基于人工鱼群算法的分数阶PI~λ控制器参数整定
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摘要
针对分数阶PI~λ控制器的参数整定,提出图像法和人工鱼群优化算法相结合的方法来对分数阶PI~λ控制器进行参数整定。分别以一阶系统和二阶系统来模拟典型的速度伺服系统,以此模型为被控对象进行分数阶PI~λ控制器的设计。在频域内,根据系统的相对稳定性和增益变化的鲁棒性等条件,推导出方程式;再根据图像法解出分数阶PI~λ控制器的参数,以解出的参数为中心位置,指定寻优的范围,进而用人工鱼群算法对其周围进行寻优。仿真表明,通过人工鱼群算法寻优得到的控制器,比单纯用图像法得到分数阶PI~λ控制器能使系统具有更好的动态响应特性,并且满足增益变化鲁棒性的条件。
For parameter tuning of fractional order PI~λcontroller,this paper proposed the artificial fish swarm algorithm combined with the image method to tune the parameter. The paper used the typical first-order and second-order system to represent the typical speed servo system and used this model to set the parameters of the fractional order PI~λcontroller for the controlled object. Firstly,in the frequency domain,according to the relative stability of the system and the robustness of the gain,the paper derived the equation. After that,using the image method,it can solve the parameters of the fractional order PI~λcontroller. Around the parameter,according to artificial fish swarm algorithm,it can optimize these parameters. Finally,simulation results show that the controller optimized has better dynamic characteristic than controller obtained by the image method and meets the conditions of robust gains.
For parameter tuning of fractional order PI~λcontroller,this paper proposed the artificial fish swarm algorithm combined with the image method to tune the parameter. The paper used the typical first-order and second-order system to represent the typical speed servo system and used this model to set the parameters of the fractional order PI~λcontroller for the controlled object. Firstly,in the frequency domain,according to the relative stability of the system and the robustness of the gain,the paper derived the equation. After that,using the image method,it can solve the parameters of the fractional order PI~λcontroller. Around the parameter,according to artificial fish swarm algorithm,it can optimize these parameters. Finally,simulation results show that the controller optimized has better dynamic characteristic than controller obtained by the image method and meets the conditions of robust gains.
引文
[1] Podlubny I. Fractional-order systems and PIλDμcontrollers[J]. IEEETrans on Automatic Control,1999,44(1):208-214.
[2] Yahyazadeh M,Haeri M. Application of fractional derivative in con-trol functions[C]//Proc of Annual IEEE India Conference. Pisca-taway,NJ:IEEE Press,2008:252-257.
[3] Oustaloup A,Levron F,Mathieu B,et al. Frequency-band complexnoninteger differentiator:characterization and synthesis[J]. IEEETrans on Circuits and Systems I:Fundamental Theory and Ap-plications,2000,47(1):25-39.
[4] Podlubny I,Dorcak L,Kostial I. On fractional derivatives,fractio-nal-order dynamic systems and PIλDμ-controllers[C]//Proc of Inter-national Conference on Decision and Control. Piscataway,NJ:IEEEPress,1998:4985-4990.
[5]杨智,陈颖.改进粒子群算法及其在PID整定中的应用[J].控制工程,2016,23(2):161-166.(Yang Zhi,Chen Ying. Improvedparticle swarm optimization and its application in PID tuning[J].Control Engineering of China,2016,23(2):161-166.)
[6] Jakhar A,Gaur P. Comparative analysis of GA tunned PID controllerfor direct torque control[C]//Proc of International Conference onComputer,Communication and Control. Piscataway,NJ:IEEE Press,2015:1-6.
[7]胡海波,黄友锐.混合粒子群算法优化分数阶PID控制参数研究[J].计算机应用,2009,29(9):2483-2486.(Hu Haibo,HuangYouyue. Research of fractional order PID controller using hybrid par-ticle swarm optimization[J]. Journal of Computer Applications,2009,29(9):2483-2486.)
