基于微粒群算法的倒立摆控制研究
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摘要
倒立摆是一个典型的单输入多输出、非线性、高阶次的不稳定系统,研究倒立摆的控制不仅能反映控制理论中有关非线性、鲁棒性以及跟踪问题等许多关键问题,同时对工业复杂对象的控制也有着重要的应用价值。
微粒群优化算法(Particle Swarm Optimization algorithm,PSO)是近年来提出的一种新型的基于群体智能的进化算法,它具有算法简单、收敛速度较快,所需领域知识少的特点。本文在对倒立摆、PSO算法研究现状进行综述的基础上,进行了基于PSO算法优化设计控制系统的研究,论文主要工作包括:
(1)基于牛顿力学原理建立了一级直线倒立摆数学模型,介绍了倒立摆LQR(Linear Quadratic Regulator)最优控制方法,并利用MATLAB7研究了倒立摆LQR控制性能。
(2)将微粒群算法应用于传统PID控制器参数优化整定,通过对不同对象的控制系统仿真实验结果表明,与传统PID控制器整定方法相比,控制系统具有更佳的闭环控制性能。
(3)为克服BP(Back-Propagaion)算法不足,本文研究利用PSO算法作为多层前馈神经网络训练算法以实现非线性函数逼近及模式识别等,通过对不同非线性函数的辨识及模式识别实验结果表明,PSO算法作为神经网络训练算法是可行的。为提高逼近精度,采用“种群爆炸”思想对PSO算法进行改进,实验结果表明,改进方法是有效的。为得到全局最优的BP网络训练算法,文中还将PSO算法与BP算法结合进行网络训练开展了研究工作,实验表明,该方法能克服BP算法不足,提高网络训练速度和精度。
(4)针对一级直线倒立摆这一复杂非线性对象,本文提出了一种基于PSO算法训练BP网络连接权值与阈值的神经网络控制方法以实现倒立摆控制,仿真结果表明了该方法的良好性能。
文章最后对全文的工作进行总结,并且提出了进一步研究的方向。
The inverted pendulum system is a typical single input and multiple outputs,nonlinear,high order,natural unstable system. Research on the accurate control of the inverted pendulum not only reflects several joints-in control theory,such as,nonlinear problems,robustness,as well as tracking,but also has great engineering value to the complex industrial objects.
Recently,Particle Swarm Optimization(PSO)algorithm comes forth as another intelligent algorithm.It is simple with concept, parameters and implementation.Inverted pendulum、PSO and its researchment actuality are summarized firstly,then PSO is applied to optimize and design the control systems.The main contributions given in this dissertation are as follows:
(1)Using Newton's mechanicstheory to establish the linear level inverted pendulum mathematical model.LQR(Linear Quadratic Regulator)controller in modern control theory is designed,and simulation performances are given by MATLAB7.0.
(2)PSO is proposed to optimize the parameters of the conventional PID controller.The simulation results of the different control systems show that the optimal PIP controller based on PSO has a satisfying performance and is better than the conventional PID controller based on the conventional.
(3)PSO algorithm is used to train the weights and the thresholds of Multilayer Feedforward Neural Networks(MFNN)instead of Back Propagation(BP)algorithm.The NN trained by PSO is applied to identify non-linear function and pattern recognition.The experimental results show that the proposed method is effective but low-precision than BP algorithm.To improve the global searching capability of PSO,the concept of 'Particle Swarm Exploding' is introduced into the PSO,experimental results show that the proposed method is effective.The hybrid algorithm combining PSO algorithm with BP algorithm is used to train the MFNN.Defects of conventional BP algorithm,i.e.the slow convergence of weight and threshold learning,premature result,and the slow training speed of PSO,are settled by it.
(4)A NNC(Neural Network Controller)is made based on PSO algorithm to control inverted pendulum and theexperiment results prove the good effectiveness of NNC method based on PSO.
Finally some conclusions and future researches are drawn in this dissertation.
微粒群优化算法(Particle Swarm Optimization algorithm,PSO)是近年来提出的一种新型的基于群体智能的进化算法,它具有算法简单、收敛速度较快,所需领域知识少的特点。本文在对倒立摆、PSO算法研究现状进行综述的基础上,进行了基于PSO算法优化设计控制系统的研究,论文主要工作包括:
(1)基于牛顿力学原理建立了一级直线倒立摆数学模型,介绍了倒立摆LQR(Linear Quadratic Regulator)最优控制方法,并利用MATLAB7研究了倒立摆LQR控制性能。
(2)将微粒群算法应用于传统PID控制器参数优化整定,通过对不同对象的控制系统仿真实验结果表明,与传统PID控制器整定方法相比,控制系统具有更佳的闭环控制性能。
(3)为克服BP(Back-Propagaion)算法不足,本文研究利用PSO算法作为多层前馈神经网络训练算法以实现非线性函数逼近及模式识别等,通过对不同非线性函数的辨识及模式识别实验结果表明,PSO算法作为神经网络训练算法是可行的。为提高逼近精度,采用“种群爆炸”思想对PSO算法进行改进,实验结果表明,改进方法是有效的。为得到全局最优的BP网络训练算法,文中还将PSO算法与BP算法结合进行网络训练开展了研究工作,实验表明,该方法能克服BP算法不足,提高网络训练速度和精度。
(4)针对一级直线倒立摆这一复杂非线性对象,本文提出了一种基于PSO算法训练BP网络连接权值与阈值的神经网络控制方法以实现倒立摆控制,仿真结果表明了该方法的良好性能。
文章最后对全文的工作进行总结,并且提出了进一步研究的方向。
The inverted pendulum system is a typical single input and multiple outputs,nonlinear,high order,natural unstable system. Research on the accurate control of the inverted pendulum not only reflects several joints-in control theory,such as,nonlinear problems,robustness,as well as tracking,but also has great engineering value to the complex industrial objects.
