CN113267998B - High-precision modeling and control method for atomic gyroscope temperature control system - Google Patents
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Abstract
A high-precision modeling and control method for an atomic gyroscope temperature control system is applied to the field of high-precision temperature control of atomic gyroscopes. Obtaining a training set by adopting an excitation mode of combining variable-slope sawtooth waves and amplitude square waves, and designing a self-adaptive gray wolf algorithm to construct a second-order hysteresis model of the atomic gyroscope temperature control system; the self-adaptive dynamic matrix control method based on the non-parametric model solves the problems of large hysteresis, poor stability, weak anti-interference capability and the like of a temperature control system and improves the dynamic performance of the system. The method has the advantages of good rapidness, small overshoot, strong stability and robustness and the like, and is suitable for high-precision control of the atomic gyroscope temperature control large hysteresis system.
Description
Technical Field
The invention relates to a high-precision modeling and control method for an atomic gyroscope temperature control system, which is applicable to the field of high-precision temperature control of atomic gyroscopes.
Background
The atomic gyroscope realizes the accurate measurement of angular velocity through the interaction of laser and atomic gas, wherein the atomic gas chamber is used as a core component, and the accuracy and stability of the atomic gyroscope are directly affected by the accuracy or not of the temperature control.
The atomic air chamber is used as a core component of the atomic gyroscope, and the temperature field of the atomic air chamber has the characteristics of large hysteresis, high temperature control precision and stability requirements, high control difficulty and the like. The current popular electric heating temperature control system adopts a PID control algorithm, and the PID control belongs to a model-free algorithm according to the characteristic of large hysteresis of a heating object, so that the method has obvious defects in the aspects of rapidity, stability and the like.
Disclosure of Invention
The invention solves the technical problems that: the temperature control system of the atomic gyroscope has the characteristic of large hysteresis and is easily influenced by external temperature, and the self-adaptive dynamic matrix control method based on the self-adaptive gray wolf system identification model is provided, a high-precision second-order hysteresis system model of the atomic gyroscope is built through a self-adaptive gray wolf algorithm, and the control precision of the second-order hysteresis system is improved by utilizing the self-adaptive dynamic matrix control method.
The technical scheme of the invention is as follows: firstly, a system training set is obtained by adopting an excitation mode of combining variable-slope sawtooth waves and amplitude square waves, then, a second-order hysteresis model of the atomic gyroscope temperature control system is built by utilizing a self-adaptive gray wolf algorithm, and secondly, a unit step non-parameter model of the temperature control system is built based on a self-adaptive prediction method, so that the problems of poor stability, great environmental influence and the like of the temperature control system are solved through self-adaptive dynamic matrix control. The implementation steps are as follows:
(1) High-precision model identification based on self-adaptive wolf algorithm
Firstly, constructing a second-order hysteresis system model of an atomic gyroscope temperature control system as follows:
wherein the hysteresis time T, the system gain K and zeroPoint z 1 Pole p 1 、p 2 Is a parameter to be identified;
the excitation voltage is input to the heating film in a mode of combining variable-slope sawtooth waves and amplitude square waves, the temperature of the system is collected as output to construct a training set, and in the whole process, the digital circuit is used for recording the excitation voltage value at the current moment and the temperature of a temperature measuring point, so that time synchronization is ensured;
by simulating the level system and hunting behavior of the wolves in the nature, a self-adaptive wolf algorithm is designed to realize the high-precision parameter identification of a second-order hysteresis system model of an atomic gyroscope temperature control system, the whole wolf group is divided into four groups of alpha, beta, delta and omega, the optimal adaptability position in the wolf group is defined as a head wolf alpha, suboptimal individuals are strong wolf beta and are again optimal as a reconnaissance wolf delta, other individuals in the group are subordinate wolves omega, alpha, beta and delta guide the subordinate wolves omega to search towards a target hunting object, and in the intelligent optimization process, the wolf group continuously updates the positions of alpha, beta, delta and omega:
D＝|C·X p (t)-X(t)|
