CN112987572B - Particle swarm optimization method of adaptive ball bar system based on priori knowledge - Google Patents
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Abstract
The invention provides a particle swarm optimization method of a self-adaptive club system based on prior knowledge, which improves a particle swarm algorithm by improving nonlinear inertia weight, using a self-adaptive change strategy containing a variation factor and combining the prior knowledge with a fitness function of traditional performance integration, and finds a balance position to stabilize the club system by using a proportional integral derivative controller of the improved particle swarm optimization algorithm on the club system; the invention provides a priori knowledge-based self-adaptive ball bar system particle swarm optimization method, which adopts the idea of integrating the priori knowledge into an improved particle swarm optimization method, fully utilizes the result of each iteration of an algorithm, and improves the interference coping capability of a ball bar system and the operation efficiency of the algorithm.
Description
Technical Field
The invention relates to a priori knowledge-based particle swarm optimization method for a self-adaptive ball bar system, and belongs to the field of swarm intelligence optimization control.
Background
The ball rod system consists of a metal ball and a track for the metal ball to freely roll, has the characteristics of nonlinearity, open loop instability, underactuation and the like, and has the advantages of very complex movement of a small ball on a guide rail, higher control difficulty and great challenge.
In order to solve the difficulty of controlling a club system, more and more engineers and technicians have recently proposed various club system control schemes with a view to studying an optimal club system control method to better and more quickly balance the club system.
Chinese patent No.: CN109782595A discloses a network predictive control method for a club system based on an event trigger mechanism, which compensates time lag caused by network transmission by using the network predictive control method according to a reconstruction system state, designs a controller uk and sends a control instruction to an actuator of the club system to achieve a control target, thereby actively compensating the network time lag and effectively saving bandwidth resources.
Chinese patent No.: CN105589332A discloses a method for balancing a club based on SFLA fuzzy controller, which focuses on the optimization of SFLA algorithm on parameters, and introduces expert experience into the rule base of the fuzzy controller, so as to use the optimized fuzzy controller to control the club system to reach a balanced state.
However, in the actual club problem, the influence of the environmental factors such as voltage pulse, mechanical friction, and slip disturbance may occur, and complete disappearance of the random disturbance may not be guaranteed, and the conventional method has low adaptability to the disturbances, and the complicated club system with unstable open loop may have difficulty in coping with the disturbances, thereby causing control failure. Meanwhile, the trapping of a local optimal solution is avoided, and the improvement of the searching efficiency and precision of the optimal solution is of great importance. Therefore, how to overcome the interference in the operation process of the club system and quickly and accurately obtain the control parameters of the club system and the like is an unsolved problem.
Disclosure of Invention
The invention aims to provide a priori knowledge-based particle swarm optimization method for an adaptive ball bar system, and aims to solve the related technical problems in the prior art.
A particle swarm optimization method of a self-adaptive ball rod system based on prior knowledge is characterized in that a particle swarm optimization is improved by improving nonlinear inertia weight, using a self-adaptive change strategy containing variation factors and combining a fitness function of the prior knowledge and a traditional performance integral, an improved particle swarm optimization is used for finding a balance position to a proportional-integral-derivative controller of the ball rod system so as to enable the ball rod system to be stable, and the method comprises the following specific steps:
step 1: designing a proportional speed compensator, and controlling an internal motor control loop with small influence on the control effect of the club system according to the time domain requirement;
step 2: designing a PID controller of an outer ring ball arm control loop according to the ball arm system structure;
and 3, step 3: three parameters K of outer ring PID controllerp,Ki,KdRespectively serving as three input variables, regarding the three input variables as a group of solutions of a three-dimensional space, and setting the dimension of the particle swarm as the number of the input variables;
and 4, step 4: preliminarily determining a group of solutions according to a Z-N setting method, preliminarily determining possible ranges of three parameters in the group of solutions, setting PSO algorithm parameters, initializing the particle swarm scale, the dimension, the maximum iteration times, the initial particle position and velocity, the minimum value and the maximum value of position coordinates, the minimum value and the maximum value of velocity scale and the control index precision;
and 5: guiding a group of solutions obtained preliminarily by using a fitness function combining prior knowledge and traditional performance integration;
and 6: and (3) carrying out particle velocity updating calculation according to a formula:
location update calculation:
in the formula (I), the compound is shown in the specification,
representing the velocity of the ith particle at the t-th iteration,
indicating the position of the ith particle at the time of the t-th iteration,
indicating the individual optima of the ith particle at the t-th iteration,
denotes global optimum at the t-th iteration, ω isInertial weight, c1、c2For learning factors, it is generally 2, r1、r2Random numbers in the intervals (0,1) respectively;
and 7: calculating the respective fitness value of the particles according to the selected fitness function, obtaining the individual optimal fPbest and the global optimal fGbest in the evolution of the generation by using a self-adaptive change strategy containing a variation factor, comparing the individual optimal fPbest and the global optimal fGbest in the evolution of the generation with the fPbest and the fGbest of the previous generation, updating the individual optimal fPbest and the global optimal fGbest in the evolution of the generation, and recording the optimal solution of the generation;
and step 8: judging a result, if the ending condition is met, jumping out of the cycle; otherwise, repeating the steps (6) to (9);
and step 9: outputting a global optimal solution to obtain 3 optimal outer loop PID controller parameter values;
step 10: and observing the control result of the operation of the ball bar system, and judging the position of the ball stabilized on the cross bar by looking up the outer ring PID controller after algorithm optimization, wherein if the ball is stabilized at the designated position, the judgment is successful, and if not, the judgment is failed.
