[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】改进的粒子群优化控制算法及其仿真研究-外文文献

Oct 2012机 床 与 液 压Hydromechatronics EngineeringVol40 No19Received: 2012 08 22* TAN Xiankun E-mail: txkcx11163 comDOI: 103969/j issn10013881201219005Improved Control Algorithm Based on Particle SwarmOptimization and Its Simulation ResearchTAN Xiankun*Polytechnic School， Chongqing Jiaotong University， Chongqing 400074， ChinaAbstract: The performance of control system is determined by the control parameter of controllerAimed at the puzzle of parameter selection for particle swarm optimization ( PSO) control algo-rithm that the phenomenon of premature convergence made the basic PSO algorithms have beeneasy to get in local optimal solution， and resulted in impossible convergence to global extremum，as well as being not so high in search precision and slower in convergence speed， the paper pro-posed a sort of improved control algorithm based on particle swarm optimization In the paper， itdiscussed the particle swarm optimization algorithms with genetic thought ( GAPSO) ， researchedon improved algorithm of PSO， and made the comparative study for proposed control algorithmby means of simulation experiment The response curve of simulation result demonstrated that itwould be better in comparison with conventional method in dynamic and steady performance， andverified the reasonability and feasibility of the improved control algorithm The research resultshows that the improved algorithm of PSO proposed by the paper is more effective for controllerparameter tuningKey words: particle swarm optimization， genetic thought， parameter tuning， improved control al-gorithm of PSO1 IntroductionParticle swarm optimization ( PSO) 1 and thegenetic algorithm( GA) all are the evolutionary algo-rithm based on the theory of biology evolutionism andgenetics etc for solving optimization problem， andeach of them has own characteristic PSO algorithmhas lots of advantages such as being faster in conver-gence rate， less in parameter tuning， simple and eas-ier in implementation， little in encoding comparedwith other algorithm and so on， and therefore it iswidely used in many fields such as optimization of ob-jective function， modeling of biologic system， train-ing of neural network， control of fuzzy system and soon In engineering control fields， in order to enhancethe speediness， accuracy and stability， the technolo-gy of advanced intelligent control has been obtainedwide generalized application， and PSO algorithm hasalways been used in controller of intelligent controlstructure so as to make the parameter tuning 2 The genetic algorithm is a sort of search methodbased on principles of biology evolution， and it hasbetter ability of global optimization and optimizationstrategy of randomization 3 4 Up to now， GA al-gorithm has been become a more mature analysismethod， and it is widely used in many fields such ascombination optimization， signal processing， machinelearning， artificial life and adaptive control and soon Compared PSO with GA algorithm， there aresome differences 5 For instance， firstly PSO algo-rithm owns better memory characteristics， and keptbetter solving particle GA algorithm only makes useof new population produced by current generation，and the new population produces through crossoverand mutation Secondly for PSO algorithm， it is sim-ple in principle， less in control parameter and re-duced in computing load Thirdly PSO gave the evo-lution equation， the position and speed of particle isin quantification and modeling， and comparatively itis stronger in operability Both PSO and GA repre-sent as the simulation and research of biological worldlaws， and it is a sort of stochastic search techniqueand owns the global optimization characteristic andimplicit parallelism And at the same time， in theface of complex control objective， it appears the dis-advantages of premature convergence and low conver-gence For this reason， the paper explored a sort ofimproved algorithm of particle swarm optimizationbased on genetic thought， and made the simulationresearch for the above mentioned2 Particle swarm optimization based on ge-netic thought21 Survey for genetic algorithmThe basic thought of genetic algorithm 6 isthat by means of encoding technology， it acts onchromosome ( binary digit string) ， and simulates theevolutionary process of population made up of chro-mosome， and is a sort of random search algorithmGenetic algorithm forms a new string populationthrough the selection， crossover and mutation of chro-mosome in randomness and organization so as tosolve， and makes evaluation for chromosome It se-lects the chromosome of better fitness to carry throughthe genetic reproduction The basic conception in thealgorithm is briefly introduced as the following 7 1) Gene encoding， the biologic shape is deter-mined by gene coding-strand In the genetic algo-rithm， by use of binary system code each decoding ofoptimization objective forms a gene coding-strand，namely the individual， and also called as the chromo-some2) Population， the population is a set of indi-vidual， namely it is a set of solution in solving prob-lem3) Crossover， the reproduction in living natureis completed through chromosome crossover， and theGA makes it be an operator In the crossover opera-tion process， there exists random information ex-change， and the aim is that it produces the new genecombination and new individual4) Mutation， the mutation operation usuallytakes mutation probability to execute NOT mutation ofcorresponding Bit， namely some gene value of chro-mosome changes from 1 to 0， or from 0 to 1， andthereby it gets the new individual The mutation op-erating operation can promotes the diversity of proge-ny individual， and expand the solution space Themutation operation decided the local search ability ofgenetic algorithm， and the combined action