[8]秦君琴,李兴财,杨有贞.分数阶PID控制器在蔬菜大棚温度控制中的应用研究[J].西南大学学报:自然科学版,2016,38(1):179-182.(Qin Junqin,Li Xingcai,Yang Youzhen. Application of frac-tional order PID controller for temperature control in vegetable green-house[J]. Jouranl of Southwest University:Natural Science Edi-tion,2016,38(1):179-182.)
[9] Mohanty A,Viswavandya M,Mohanty S,et al. An optimised FOPIDcontroller for dynamic voltage stability and reactive power managementin a stand-alone micro grid[J]. International Journal of ElectricalPower&Energy Systems,2016,78(6):524-536.
[10]Jauregui C,Mermoud M D,Lefranc G,et al. Conical tank level con-trol with fractional PID[J]. IEEE Latin America Transactions,2016,14(6):2598-2604.
[11]Altintas G,Aydin Y. A comparison on genetic algorithm based inte-ger order and fractional order PID control of magnetic bearing system[C]//Proc of IEEE International Conference on Mechatronics. Pisca-taway,NJ:IEEE Press,2017:20-24.
[12]Singh R,Kumar A,Sharma R. Fractional order PID control using antcolony optimization[C]//Proc of the 1st IEEE International Confe-rence on Power Electronics,Intelligent Control and Energy Systems.Piscataway,NJ:IEEE Press,2016:1-6.
[13]Jain R V,Aware M V,Junghare A S. Tuning of fractional order PIDcontroller using particle swarm optimization technique for DC motorspeed control[C]//Proc of the 1st IEEE International Conference onPower Electronics,Intelligent Control and Energy Systems. Pisca-taway,NJ:IEEE Press,2016:1-4.
[14]Wang Chunyang,Fu Weicheng,Shi Yaowu. Fractional order propor-tional integral differential controller design for first order plus time de-lay system[C]//Proc of the 25th Chinese Control and Decision Con-ference. Piscataway,NJ:IEEE Press,2013:3259-3262.
[15]李晓磊,邵之江,钱积新.一种基于动物自治体的寻优模式:鱼群算法[J].系统工程理论与实践,2002,22(11):32-38.(Li Xiao-lei,Shao Zhijiang,Qian Jixin. An optimization method based on au-tonomous animats:fish-swarm algorithm[J]. System Engineering-Theory&Practice,2002,22(11):32-38.)
[16]Luo Ying,Chen Yangquan,Pi Youguo. Experimental study of frac-tional order proportional derivative controller synthesis for fractionalorder systems[J]. Mechatronics,2011,21(1):204-214.
[17]Luo Ying,Li Hongsheng,Chen Yangquan. Fractional order propor-tional and derivative controller synthesis for a class of fractional ordersystems:tuning rule and hardware-in-the-loop experiment[C]//Procof the 48th IEEE Conference on Decision and Control. Piscataway,NJ:IEEE Press,2009:5460-5465.
[18]刘金琨.先进PID控制MATLAB仿真[M].北京:电子工业出版社,2016.(Liu Jingkun. Advanced PID control MATLAB simulation[M]. Beijing:Electronic Industry Press,2016.
[19]Farhadi P,Sojoudi T. PEMFC voltage control using PSO-tunned-PIDcontroller[C]//Proc of IEEE NW Russia Young Researchers in Elec-trical and Electronic Engineering Conference. Piscataway,NJ:IEEEPress,2014:32-35.
[2] Yahyazadeh M,Haeri M. Application of fractional derivative in con-trol functions[C]//Proc of Annual IEEE India Conference. Pisca-taway,NJ:IEEE Press,2008:252-257.
[3] Oustaloup A,Levron F,Mathieu B,et al. Frequency-band complexnoninteger differentiator:characterization and synthesis[J]. IEEETrans on Circuits and Systems I:Fundamental Theory and Ap-plications,2000,47(1):25-39.
[4] Podlubny I,Dorcak L,Kostial I. On fractional derivatives,fractio-nal-order dynamic systems and PIλDμ-controllers[C]//Proc of Inter-national Conference on Decision and Control. Piscataway,NJ:IEEEPress,1998:4985-4990.
[5]杨智,陈颖.改进粒子群算法及其在PID整定中的应用[J].控制工程,2016,23(2):161-166.(Yang Zhi,Chen Ying. Improvedparticle swarm optimization and its application in PID tuning[J].Control Engineering of China,2016,23(2):161-166.)