Preferably, the particle swarm initialization scale is 40, the dimension is 3, the maximum iteration number is 50, the initial particle position is set to be a solving value of a traditional Z-N integer method, the initial velocity is 0, the position coordinate is 0 and 80 at the minimum, the velocity scale is 4 and 4 at the minimum, and the control index precision is 0.0001.
Preferably, the POS algorithm is a nonlinear inertia weight, wherein the inertia weight is omegaIterThe expression is as follows:
in the formula, omegaMaxIs the maximum value of the inertial weight, ωMinIs the minimum value of the inertial weight, Iter represents the current iteration number, IterMaxThe maximum number of iterations is indicated.
Preferably, according to the inertial weight ωIterThe expression calculates the velocity formula of the particle:
preferably, the PSO algorithm includes an adaptive elite variation strategy with a variation factor, and f (xm) is calculated based on a perturbation function of a standard cauchy distribution and key parameters of the present club system:
in the formula, hc represents the Hill parameter and is defined as follows:
in the formula (I), the compound is shown in the specification,
is the average value of the ith particle over the jth dimensional space at the Iter iteration,
thereafter, the optimum value Pbest of all particles is calculatedjThe distance r (j) from the mean to the jth dimension of (c):
obtaining an adaptive variation parameter xm (j):
finally, obtaining an updating formula of the adaptive change strategy of Gbest:
Gbest*＝Gbest+F(xm)
in the formula, Gbest represents a value of Gbest adjusted by variation.
PreferablyAnd establishing a new performance standard according to the adaptive elite variation strategy of the variation factor:
in the formula, k1、k2、k3Setting the weighting factor to k as the weighting factor according to the structure of the club system and the specific experimental results1＝20、k2＝10、k3＝2。
Has the advantages that: the invention provides a priori knowledge-based particle swarm optimization method for a self-adaptive ball bar system, which adopts the idea of fusing the priori knowledge into an improved particle swarm optimization method, fully utilizes the result of each iteration of an algorithm, improves the interference coping capability of the ball bar system and the operation efficiency of the algorithm, and has the following advantages compared with the prior art:
1) the method is faster and more efficient, the control on the club system is more accurate, the solving precision can be rapidly improved, and the effect is more excellent;
2) the club system controller optimized by the algorithm has stronger robustness, stronger comprehensive adaptability, more appropriate transition process and improved adaptive level;
3) the PSO algorithm combined with the priori knowledge improves the anti-interference capability of the ball bar system, enhances the global search capability of the particles, reduces the possibility of falling into the local optimum and improves the convergence speed of the particles.
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FIG. 1 is a schematic flow chart of a prior knowledge-based particle swarm optimization method for an adaptive ball bar system.
Detailed Description
The invention is described below with reference to the accompanying drawings, which are intended to cover several modifications and embodiments of the invention. .
