二级倒立摆T-S模糊控制器优化设计
|
摘要
针对多维变量的被控对象进行模糊控制时存在"规则爆炸"等问题,提出基于融合函数的T-S模糊控制器设计思想。以二级倒立摆为被控对象,运用拉格朗日方程建立数学模型;运用极点配置、函数融合等方法,并结合并行分布补偿思想(PDC)进行降维T-S模糊控制器的设计,并采用改进遗传算法进行T-S模糊控制器的鲁棒优化。仿真结果表明,所设计的基于融合函数的T-S模糊控制器可实现对二级倒立摆的控制,其控制精度、鲁棒性等都优化于极点配置的线性反馈控制器。
Since the controlled object with multidimensional variable has the problem of "rule explosion" for fuzzy control,a design thought of T-S fuzzy controller based on fusion function is proposed. Taking double inverted pendulum as the controlled object,the Lagrange equation is used to establish the mathematical model. The methods of pole assignment and function fusion,and parallel distributed compensation(PDC) thought are adopted to design the dimension reduced T-S fuzzy controller. The improved genetic algorithm is employed to optimize the robustness of T-S fuzzy controller. The simulation results show that the designed T-S fuzzy controller based on fusion function can realize the control of the double inverted pendulum,and its control precision and robustness are better than those of the linear feedback controller based on pole assignment.
Since the controlled object with multidimensional variable has the problem of "rule explosion" for fuzzy control,a design thought of T-S fuzzy controller based on fusion function is proposed. Taking double inverted pendulum as the controlled object,the Lagrange equation is used to establish the mathematical model. The methods of pole assignment and function fusion,and parallel distributed compensation(PDC) thought are adopted to design the dimension reduced T-S fuzzy controller. The improved genetic algorithm is employed to optimize the robustness of T-S fuzzy controller. The simulation results show that the designed T-S fuzzy controller based on fusion function can realize the control of the double inverted pendulum,and its control precision and robustness are better than those of the linear feedback controller based on pole assignment.
引文
[1]贺廉云.融合函数在模糊控制器设计中的应用[J].科技通报,2011,27(5):682-685.HE L Y. Application of the fusion function in the fuzzy controller designing[J]. Bulletin of science and technology,2011,27(5):682-685.
[2]张卓,张井岗.跷跷板系统的模糊控制策略研究[J].太原科技大学学报,2016,37(6):447-452.ZHANG Z,ZHANG J G. A fuzzy control method for seesaw system[J]. Journal of Taiyuan University of Science and Technology,2016,37(6):447-452.
[3]陈梅,陈艳燕.两轮智能车跟踪控制系统的研究[J].合肥工业大学学报(自然科学版),2015,38(3):319-324.CHEN M,CHEN Y Y. Study of tracking control system of twowheeled intelligent vehicle[J]. Journal of Hefei University of Technology(natural science),2015,38(3):319-324.
[4]张碧波.基于模糊控制的三级倒立摆系统的控制器设计[D].石家庄:河北科技大学,2015:21-38.ZHANG B B. Design of controller on triple inverted pendulum system based on fuzzy control[D]. Shijiazhuang:Hebei University of Science and Technology,2015:21-38.
[5]张敏.二级倒立摆云模型PID控制研究[D].大连:大连海事大学,2016:23-27.ZHANG M. Research on cloud model PID control of double inverted pendulum[D]. Dalian:Dalian Maritime University,2016:23-27.
[6]邢景虎,陆华才.二级倒立摆两种控制方法的对比研究[J].佳木斯大学学报(自然科学版),2017,35(2):263-266.XING J H,LU H C. Comparative study on two control methods of the double inverted pendulum[J]. Journal of Jiamusi University(natural science edition),2017,35(2):263-266.
[7]邢景虎,陈其工,江明.二级倒立摆基于融合函数的模糊控制[J].合肥工业大学学报(自然科学版),2011,34(8):1155-1159.XING J H,CHEN Q G,JIANG M. Fusion function based fuzzy control for a double inverted pendulum[J]. Journal of Hefei University of Technology(natural science edition),2011,34(8):1155-1159.
[8]尹逊和,樊雪丽,杜洋,等.二级倒立摆系统的实物控制[J].计算机工程与应用,2016,52(20):242-250.YIN X H,FAN X L,DU Y,et al. Physical control of double inverted pendulum system[J]. Computer engineering and applications,2016,52(20):242-250.
[9]李平,张重阳,陶文华,等.二级倒立摆的Sugeno型模糊神经网络控制[J].控制工程,2009,16(4):458-463.LI P,ZHANG C Y,TAO W H,et al. Sugeno fuzzy neural network control for double inverted pendulum[J]. Control engineering of China,2009,16(4):458-463.
[10]李露,李峰,邓雄峰.二级倒立摆的参数自校正模糊PI控制[J].微型机与应用,2014,33(12):79-82.LI L,LI F,DENG X F. The parameter self-tuning fuzzy PI control of double inverted pendulum[J]. Microcomputer and its applications,2014,33(12):79-82.
[11]宋清昆,李东威.二级倒立摆控制器设计及稳定性研究[J].计算机仿真,2015,32(4):305-309.SONG Q K,LI D W. The design and stability study of double inverted pendulum controller[J]. Computer simulation,2015,32(4):305-309.
[12]王凯,黄玲,都磊.二级倒立摆的T-S模糊建模和模糊控制[J].控制工程,2015,7(22):47-50.WANG K,HUANG L,DU L. T-S fuzzy modeling and fuzzy control of inverted pendulum[J]. Control engineering of China,2015,7(22):47-50.