togetherwith crossover operator completes the global and localsearch of optimal solution5) Fitness， the survivability of biosome dependson fitness degree of environment The fitness reflec-ted the evolution law in nature of survival of the fittestand natural selection In the optimization problem，the corresponding function value of each solutionpresents the good or bad trend with solved problemAnd the evaluation value is called as the fitness of al-gorithm6) Selection， also it is called as reproduction orcopy operation， and the individual of high fitnesswould be put in a certain set so as to get ready forcrossover and mutation operation It selects excellentchromosome of high fitness and performance as theparent individual， and therefore the excellent charac-teristic can widely distributed in the large scope ofnext generation population， thereby it can speedilysolve the problemThere are three sorts of crossover， mutation andselection operating operator， in which the crossoverand mutation operation are used for producing thenew individual so as to completes the reproductionoperation The selection operation is used for comple-ting the copy operating22 Basic step of genetic algorithmGA dominates the solution of problem to be asthe chromosome inner the biosome， and it makes theselection according to individual of high fitnessThrough operating operator of crossover and muta-tion， it forms the new population from generation togeneration so as to conjecture the improved set ofsearching optimization for next generation， thereby fi-nally it converges to an individual of most adaptiveenvironment， and finds the optimal solution The ge-netic algorithm involves five essential factors， param-eter encoding， setting of initial population， and de-sign in fitness function， genetic operation and controlparameter The above five key factors formed the corecontent of genetic algorithm The basic glow of algo-rithm is as the following 8 92TAN Xiankun: Improved Control Algorithm Based on Particle SwarmOptimization and Its Simulation Research1) Select encoding pattern and determine fitnessfunction2) Determine genetic strategy， and initializepopulation including population size， method of se-lection and crossover as well as mutation， parametersof crossover probability Pcand mutation probabilityPmand so on3) Compute the fitness of individual Bit string inthe population after decoding4) Make genetic operator act on current popula-tion according to the selected genetic strategy， inclu-ding that Selection， it charges in selecting some indi-viduals of high fitness directly to inherit into nextgeneration population from current population Cross-over， it makes each individual in the match set afterSelection operation randomly match into the pairs，and takes the crossover probability to carry throughthe exchange for partial gene of them so as to producenew individual Mutation， it makes specified popula-tion after crossover carry through the mutation withmutation probability5) End the condition judgement If it satisfiesthe end condition then it stops the computing， andoutput the individual of maximum fitness to be as theoptimal solution Otherwise it returns to step 3 Improved algorithm of PSOThe wide space search and crossover-mutation a-bility can high efficiently search the global optimalsolution By means of that， it can improve the PSOalgorithm In the iteration process， the particle indi-vidual of one third of the best fitness makes selectionoperation directly go into the next generation， andthen makes crossover between any two form particleof one third in next generation， and the final particleof one third forms through mutation operation for theselected particle By means of genetic crossover oper-ator operating， it increased the diversity of particle，and took full advantage of particle characteristic inbest fitness so as to make better characteristic carrythrough the heredity， and it quickened the conver-gence speed of particle It enlarged the search areathrough mutation operation of partial particle， and a-voided the premature phenomenon of local optimiza-tion In the improved PSO algorithm， it adopts non-linear descending mode for the inertia weight in PSOalgorithm， and it can improve the convergence per-formance of the original algorithm31 Nonlinear descending of inertia weightThe inertia weight system w determined the abil-ity of global and local search in algorithm If the wvalue is larger then the influence of particle subjectedto previous speed of a moment also is larger It canavoid getting in least local extremum， and the globalsearch ability would be stronger If the w value isless then the influence of particle subjected to previ-ous speed of a moment also is less， and the search a-bility of local particle would be stronger， and there-fore it would be propitious to algorithm convergenceThe formula ( 1) shows a sort of descending functionof nonlinear inertia weight 9， and it has better con-vergence speed than linear inertia weight coefficient，and obtains better solving qualitywi=wstart w( )endtit( )max2+wstart w( )end2tit( )max+ wstart( 1)In which， tmax， wstart， wendis respectively the most iter-ation number of times， maximum and minimum of in-itial inertia weight， and tiis the current iterationnumber of generation From formula ( 1) ， it can beseen that the iteration weight coefficient has maximumat the beginning of iteration， and in the process of it-eration it presents a sort of nonlinear descending， andat the last time of iteration process it reaches to theminimum So it can obtain the balance ability ofglobal and local search32 Operating realization of genetic operator1) Realization of selection operation， adoptingproportion selection operating， it first computes thesummation of all individual fitness in the population，and then computes the proportion of individual fitnessin the