X(t+1)＝X p (t)-A·D
wherein D is the distance between the individual wolves and the prey, t is the number of current iterations, X p For the target position, X is the position vector of the wolf, A is the surrounding step length, C is [0,2]A and C are respectively determined by the following formulas:
A＝2a·rand 1 -a
C＝2·rand 2
in rand 1 And rand 2 Are all [0,1 ]]The random number in the system, max is the maximum iteration number, a is the self-adaptive convergence factor, the self-adaptive convergence factor is slowly reduced in early iteration through a logarithmic function and is rapidly reduced in later iteration, so that the convergence at different stages of the system is rapid, the good balance between local optimization is avoided, the diversity of the system is effectively improved, and the global searching capability of the system is improved;
when the position of the prey is judged by the wolf, the head wolf alpha brings the beta and delta to guide the wolf group to surround the prey, the wolf with highest adaptability has larger influence on subordinate wolves, and in order to improve the optimizing speed, the invention provides a new weight updating mechanism mathematical formula based on the fitness, which is as follows:
wherein X is α 、X β 、X δ Respectively representing the current positions of alpha, beta and delta, C 1 、C 2 、C 3 Represents a random vector, X (t) represents the current position of ω, w 1 、w 2 And w 3 Is the updated weight values of alpha, beta and delta wolf respectively, X (t+1) represents the final position of subordinate wolf omega, f 1 Is an fitness function;
the fitness function is specifically defined as follows:
wherein O is ture Is the system output sequence which is actually acquired,is the current individual wolf->Corresponding toAn output sequence of the simulation system of (a);
since the position of subordinate wolves is mainly determined by the head wolves, it is easy to sink into local optimum in the final evolutionary stage, so the last 20% of wolves are repositioned in the latter half of the iteration:
wherein,and->Is the upper and lower limits of individual wolves;
(2) Adaptive predictive control
The dynamic matrix control algorithm itself comprises three parts: predictive model, rolling optimization, and feedback correction;
first, a unit step sequence model a= [ a ] is obtained based on the obtained second-order hysteresis model 1 ,…,a N ]According to the proportion and superposition property of the linear system, the output value of the object in the future P steps can be predicted, and a prediction model is constructed as follows:
where j=1, 2, … P
The simplified expression is in matrix form:
wherein A is a dynamic matrix, Y 0 (k) Is the current system state and is known;
in order to ensure the robustness and stability of the system, the invention adopts single-step prediction, and needs to enable the closed loop response to reach an expected value along a smooth curve, so as to improve the overall dynamic performance of the system, a reference track is established and a self-adaptive softening function is provided as follows:
w(k+j)＝α j y(j|k)+(1-α j )y r (j＝1，2，…，n)
where y (j|k) is the actual output value of the system, y r Is the expected value of the system, alpha E (0 1) is a softening coefficient, and the self-adaptive softening coefficient improves the overall dynamic performance of the system, so that the current temperature y (k) is far away from the expected temperature y r When the system quickly approaches the expected value, the current temperature y (k) approaches the expected temperature y r When the method is used, overshoot is reduced, and stability is improved;
in the control process, in order to ensure that the change of the control increment delta u is not too large, soft constraint is added into the optimization performance index, as follows:
where λ is the control weighting coefficient, the control increment Δu at time k is determined by minimizing the value of the optimization criterion J;
order the
Obtaining: Δu= (a T QA+R) -1 A T Q(W-Y 0 )
Then, according to a prediction model of the system, a single-step prediction output value under the action of the control increment delta U can be obtained:
because of the change of the external environment, in order to timely utilize real-time temperature information to carry out feedback correction, the accuracy and stability of predictive control are improved, so that output predictive errors are formed:
at time K+1, the time base point changes, so that the use is made ofObtaining a predicted initial value of K+1 moment through time base point displacement, and then continuously predicting an output value of future P moment;
order the
Wherein:for displacement matrix +.>Outputting a prediction system after error correction at the time of t=kT, wherein h is an error correction vector;
with Y 0 And (K+1), the optimization calculation at the moment k+1 can be performed, delta u (K+1) is further obtained, the system forms a closed-loop negative feedback system, and model prediction, feedback correction and rolling optimization of the next time period are continued.
