S5 includes that the finder update formula is as follows:
；；；；;
In the method, in the process of the invention, Is shown in the firstOn dimension (C)Only sparrow passes throughThe position at +1 iteration,Is a random number which is used to determine the random number,Is the alert value of the person in question,Representing the random numbers belonging to a normal distribution,1 For each elementThe matrix is formed by a matrix of,In order to be of the maximum dimension,Representing a security value;
the improved discoverer update formula is as follows:
；
In the method, in the process of the invention, For a globally optimal solution,In order to adapt the inertial weight factor,Is a random number;
S5 includes the following follower update formula:
；；
In the method, in the process of the invention, Representing the worst position of the current global situation,Indicating the optimal position currently occupied by the finder,Is thatIs a matrix of the (c) in the matrix,Each element of the matrix is randomly assigned with 1 or-1;
The updated follower formula after improvement is as follows:
；
In the method, in the process of the invention, In order to control the parameters of the spiral,A parameter that varies linearly;
The alerter update formula is as follows:
；；
In the method, in the process of the invention, Is the current global optimum position and,Is a random number subject to a normal distribution with a mean value of 0 and a variance of 1,A random number is used as a control step length parameter to represent the direction of the sparrow moving position; is the minimum constant, and ensures that the denominator is not zero; For a global optimum fitness value, Is the global worst fitness value,Representing the fitness value of the current sparrow individual;
S6, after each iteration update, the target position is updated by using dynamic random disturbance according to the dynamic reverse learning and the cauchy variation strategy, so that the target position is prevented from being trapped into local optimum;
S6, integrating a dynamic reverse learning strategy into a sparrow search algorithm:
；
；
In the method, in the process of the invention, Is the firstThe inverse solution of the optimal solution is replaced, and u is the control quantity input of the quick reflector system;
Introducing cauchy variation into position updates:
；
In the method, in the process of the invention, Is cauchy variation;
Alternately executing the dynamic reverse learning strategy and the cauchy variation strategy, and selecting probability The calculation formula is as follows:
；
and S7, stopping updating when the iteration times reach a set value, outputting the global optimal position of the sparrow population, and finishing parameter setting of the active disturbance rejection controller.
2. The method for determining the parameters of a fast mirror auto-disturbance rejection controller for improving a sparrow search according to claim 1, wherein the transfer function of the fast mirror systemComprising the following steps:
；
In the method, in the process of the invention, Is the state quantity of the fast mirror model.
3. The method for determining parameters of a fast mirror auto-disturbance rejection controller for improving a sparrow search according to claim 2, wherein the fast mirror model is differentiated in the form of:
；
In the method, in the process of the invention, For the output of the system,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is a quantitative parameter of the linear expansion state observer,Is thatIs a part of the known art of the present invention,As an unknown overall disturbance, the total disturbance,In order to control the signal of the power supply,AndAs a result of the parameters being known in the art,，。
4. The method for determining parameters of a fast mirror auto-disturbance-rejection controller for improving a sparrow search according to claim 3, wherein the linear extended state observer comprises setting a variable：
；
In the method, in the process of the invention,For the total disturbance, let，，：
；
In the method, in the process of the invention,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
Rewriting into a matrix form:
；，，，；
In the method, in the process of the invention, 、、、Are known matrices.
5. The method for determining parameters of a fast mirror auto-disturbance-rejection controller for improving a sparrow search according to claim 4, wherein the linear extended state observer is:
；
In the method, in the process of the invention, 、AndRespectively is、AndIs used for the estimation of (a),、AndIn order for the gain of the observer to be achieved,Is thatIs used for the purpose of determining the derivative of (c),Is thatIs used for the purpose of determining the derivative of (c),Is thatIs a derivative of (2);
the linear expansion state observer is rewritten into a matrix form as follows:
；；；；
In the method, in the process of the invention, Is an observation state vector of the linear extended state observer,Is thatIs used for the purpose of determining the derivative of (c),For the observer gain matrix to be designed,In order for the observer to input,Output of the linear state observer;
The poles of the characteristic equation in the linear expansion state observer in a matrix form are all configured to the same position by utilizing a pole configuration method And (3) the following steps:
；
In the method, in the process of the invention, For the pole configuration equation,Is a three-order identity matrix,Bandwidth for observer;
Obtaining an observer gain matrix:
。
6. The method for determining the parameters of the fast mirror auto-disturbance-rejection controller for improving a sparrow search according to claim 5, wherein the linear state error feedback control law comprises:
；
In the method, in the process of the invention, In order to control the input of the quantity,For the purpose of scaling up the coefficients of the power,For the input to the system,Is a differential amplification factor;
the control quantity input of the quick reflector system is as follows:
；
closed loop transfer function The method comprises the following steps:
；；
In the method, in the process of the invention, Is the controller bandwidth.
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| Application Number | Priority Date | Filing Date | Title |
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| CN202410614155.8A CN118192277B (en) | 2024-05-17 | 2024-05-17 | Quick reflector auto-disturbance rejection controller parameter determination method for improving sparrow search |
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