一种改进的粒子群算法的分数阶控制研究
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摘要
分数阶PID控制器在工程应用中出现了控制参数多且难以整定等问题。针对这些问题,提出一种改进的粒子群分数阶控制算法,并在单级倒立摆控制系统中进行实验验证。该算法将混沌算法与惯性权重调整的粒子群算法相融合,对粒子群进行混沌初始化,并将陷入局部最优的粒子进行混沌搜索,既优化了惯性权重非线性调整方法来提高算法的收敛精度,又得到了全局最优解。实验结果表明,CAPSO算法在分数阶控制器的参数整定方面优于主导极点法、粒子群优化(PSO)等算法。与PSO算法相比,具有收敛速度快、超调量小、稳定性好、抗干扰性强等特点;经CAPSO算法优化的分数阶控制器动态响应特性要优于整数阶PID控制器。
The fractional PID controller exists too many control parameters and difficult parameter tuning and other problems in engineering.Therefore,we propose a fractional order control algorithm called chaotic adaptive particle swarm optimization( CAPSO),which is verified by the single inverted pendulum control system. This algorithm combines the chaos algorithm with inertia weight adjustment of the particle swarm algorithm. After the chaotic initialization of particle swarm, it exerts chaotic search on the swarms falling into the local optimal particle,not only optimizing nonlinear inertia weight adjustment method to improve its convergence accuracy,but also getting the global optimum solution. The experiment shows that the CAPSO is better than the dominant pole method and PSO in the parameter tuning of the fractional order controller. Compared with PSO, it has many merits of the fast convergence speed, small overshoot, strong stability and anti-interference. The dynamic response of the system with fractional order controller optimized by CAPSO is better than that with integer order PID controller.
The fractional PID controller exists too many control parameters and difficult parameter tuning and other problems in engineering.Therefore,we propose a fractional order control algorithm called chaotic adaptive particle swarm optimization( CAPSO),which is verified by the single inverted pendulum control system. This algorithm combines the chaos algorithm with inertia weight adjustment of the particle swarm algorithm. After the chaotic initialization of particle swarm, it exerts chaotic search on the swarms falling into the local optimal particle,not only optimizing nonlinear inertia weight adjustment method to improve its convergence accuracy,but also getting the global optimum solution. The experiment shows that the CAPSO is better than the dominant pole method and PSO in the parameter tuning of the fractional order controller. Compared with PSO, it has many merits of the fast convergence speed, small overshoot, strong stability and anti-interference. The dynamic response of the system with fractional order controller optimized by CAPSO is better than that with integer order PID controller.
引文
[1]杨世勇,徐莉苹,王培进.单级倒立摆的PID控制研究[J].控制工程,2007,14:23-25.
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[5]张志强.基于模糊滑模变结构的倒立摆控制方法研究[D].兰州:兰州理工大学,2008.
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[17]史金光,王中原,孙洪辉,等.制导炮弹分数阶控制器参数整定方法研究[J].战术导弹技术,2013,26(5):76-80.
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[20]蒋晓屾,任佳,顾敏明.多维度惯性权重衰减混沌化粒子群算法及应用[J].仪器仪表学报,2015,36(6):1333-1341.
[21]邹毅,朱晓萍,王秀平.一种基于混沌优化的混合粒子群算法[J].计算机技术与发展,2009,19(11):18-22.
[22]王京,于舒娟.模拟退火混沌粒子群算法的盲检测[J].计算机技术与发展,2011,21(1):35-37.
[23] LIU Bo,WANG Ling,JIN Yihui,et al. Improved particle sw arm optimization combined w ith chaos[J].Chaos,Solitons and Fractals,2005,25(5):1261-1271.
[24] WANG Jianzhou,ZHU Suling,ZHAO Weigang,et al.Optimal parameters estimation and input subset for grey model based on chaotic particle sw arm optimization algorithm[J].Expert Systems w ith Applications,2011,38(7):8151-8158.