A particle swarm optimization method of a self-adaptive ball rod system based on prior knowledge is characterized in that a particle swarm optimization is improved by improving nonlinear inertia weight, using a self-adaptive change strategy containing variation factors and combining a fitness function of the prior knowledge and a traditional performance integral, an improved particle swarm optimization is used for finding a balance position to a proportional-integral-derivative controller of the ball rod system so as to enable the ball rod system to be stable, and the method comprises the following specific steps:
step 1: designing a proportional speed compensator, and controlling an internal motor control loop with small influence on the control effect of the club system according to the time domain requirement;
step 2: designing a PID controller of an outer ring ball arm control loop according to the ball arm system structure;
and 3, step 3: three parameters K of outer ring PID controllerp,Ki,KdRespectively serving as three input variables, regarding the three input variables as a group of solutions of a three-dimensional space, and setting the dimension of the particle swarm as the number of the input variables;
and 4, step 4: preliminarily determining a group of solutions according to a Z-N setting method, preliminarily determining the possible ranges of three parameters in the group of solutions, setting PSO algorithm parameters, initializing the particle swarm size, the dimension, the maximum iteration times, the initial particle position and velocity, the minimum value and the maximum value of position coordinates, the minimum value and the maximum value of velocity scale and the control index precision;
and 5: guiding a group of solutions obtained preliminarily by using a fitness function combining prior knowledge and traditional performance integration;
step 6: and (3) carrying out particle velocity updating calculation according to a formula:
and (3) position updating calculation:
in the formula (I), the compound is shown in the specification,
representing the velocity of the ith particle at the t-th iteration,
indicating the position of the ith particle at the time of the t-th iteration,
indicating the individual optima of the ith particle at the t-th iteration,
represents the global optimum at the t-th iteration, ω is the inertial weight, c1、c2For learning factors, it is generally 2, r1、r2Random numbers in the intervals (0,1) respectively;
and 7: calculating the respective fitness value of the particles according to the selected fitness function, obtaining the individual optimal fPbest and the global optimal fGtest in the evolution of the generation by using a self-adaptive change strategy containing a variation factor, comparing the individual optimal fPbest and the global optimal fGtest with the fPbest and the fGtest of the previous generation, updating the individual optimal fPbest and the global optimal fGtest in the evolution of the generation, and recording the optimal solution of the generation;
and 8: judging a result, and if the ending condition is met, jumping out of the cycle; otherwise, repeating the steps (6) - (9);
and step 9: outputting a global optimal solution to obtain 3 optimal outer loop PID controller parameter values;
step 10: and observing the control result of the operation of the ball bar system, and judging that the ball is stabilized at the position of the cross bar by looking up the outer ring PID controller after algorithm optimization, wherein if the ball is stabilized at the designated position, the judgment is successful, and otherwise, the judgment is failed.
Preferably, the particle swarm initialization scale is 40, the dimension is 3, the maximum iteration number is 50, the particle initial position is set to be a solving value of a traditional Z-N integer method, the initial speed is 0, the position coordinate is 0 and 80 at minimum, the speed scale is 4 and 4 at minimum, and the control index precision is 0.0001.
Preferably, the POS algorithm is a nonlinear inertial weight, the inertial weight ω beingIterThe expression is as follows:
in the formula, ωMaxIs the maximum value of the inertial weight, ωMinIs the minimum value of the inertial weight, Iter represents the current iteration number, IterMaxThe maximum number of iterations is indicated.
Preferably, according to the inertial weight ωIterThe expression calculates the velocity formula of the particle:
preferably, the PSO algorithm includes an adaptive elite variation strategy with a variation factor, and based on a perturbation function of a standard cauchy distribution and key parameters of the club system, f (xm) is calculated:
in the formula, hc represents the Hill parameter and is defined as follows:
in the formula (I), the compound is shown in the specification,
is the average value of the ith particle over the jth dimensional space at the Iter iteration,
thereafter, the optimum value Pbest of all particles is calculatedjDistance r (j) from the mean to the j-th dimension:
obtaining an adaptive variation parameter xm (j):
finally, obtaining an updating formula of the adaptive change strategy of Gbest:
Gbest*＝Gbest+F(xm)
in the formula, Gbest represents a value of Gbest after being adjusted by variation.
Preferably, a new performance criterion is established according to the adaptive elite mutation strategy of the mutation factors:
in the formula, k1、k2、k3Setting the weighting factor to k as the weighting factor according to the structure of the club system and the specific experimental results1＝20、k2＝10、k3＝2。
The traditional inertia weight of the PSO algorithm is a fixed numerical value, in a nonlinear ball bar system, the balance of local searching and global searching of particles is broken possibly, so that the particles are trapped into local optimum early, in order to improve the overall optimizing capability of the system and reduce the possibility of trapping into local optimum solution, the overall searching capability and convergence speed of the particles are improved, and the particles have stronger overall optimizing and local searching capabilities at the same time, thereby improving the overall performance of the PSO algorithm.
In the actual ball arm problem, the invention has the influence of environmental factors such as voltage pulse, mechanical friction, sliding interference and the like, and can not ensure the complete disappearance of random interference, while the traditional method has low adaptability to the interference, and a complex ball arm system with unstable open loop can hardly respond to the interference to cause control failure.
In order to deal with the interferences, the ITAE is used as a part of performance indexes, and meanwhile, the real-time overshoot, rise time, regulation time and peak time of the system are added, so that the performance parameters obtained in each iteration process of the system are utilized as fully as possible.