Compared with the prior art, the invention has the advantages that:
(1) According to the invention, a non-parameter model is introduced into a control algorithm, the problem of large hysteresis is solved by adopting a mode of combining prediction and control and adopting self-adaptive dynamic matrix control, so that large overshoot of output is avoided, the accuracy and rapidity of a system are improved, and the PID control has better dynamic performance particularly when the external environment changes;
(2) In the model identification, the invention adopts an excitation mode of combining temperature rise and temperature reduction, and combining variable-slope sawtooth wave and amplitude square wave, so that the performance of the system is better reflected in a training set; adopting a gray wolf optimization identification algorithm to obtain a transfer function of system optimization, and improving the accuracy of a non-parameter model;
(3) Aiming at the demand characteristics of high accuracy, high stability and high robustness of the atomic gyroscope temperature control, the invention provides a logarithmic self-adaptive convergence factor, a weight updating mechanism based on fitness and a repositioning method in the latter half iteration in the gray wolf optimization identification part, improves the rapidity of an identification algorithm and effectively avoids global optimization. In a dynamic matrix control part, a softening function is innovatively provided, and the relation between the rapidity and the robustness of the system is weighed in different stages of control, so that the control precision and the control stability are improved.
Drawings
FIG. 1 is a diagram of an atomic gyro temperature control system;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a specific form of two excitation signals;
FIG. 4 is a calculation flow of the gray wolf optimization algorithm;
FIG. 5 is a dynamic matrix control flow;
the specific implementation process comprises the following steps:
the invention provides a high-precision modeling and control method for an atomic gyro temperature control system, aiming at the defects of low temperature control stability, serious overshoot, poor rapidity and the like of a model-free temperature control system adopted by the atomic gyro temperature control system, so that the control precision of the temperature control system is improved.
The atomic gyro temperature control system is formed as shown in fig. 1, and is assumed to be a second-order hysteresis system according to experience, and the transfer function is as follows:
wherein the hysteresis time T, the system gain K and the zero point z 1 Pole p 1 、p 2 Is a parameter to be identified;
(1) High-precision identification of model parameters
The identification flow is shown in fig. 2, in order to avoid the influence caused by the environmental temperature change, the system state under zero input needs to be measured for 60 seconds before the excitation is applied, the air chamber temperature sequence acquired before the excitation is used as the initial state of the system by averaging, and then the system excitation voltage is applied; the system excitation voltage is in the form of a combination of a variable slope sawtooth wave and a variable amplitude square wave. The ramp rate variable saw tooth wave excitation signal is shown in fig. 3, firstly, the control voltage is increased from 0v to a maximum value of 5v at a constant speed, the time for increasing the voltage is 15 seconds, then the control voltage is increased to 0v, natural cooling is carried out, the control voltage is maintained for a period of time, and 5 periods are completed to form a group; the boost time was then adjusted to 30 seconds, 60 seconds, 90 seconds, 120 seconds, 180 seconds, 240 seconds, 300 seconds, each boost rate was cycled 5 times, and then cooled for 60 seconds; then, excitation is continued by using square waves with amplitude values of 240S, the amplitude values of the first 5 periods are 1V as a group, then the amplitude values are respectively 1.5V, 2V, 2.5V, 3V, 3.5V, 4V, 4.5V and 5V, each cycle is carried out for 5 times, as shown in figure 3, and finally acquisition is finished. In the whole process, the digital circuit is used for recording the excitation voltage value at the current moment and the temperature of the temperature measuring point, so that the time synchronization is ensured.
By simulating the grade system and hunting behavior of the wolves in the nature, designing a self-adaptive wolf algorithm to realize the high-precision parameter identification of the second-order hysteresis system model of the atomic gyroscope temperature control system, wherein the parameter identification flow of the self-adaptive wolf optimization algorithm is shown in a figure 4, the wolf optimization algorithm simulates the grade system and hunting behavior of the wolves in the nature, and N individual position vector information in the population is set as X= (P) 1 ,P 2 ,...,P i ,...,P N ) (i=1.,), N), each P i Representing position vector information of 1 individual, P i Can be expressed as: p (P) i ＝(p 1 ,p 2 ,...,p i ,...,p dim ) Where pi is a wolf group attribute (i=1,..dim), dim is a population dimension, p i ＝l i +λ(u i -l i )，u i And l i Is p i Upper and lower bounds of (1), upper and lower bounds information from the outsideAnd inputting part information, wherein lambda is a random number between 0 and 1.