[6] Jakhar A,Gaur P. Comparative analysis of GA tunned PID controllerfor direct torque control[C]//Proc of International Conference onComputer,Communication and Control. Piscataway,NJ:IEEE Press,2015:1-6.
[7]胡海波,黄友锐.混合粒子群算法优化分数阶PID控制参数研究[J].计算机应用,2009,29(9):2483-2486.(Hu Haibo,HuangYouyue. Research of fractional order PID controller using hybrid par-ticle swarm optimization[J]. Journal of Computer Applications,2009,29(9):2483-2486.)
[8]秦君琴,李兴财,杨有贞.分数阶PID控制器在蔬菜大棚温度控制中的应用研究[J].西南大学学报:自然科学版,2016,38(1):179-182.(Qin Junqin,Li Xingcai,Yang Youzhen. Application of frac-tional order PID controller for temperature control in vegetable green-house[J]. Jouranl of Southwest University:Natural Science Edi-tion,2016,38(1):179-182.)
[9] Mohanty A,Viswavandya M,Mohanty S,et al. An optimised FOPIDcontroller for dynamic voltage stability and reactive power managementin a stand-alone micro grid[J]. International Journal of ElectricalPower&Energy Systems,2016,78(6):524-536.
[10]Jauregui C,Mermoud M D,Lefranc G,et al. Conical tank level con-trol with fractional PID[J]. IEEE Latin America Transactions,2016,14(6):2598-2604.
[11]Altintas G,Aydin Y. A comparison on genetic algorithm based inte-ger order and fractional order PID control of magnetic bearing system[C]//Proc of IEEE International Conference on Mechatronics. Pisca-taway,NJ:IEEE Press,2017:20-24.
[12]Singh R,Kumar A,Sharma R. Fractional order PID control using antcolony optimization[C]//Proc of the 1st IEEE International Confe-rence on Power Electronics,Intelligent Control and Energy Systems.Piscataway,NJ:IEEE Press,2016:1-6.
[13]Jain R V,Aware M V,Junghare A S. Tuning of fractional order PIDcontroller using particle swarm optimization technique for DC motorspeed control[C]//Proc of the 1st IEEE International Conference onPower Electronics,Intelligent Control and Energy Systems. Pisca-taway,NJ:IEEE Press,2016:1-4.
[14]Wang Chunyang,Fu Weicheng,Shi Yaowu. Fractional order propor-tional integral differential controller design for first order plus time de-lay system[C]//Proc of the 25th Chinese Control and Decision Con-ference. Piscataway,NJ:IEEE Press,2013:3259-3262.
[15]李晓磊,邵之江,钱积新.一种基于动物自治体的寻优模式:鱼群算法[J].系统工程理论与实践,2002,22(11):32-38.(Li Xiao-lei,Shao Zhijiang,Qian Jixin. An optimization method based on au-tonomous animats:fish-swarm algorithm[J]. System Engineering-Theory&Practice,2002,22(11):32-38.)
[16]Luo Ying,Chen Yangquan,Pi Youguo. Experimental study of frac-tional order proportional derivative controller synthesis for fractionalorder systems[J]. Mechatronics,2011,21(1):204-214.
[17]Luo Ying,Li Hongsheng,Chen Yangquan. Fractional order propor-tional and derivative controller synthesis for a class of fractional ordersystems:tuning rule and hardware-in-the-loop experiment[C]//Procof the 48th IEEE Conference on Decision and Control. Piscataway,NJ:IEEE Press,2009:5460-5465.
[18]刘金琨.先进PID控制MATLAB仿真[M].北京:电子工业出版社,2016.(Liu Jingkun. Advanced PID control MATLAB simulation[M]. Beijing:Electronic Industry Press,2016.
[19]Farhadi P,Sojoudi T. PEMFC voltage control using PSO-tunned-PIDcontroller[C]//Proc of IEEE NW Russia Young Researchers in Elec-trical and Electronic Engineering Conference. Piscataway,NJ:IEEEPress,2014:32-35.