[2]杨平,徐春梅,王欢,等.直线型一级倒立摆状态反馈控制设计及实现[J].上海电力学院学报,2007,23(1):21-25.
[3]侯涛,范多旺,杨剑锋.基于T-S型的平面倒立摆双闭环模糊控制研究[J].控制工程,2012,19(5):753-756.
[4]司昌龙.拟人智能控制及控制律转化研究[D].北京:北京航空航天大学,2003.
[5]张志强.基于模糊滑模变结构的倒立摆控制方法研究[D].兰州:兰州理工大学,2008.
[6] PODLUBNY I.Fractional-order system and PIλDμcontroller[J]. IEEE Transactions on Automating Controller,1999,44(1):208-214.
[7]曹军义,曹秉刚.分数阶控制器的数字实现及其特性[J].控制理论与应用,2006,23(5):791-794.
[8] XUE Dingyu,ZHAO Chunna,CHEN Yangquan. Fractional order PID control of a DC-motor w ith elastic shaft:a case study[C]//American control conference. M inneapolis,M N,USA:IEEE,2011.
[9] BISWAS A,DAS S,ABAHAM A,et al.Design of fractional-order PIλDμcontrollers w ith an improved differential evolution[J]. Engineering Applications of Artificial Intelligence,2009,22(2):343-350.
[10]梁涛年,陈建军.分数阶参数不确定系统PIλ的控制器[J].控制理论与应用,2011,28(3):400-406.
[11]严慧,于盛林,李远禄.分数阶PIλDμ控制器参数设计方法—极点阶数搜索法[J].信息与控制,2007,36(4):445-450.
[12]李大字,刘展,靳其兵,等.分数阶控制器参数整定策略研究[J].系统仿真学报,2007,19(19):4402-4406.
[13]薛定宇,赵春娜.分数阶系统的分数阶PID控制器设计[J].控制理论与应用,2007,24(5):771-776.
[14] VINAGRE B M.Modeladoy control de sistemas dina-micos caracterizados porecuaciones integrodiferenciales de orden fraccional[D].M adrid:Univer-sidad Nacional de Educacion a Distancia,2001.
[15] MAIONE G,LINO P. New tuning rules for fractional PIλcontrollers[J]. Nonlinear Dynamics,2007,49(1-2):251-257.
[16]张邦楚,王少锋,韩子鹏,等.飞航导弹分数阶PID控制及其数字实现[J].宇航学报,2005,26(5):653-657.
[17]史金光,王中原,孙洪辉,等.制导炮弹分数阶控制器参数整定方法研究[J].战术导弹技术,2013,26(5):76-80.
[18] CHATTERJEE A,SIARRY P.Nonlinear inertia weight variation for dynamic adaption in particle sw arm optimization[J].Computer and Operations Research,2006,33(3):859-871.
[19] OUSTLOUP A,LEVRON F,MATHIEU B,et al.Frequencyband complex noninteger differentiator:characterization and synthesis[J]. IEEE Transactions on Circuit and Systems-I:Fundamental Theory and Applications,2000,47(1):25-39.
[20]蒋晓屾,任佳,顾敏明.多维度惯性权重衰减混沌化粒子群算法及应用[J].仪器仪表学报,2015,36(6):1333-1341.
[21]邹毅,朱晓萍,王秀平.一种基于混沌优化的混合粒子群算法[J].计算机技术与发展,2009,19(11):18-22.
[22]王京,于舒娟.模拟退火混沌粒子群算法的盲检测[J].计算机技术与发展,2011,21(1):35-37.
[23] LIU Bo,WANG Ling,JIN Yihui,et al. Improved particle sw arm optimization combined w ith chaos[J].Chaos,Solitons and Fractals,2005,25(5):1261-1271.
[24] WANG Jianzhou,ZHU Suling,ZHAO Weigang,et al.Optimal parameters estimation and input subset for grey model based on chaotic particle sw arm optimization algorithm[J].Expert Systems w ith Applications,2011,38(7):8151-8158.