The whole wolf group is divided into four groups of alpha, beta, delta and omega, the most adaptive individual in the wolf group is defined as head wolf alpha, the next individual is strong wolf beta, the next individual is reconnaissance wolf delta, the other individuals in the group are subordinate wolf omega, and the alpha, beta and delta guide the subordinate wolf omega to search towards a target hunting object. In the intelligent optimization process, the wolf group continuously updates the positions of alpha, beta, delta and omega:
D＝|C·X p (t)-X(t)|
X(t+1)＝X p (t)-A·D
wherein D represents the distance between the individual wolves and the prey, t represents the number of current iterations, X p Is a prey location; x is the position vector of the wolf, A is the surrounding step length, C is [0,2 ]]A and C are respectively determined by the following formulas:
A＝2a·rand 1 -a
C＝2·rand 2
in rand 1 And rand 2 Are all [0,1 ]]The random number in the system, max is the maximum iteration number, a is the self-adaptive convergence factor, and the random number is slowly reduced in early iteration and rapidly reduced in later iteration through a logarithmic function, so that the convergence at different stages of the system is rapid, the good balance between local optimality is avoided, the diversity of the system is effectively improved, and the global searching capability of the system is improved.
When the position of the prey is judged by the wolves, the wolves are led by the wolves alpha, beta and delta to guide the wolves to surround the prey, and the positions of the three wolves are used for judging the approximate position of the prey to gradually approach the prey because the alpha, the beta and the delta are closest to the prey. The wolf with highest fitness has larger influence on subordinate wolves, and in order to improve the optimizing speed, the invention provides a new fitness-based weight updating mechanism mathematical formula as follows:
wherein X is α 、X β 、X δ Respectively representing the current positions of alpha, beta and delta, C 1 、C 2 、C 3 Represents a random vector, X (t) represents the current position of ω, w 1 、w 2 And w 3 Is the updated weight values of alpha, beta and delta wolf respectively, X (t+1) represents the final position of subordinate wolf omega, f 1 Is an fitness function;
the fitness function is specifically defined as follows:
wherein O is ture Is the system output sequence which is actually acquired,is the current individual wolf->And (3) outputting a sequence of the corresponding simulation system.
Since the position of subordinate wolves is mainly determined by the head wolves, it is easy to sink into local optimum in the final evolutionary stage, so the last 20% of wolves are repositioned in the latter half of the iteration:
here, theAnd->Is the upper and lower limits of the individual wolves. In principle, the diversity of the system is improved, so that local optimization is avoided, and the optimized transfer function of the system can be finally obtained through iteration.
(2) Adaptive predictive control
The dynamic matrix control algorithm itself comprises three parts: predictive model, scroll optimization, and feedback correction, as shown in fig. 5.
Obtaining a unit step sequence model a= [ a ] based on the obtained second-order hysteresis model 1 ,…,a N ]According to the proportion and superposition property of the linear system, the output value of the object in the future P steps can be predicted, and a prediction model is constructed as follows:
where j=1, 2, … P
The simplified expression matrix is in the form of:
wherein A is a dynamic matrix, Y 0 (k) Is the current system state and is known;
in order to ensure the robustness and stability of the system, the invention adopts single-step prediction, and the closed loop response needs to reach the expected value along a smooth curve, so that a reference track is established as follows:
w(k+j)＝α j y(j|k)+(1-α j )y r (j＝1，2，…，n)
where y (j|k) is the actual output value of the system, y r Is the expected value of the system, alpha E (0 1) is the self-adaptive softening coefficient, and the self-adaptive softening coefficient improves the overall dynamic performance of the system, so that the current temperature y (k) is far away from the expected temperature y r When the system quickly approaches the expected value, the current temperature y (k) approaches the expected temperature y r When the method is used, overshoot is reduced, and stability is improved;
in the control process, in order to ensure that the change of the control increment delta u is not too large, soft constraint is introduced into the optimization performance index, as follows:
wherein J is an optimized performance index, and lambda is a control weighting coefficient;
to calculate the optimal control increment Deltau, letObtaining:
ΔU＝(A T QA+R) -1 A T Q(W-Y 0 )
therefore, according to the prediction model of the system, a single-step prediction output value under the action of the control increment delta U can be obtained:thereby realizing the rolling optimization of the control algorithm.