whole fitness summation To select one thirdparticle of best performance makes selection operatingdirectly go into the next generation so as to keep theheredity of best evolution ability in particle popula-tion， and it can better search optimal solution quick-ly2) Realization of crossover operating， first it se-lects the particle of one third to put into a set， andpays a random crossover probability of each particlein the set， and then makes crossover operating be-tween any two Here it must pay attention to that itshould ensure to produce next generation particle ofthe same number so as to maintain the number not tochange of population particle The update formula of03 Hydromechatronics Engineeringposition and speed for new particle is shown as re-spectively the formula ( 2) and ( 3) Secondly itmakes the fitness evaluation again for sub-particle ofnew generation produced， and makes the comparisonwith parent particle fitness If the fitness of sub-parti-cle is better than parent particle fitness then it wouldbe replaced， and otherwise it keeps parent particle togo into the next generationX1( )t= rand( ) X1( )t+1 rand( )( )X2( )tX2t( )= rand( ) X2( )t+1 rand( )( )X1( )t( 2)V1( )t=V1( )t+ V2( )tV1( )t+ V2( )t V1( )tV2( )t=V1( )t+ V2( )tV1( )t+ V2( )t V2( )t( 3)In which， X represents the position vector in D di-mension space， X( t) and V( t) is respectively theposition vector and speed vector of the space used forselecting cross operating particle， and X( t) and V( t) is respectively the space position and speed vec-tor of new generation particle after cross Rand ( ) isa random vector of search space over interval 0， 1 3) Realization of mutation operating It first se-lects an anew initializing method in this paper so as tomake initial mutation for partial dimension of selectedparticle， and it can avoid appear to get into the pre-mature convergence Secondly it makes the compari-son between fitness of new generation and parent par-ticle， and its process is similar to crossover operatingin step 233 Algorithm flowThe operation step of improved PSO algorithm isas the following1) Initialize particle swarmSetting population size m， search space dimen-sion n， producing m particles randomly in space Rn，forming population matrix X = x1， x2， ， xi， ，xm ， producing speed value of each particle random-ly， forming speed change matrix of particle V =v1， v2， ， vi， ， v m， setting learning factor c1andc2， inertia weight coefficient wstartand wend， encodingpattern， most iteration number of times tmax， and fi-nally setting iteration number of times in current gen-eration to be as 12) Update inertia weight coefficient according toformula ( 1) ， to make evaluation of population， andto compute fitness F( Xi) of each particle accordingto the objective function3) Execute genetic operator operating First tocompute fitness of each particle individual and makethe order according to step 2， and to select optimalparticle of one third directly to be as the next genera-tion particle Secondly to make cross operation forthem， to produce the particle of one third of nextgeneration， and the formula of position and speedcross is respectively the formula ( 2) and ( 3) Fi-nally to make random initializing operating for themso as to enlarge the parameter search area and jumpout the local convergence4) Update individual extremum of each particlein the population， and make comparison betweencurrent F( Xi) and itself individual extremum Pi IfF( Xi) excels Pithen it would update the individualextremum Piby F( Xi) 5) Update the global extremum of population，and make the comparison among all Piproduced new-ly by each particle in the whole population with glob-al Pgin history If there exists that Pifitness value ofparticle excels Pgthen the global extremum Pgwouldbe updated by Pi6) Update the speed and position of particle byformula ( 2) and ( 3) ， and produce the new popula-tion X( t +1) 7) Judge whether it satisfies the end condition( usually it is set as the error precision or most itera-tion generation of times) If it is not satisfied then itwould be returned to step 2， and otherwise it stopsthe search and outputs the resultFig 1 shows the flow of improved PSO algorithmof inertia factor nonlinear descending with fused ge-netic algorithmFig1 Flow of improved PSO algorithm13TAN Xiankun: Improved Control Algorithm Based on Particle SwarmOptimization and Its Simulation Research4 Simulation and its analysis41 Design of control algorithmHere it takes two sorts of control algorithm tomake the simulation for convenience of comparison，and they are respectively the improved PID control al-gorithm and human simulated intelligent control algo-rithm1) Improved PID algorithmu = sgn( e) U，e( ) Eu = Kpe + Kit0edt + Kdee ( )E( 4)In which， E is the error feature threshold levelin the feature model， and the control parameter nee-ded tuning is respectively U， Kp， Kiand Kd WhereU can be gotten from experience， and Kp， Kiand Kdcan be gotten by means of parameter tuning methodproposed in this paper2) HSIC based control algorithmu = sgn( e) U，e E( )1u = KP1e + KD1ee E1 e E( )2u = KP2e + KD2ee E2 e E( )1u = KP3e + KD3ee E2 e E1 e E3 e E( )2u = un1 eE3 e E( )2( 5)In which， E， is respectively the threshold level oferror and its change rate in the feature model， andthe control parameter is respectively U， Kp1， KD2，KP2， Kd2， Kp3and KD3 Where U can be gottenthrough the experience， the other can be gotten bymeans of parameter tuning method proposed in thispaper In order to get better control process and dy-namic characteristic， the objective function of im-proved PSO algorithm is selected as formula ( 6) J = w1t0(e( t)+ u2( t) ) dt + w2 ( 6)Where is the overshoot of system， and w1， w2is re-spectively the weight value42 Parameter tuningFor the above control algorithms， it adopts im-proved PSO algorithm to tune the control parameter，a