[13]谌海云,杜振华,邹宁波,等.多种群遗传算法的倒立摆LQR控制器设计[J].控制工程,2014,21(3):90-93.CHEN H Y,DU Z H,ZOU N B,et al. LQR controller design for inverted pendulum based on multi-population genetic algorithm[J]. Control engineering of China,2014,21(3):90-93.
[14]罗刘敏,刘晓青,谢娟娟,等.基于极点配置的倒立摆控制器设计[J].电脑知识与技术,2015,32(11):181-183.LUO L M,LIU X Q,XIE J J,et al. Design of inverted pendulum controller based on the theory of pole[J]. Computer knowledge and technology,2015,32(11):181-183.
[15]王莹莹,王向东,王冬青.基于模糊控制算法的二级倒立摆控制器设计[J].青岛大学学报,2015,30(4):62-63.WANG Y Y,WANG X D,WANG D Q. Design of double inverted pendulum controller based on fuzzy control algorithm[J]. Journal of Qingdao University,2015,30(4):62-63.
[2]张卓,张井岗.跷跷板系统的模糊控制策略研究[J].太原科技大学学报,2016,37(6):447-452.ZHANG Z,ZHANG J G. A fuzzy control method for seesaw system[J]. Journal of Taiyuan University of Science and Technology,2016,37(6):447-452.
[3]陈梅,陈艳燕.两轮智能车跟踪控制系统的研究[J].合肥工业大学学报(自然科学版),2015,38(3):319-324.CHEN M,CHEN Y Y. Study of tracking control system of twowheeled intelligent vehicle[J]. Journal of Hefei University of Technology(natural science),2015,38(3):319-324.
[4]张碧波.基于模糊控制的三级倒立摆系统的控制器设计[D].石家庄:河北科技大学,2015:21-38.ZHANG B B. Design of controller on triple inverted pendulum system based on fuzzy control[D]. Shijiazhuang:Hebei University of Science and Technology,2015:21-38.
[5]张敏.二级倒立摆云模型PID控制研究[D].大连:大连海事大学,2016:23-27.ZHANG M. Research on cloud model PID control of double inverted pendulum[D]. Dalian:Dalian Maritime University,2016:23-27.
[6]邢景虎,陆华才.二级倒立摆两种控制方法的对比研究[J].佳木斯大学学报(自然科学版),2017,35(2):263-266.XING J H,LU H C. Comparative study on two control methods of the double inverted pendulum[J]. Journal of Jiamusi University(natural science edition),2017,35(2):263-266.
[7]邢景虎,陈其工,江明.二级倒立摆基于融合函数的模糊控制[J].合肥工业大学学报(自然科学版),2011,34(8):1155-1159.XING J H,CHEN Q G,JIANG M. Fusion function based fuzzy control for a double inverted pendulum[J]. Journal of Hefei University of Technology(natural science edition),2011,34(8):1155-1159.
[8]尹逊和,樊雪丽,杜洋,等.二级倒立摆系统的实物控制[J].计算机工程与应用,2016,52(20):242-250.YIN X H,FAN X L,DU Y,et al. Physical control of double inverted pendulum system[J]. Computer engineering and applications,2016,52(20):242-250.
[9]李平,张重阳,陶文华,等.二级倒立摆的Sugeno型模糊神经网络控制[J].控制工程,2009,16(4):458-463.LI P,ZHANG C Y,TAO W H,et al. Sugeno fuzzy neural network control for double inverted pendulum[J]. Control engineering of China,2009,16(4):458-463.
[10]李露,李峰,邓雄峰.二级倒立摆的参数自校正模糊PI控制[J].微型机与应用,2014,33(12):79-82.LI L,LI F,DENG X F. The parameter self-tuning fuzzy PI control of double inverted pendulum[J]. Microcomputer and its applications,2014,33(12):79-82.
[11]宋清昆,李东威.二级倒立摆控制器设计及稳定性研究[J].计算机仿真,2015,32(4):305-309.SONG Q K,LI D W. The design and stability study of double inverted pendulum controller[J]. Computer simulation,2015,32(4):305-309.
[12]王凯,黄玲,都磊.二级倒立摆的T-S模糊建模和模糊控制[J].控制工程,2015,7(22):47-50.WANG K,HUANG L,DU L. T-S fuzzy modeling and fuzzy control of inverted pendulum[J]. Control engineering of China,2015,7(22):47-50.
[13]谌海云,杜振华,邹宁波,等.多种群遗传算法的倒立摆LQR控制器设计[J].控制工程,2014,21(3):90-93.CHEN H Y,DU Z H,ZOU N B,et al. LQR controller design for inverted pendulum based on multi-population genetic algorithm[J]. Control engineering of China,2014,21(3):90-93.
[14]罗刘敏,刘晓青,谢娟娟,等.基于极点配置的倒立摆控制器设计[J].电脑知识与技术,2015,32(11):181-183.LUO L M,LIU X Q,XIE J J,et al. Design of inverted pendulum controller based on the theory of pole[J]. Computer knowledge and technology,2015,32(11):181-183.
[15]王莹莹,王向东,王冬青.基于模糊控制算法的二级倒立摆控制器设计[J].青岛大学学报,2015,30(4):62-63.WANG Y Y,WANG X D,WANG D Q. Design of double inverted pendulum controller based on fuzzy control algorithm[J]. Journal of Qingdao University,2015,30(4):62-63.