The search rate of the improved inertia weight can be adaptively changed along with the change of the iteration number in the inertia weight calculation. When the iteration times are small, the inertia weight is correspondingly large, and the particles can be effectively prevented from falling into local optimum; when the iteration times are larger, the inertia weight is correspondingly smaller, and the search accuracy can be better improved.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and decorations can be made without departing from the invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A particle swarm optimization method of a self-adaptive ball bar system based on prior knowledge is characterized in that a particle swarm algorithm is improved by improving nonlinear inertia weight, using a self-adaptive change strategy containing variation factors and combining a fitness function of the prior knowledge and traditional performance integration, a proportional integral derivative controller of the ball bar system is found by using the improved particle swarm optimization algorithm, and a balance position is found to enable the ball bar system to be stable, and the method specifically comprises the following steps:
step 1: designing a proportional speed compensator, and controlling an internal motor control loop with small influence on the control effect of the club system according to the time domain requirement;
and 2, step: designing a PID controller of an outer ring ball arm control loop according to the ball arm system structure;
and 3, step 3: three parameters K of outer ring PID controllerp,Ki,KdRespectively serving as three input variables, regarding the three input variables as a group of solutions of a three-dimensional space, and setting the dimension of the particle swarm as the number of the input variables;
and 4, step 4: preliminarily determining a group of solutions according to a Z-N setting method, preliminarily determining possible ranges of three parameters in the group of solutions, wherein the nonlinear inertia weight adopts a PSO algorithm, and the inertia weight omega adopts a PSO algorithmIterThe expression is as follows:
in the formula, ωMaxIs the maximum value of the inertial weight, ωMinIs the minimum value of the inertial weight, Iter represents the current iteration number, IterMaxRepresenting the maximum number of iterations;
setting PSO algorithm parameters, and initializing particle swarm scale, maximum iteration times, particle positions and particle speeds;
and 5: guiding a group of solutions obtained preliminarily by using a fitness function combining prior knowledge and traditional performance integration;
step 6: and (3) carrying out particle velocity updating calculation according to a formula:
location update calculation:
in the formula, Vi tRepresenting the velocity of the ith particle at the t-th iteration,
indicating the position of the ith particle at the time of the t-th iteration,
indicating the individual optima of the ith particle at the t-th iteration,
represents the global optimum at the t-th iteration, ω is the inertial weight, c1、c2For learning factors, 2, rand is common1、rand2Random numbers in the intervals (0,1) respectively;
and 7: the PSO algorithm comprises a self-adaptive elite variation strategy with variation factors, and F (xm) is calculated based on a disturbance function of standard Cauchy distribution and key parameters of the club system:
in the formula, hc represents the Hill parameter and is defined as follows:
in the formula (I), the compound is shown in the specification,
is the average value of the ith particle in the jth dimension space at the Iter iteration,
thereafter, the optimum Pbest of all particles is calculatedjDistance r (j) from the mean to the j-th dimension:
obtaining an adaptive variation parameter xm (j):
finally, obtaining an updating formula of the adaptive change strategy of Gbest:
Gbest*＝Gbest+F(xm)
in the formula, Gbest represents a numerical value of Gbest after being subjected to variation regulation;
calculating the respective fitness value of the particles according to the selected fitness function, obtaining the individual optimal fPbest and the global optimal fGtest in the evolution of the generation by using a self-adaptive change strategy containing a variation factor, comparing the individual optimal fPbest and the global optimal fGtest with the fPbest and the fGtest of the previous generation, updating the individual optimal fPbest and the global optimal fGtest in the evolution of the generation, and recording the optimal solution of the generation;
and 8: judging a result, and if the ending condition is met, jumping out of the cycle; otherwise, repeating the steps (6) to (9);
and step 9: outputting a global optimal solution to obtain 3 optimal outer loop PID controller parameter values;
step 10: and observing the control result of the operation of the ball bar system, and judging that the ball is stabilized at the position of the cross bar by looking up the outer ring PID controller after algorithm optimization, wherein if the ball is stabilized at the designated position, the judgment is successful, and otherwise, the judgment is failed.
2. The method for optimizing the particle swarm for the adaptive ball bar system based on the priori knowledge of claim 1, wherein the particle swarm initialization scale is 40, the dimension is 3, the initial particle position is set as the solution value of the traditional Z-N integer method, the position coordinate is 0 and 80 at the minimum, the speed scale is 4 and 4 at the minimum, and the control index precision is 0.0001.
3. The particle swarm optimization method for the prior-knowledge-based adaptive club system according to claim 1, wherein the inertial weight ω is a function ofIterThe expression calculates the velocity formula of the particle:
4. the particle swarm optimization method for the prior-based adaptive sphere bar system as claimed in claim 1, wherein the new performance criteria are established according to the adaptive elite variation strategy of the variation factor:
in the formula, k1、k2、k3Setting the weighting factor to k as the weighting factor according to the structure of the club system and the specific experimental results1＝20、k2＝10、k3＝2。
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