Recently,Particle Swarm Optimization(PSO)algorithm comes forth as another intelligent algorithm.It is simple with concept, parameters and implementation.Inverted pendulum、PSO and its researchment actuality are summarized firstly,then PSO is applied to optimize and design the control systems.The main contributions given in this dissertation are as follows:
(1)Using Newton's mechanicstheory to establish the linear level inverted pendulum mathematical model.LQR(Linear Quadratic Regulator)controller in modern control theory is designed,and simulation performances are given by MATLAB7.0.
(2)PSO is proposed to optimize the parameters of the conventional PID controller.The simulation results of the different control systems show that the optimal PIP controller based on PSO has a satisfying performance and is better than the conventional PID controller based on the conventional.
(3)PSO algorithm is used to train the weights and the thresholds of Multilayer Feedforward Neural Networks(MFNN)instead of Back Propagation(BP)algorithm.The NN trained by PSO is applied to identify non-linear function and pattern recognition.The experimental results show that the proposed method is effective but low-precision than BP algorithm.To improve the global searching capability of PSO,the concept of 'Particle Swarm Exploding' is introduced into the PSO,experimental results show that the proposed method is effective.The hybrid algorithm combining PSO algorithm with BP algorithm is used to train the MFNN.Defects of conventional BP algorithm,i.e.the slow convergence of weight and threshold learning,premature result,and the slow training speed of PSO,are settled by it.
(4)A NNC(Neural Network Controller)is made based on PSO algorithm to control inverted pendulum and theexperiment results prove the good effectiveness of NNC method based on PSO.
Finally some conclusions and future researches are drawn in this dissertation.
引文
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[4]刘珊中,朱邦太,邓兵.基于H_∞控制的倒立摆平衡系统鲁棒性研究[J].电光与控制.2000(2):1-6
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[6]董翠玲,周凤岐.二级倒立摆的模糊控制[J].机床与液压.2006(4)
[7]过润秋,洪旭,苏旺旺.基于模糊控制理论的二级倒立摆控制算法[J].西安电子科技大学学报.2006,33(1)
[8]蒋国飞,吴沧浦.基于Q学习算法和BP神经网络的倒立摆控制[J].自动化学报.1998,24(5)
[9]张乃尧,栗天.基于模糊神经网络的模型参考自适应控制[J].自动化学报,1996(7)
[10]杨振强,朴营国,程树康.二级倒立摆的状态变量合成模糊神经网络控制[J].控制与决策.2002,17(1)
[11]邢君,王磊,戴冠中.基于BP算法的自适应模糊控制系统研究[J].控制理论与应用.1996,13(6):797-801.
[12]杨国军,崔平远,李琳琳.遗传算法在神经网络控制中的应用与实现[J].系统仿真学报.2001,13(5)
[13]W.Wei,W.Von Seelen.Recurrent neuro-controller design for an inverted pendulum using evolution strategy[J].International Journal of Systems Science,2001,Volume:32(5),Pages:643-650
[14]F.Pasemann.Evolving neuro controllers for balancing an inverted pendulum Network.Computation in Neural Systems[J].Volume:9,Pages:495-511
[15]葛锁良,陈学军,邱丹.神经网络预测控制及其在二级倒立摆中的仿真[J].自动化技术与应用.2005,24(6)
[16]张飞舟,范跃祖,沈程智等.利用云模型实现智能控制倒立摆[J].控制理论与应用.2000,17(4)
[17]陈晖,李德毅,沈程智等.云模型在倒立摆控制中的应用[J].计算机研究与发展.1999,56(10)
[18]Kennedy,J,Eberhart,R..Particle swarm optimization[C].IEEE International Conference on Neural Networks-Conference Proceedings,v 4,1995,p 1942-1948
[19]Eberhart,R.Kennedy,J.A new optimizer using particle swarm theory[C].Proceedings of the Sixth International Symposium on Micro Machine and Human Science.Nagoya Japan IEEE Press 1995,39-43.
[20]Eberhart,R.C.Shi,Y.Particle swarm optimization:Developments,applications and resources[C].Proceedings of the IEEE Conference on Evolutionary Computation,ICEC,v 1,2001,p 81-86
[21]Hu,Xiaohui,Shi,Yuhui,Eberhart,Russ Recent advances in particle swarm[C].Proceedings of the 2004 Congress on Evolutionary Computation,CEC2004,2004,p 90-97
[22]Kennedy,J.Eberhart,R.A discrete binary version of the particle swarm algorithmiC].Proceedings of IEEE International Conference on Computational Cybernetics and Simulation Systems, Man,and Cybernetics, Orlando, FL. IEEE Press 1997,4104-4108
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