Because of the change of external environment, the actual system can change and model mismatch occurs, and in order to timely utilize real-time temperature information to carry out feedback correction, the accuracy and stability of predictive control are improved, so that output predictive errors are formed:
at time K+1, the time base point changes, so that the use is made ofThe element of (2) obtains the predicted initial value at the moment K+1 through the displacement of the time base point, and then continuously predicts the output value at the moment P in the future, so that
Wherein:called displacement matrix>Outputting a prediction system after error correction at the time of t=kT, wherein h is an error correction vector;
with Y 0 And (K+1), the optimization calculation at the moment k+1 can be performed, delta u (K+1) is further obtained, the system forms a closed-loop negative feedback system, and model prediction, feedback correction and rolling optimization of the next time period are continued.
According to the dynamic matrix control method based on the identification of the gray wolf optimization system for the atomic gyro system, which is provided by the invention, the model identification and the predictive control are combined together, so that the overall temperature rising rapidity, the temperature control stability and other dynamic performances of the atomic gyro temperature control system are improved.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Claims (3)
1. A high-precision modeling and control method for an atomic gyroscope temperature control system is characterized by comprising the following steps of:
(1) High-precision model identification based on self-adaptive gray wolf algorithm: fully exciting an atomic gyro temperature control system to obtain a training set by using an excitation mode of combining variable-slope sawtooth waves and amplitude square waves, and providing a self-adaptive gray wolf algorithm for parameter identification to construct a second-order hysteresis system model of the atomic gyro temperature control system;
the self-adaptive gray wolf optimization algorithm is characterized in that: an adaptive convergence factor a with strong adaptability is proposed:
wherein a is an adaptive convergence factor, t is the current iteration number, and max is the maximum iteration number;
the convergence factor is slowly reduced in early iteration and is rapidly reduced in later iteration, so that good balance between rapid convergence and local optimum avoidance is realized, and the system diversity is effectively improved;
the self-adaptive gray wolf algorithm is characterized in that: a new wolf group position optimization method based on a fitness-based weight updating mechanism is provided:
wherein w is 1 、w 2 And w 3 Are updated weight values for alpha, beta and delta wolf, respectively,for the final position of the subordinate wolf omega, f 1 Is an fitness function;
in order to avoid sinking into local optimum, a wolf group updating mechanism is provided, the system diversity is improved, and the last 20% of wolves are repositioned in the second half iteration:
wherein,and->Is the upper and lower limits of the individual wolf search range;
(2) High-precision temperature control based on adaptive prediction: and according to the characteristic of large hysteresis of the atomic gyroscope temperature control system, system noise is eliminated through smooth filtering, and the control precision of the system is improved by utilizing a self-adaptive dynamic matrix control method.
2. The excitation method of combination of variable-slope sawtooth wave and amplitude square wave according to claim 1, wherein the excitation method comprises the following steps: exciting voltage is input to the heating film input system in a mode of combining variable-slope sawtooth waves and amplitude square waves, the variable-slope sawtooth waves change slope once every 5 periods, and each period has cooling time; the amplitude of the amplitude-variable square wave is changed every 5 periods, so that the characteristics of an excitation system are fully ensured to obtain the dynamic performance of the system, and the system temperature is not too high.
3. The adaptive dynamic matrix control method of claim 1, wherein: in order to improve the overall dynamic performance of the system and replace a single softening coefficient, an adaptive softening function is innovatively provided:
achieving the current temperature y (k) far from the expected temperature y r When the system quickly approaches the expected value, the current temperature y (k) approaches the expected temperature y r And in addition, the overshoot is reduced, the stability is improved, and the overall performance of the system is improved on the basis of the stability.
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