倒立摆的模糊控制研究
|
摘要
倒立摆系统是一个典型的多变量、非线性、强藕合和快速运动的自然不稳定系统。因此倒立摆在研究双足机器人直立行走、火箭发射过程的姿态调整和直升机飞行控制领域中有重要的现实意义,相关的科研成果已经应用到航天科技和机器人学等诸多领域。
本文围绕一级倒立摆系统,采用模糊控制理论研究了倒立摆的控制系统仿真问题。仿真的成功证明了本文设计的模糊控制器有很好的稳定性。主要研究工作如下:
1)使用了牛顿力学和Lagrange方程对倒立摆进行数学建模,推导出倒立摆系统传递函数和状态空间方程。
2)分析了模糊控制理论的数学基础,对模糊控制的方法进行了研究:介绍了模糊子集、模糊关系和模糊推理等相关知识,在此基础上进一步分析了模糊控制器的结构与组成,对精确量的模糊化、模糊控制算法设计方法以及输出信息的模糊判决作了进一步的介绍。
3)介绍了如何利用Simulikn建立倒立摆系统模型,特别是利用Mask封装功能,使模型更具灵活性,给仿真带来很大方便。
4)一级倒立摆系统的控制器设计与仿真:考虑到同时控制倒立摆的四个状态变量x,(?),θ,(?),必然会使模糊控制规则复杂并且数目庞大(即所谓的规则爆炸),本文设计了两个模糊控制器即位置模糊控制器和角度模糊控制器,用这两个模糊控制器进行串联控制,并把位置模糊控制器控制输出作为一个虚拟角度乘以一个系数与摆杆的实际角度叠加形成一个广义角,以这个广义角和摆杆的角速度作为输入量输入给角度模糊控制器对摆杆的角度进行控制;通过matlab的Simulikn实现了倒立摆模糊控制系统的仿真,仿真结果证明:模糊控制器不仅可以稳定倒立摆系统,还可以使小车定位在特定位置。
5)对于二级倒立摆采用了分层模糊控制的思想,解决了规则爆炸问题,仿真结果显示对摆杆的控制效果较好。
Inverted pendulum system is a typical multivariable,nonlinear,strong-coupling with fast motion and natural instability system.So the research of inverted pendulum has many important realistic meaning in the areas such as,the walking of biped robot,the posture adjustment in launching process of rocket,and the flying control of helicopter.Many correlative productions have applications in many fields of technology of spaceflight and subject of robot.
Fuzzy control theory is introduced to study simulation and the simulation and the controlling problem in inverted pendulum in this paper.Success of simulation proves that the designed fuzzy controller has very good stability.Main research work is declared below:
1) The Newton's mechanics and Lagrange Equation is used to drive the mathematical model of inverted pendulum and the transfer function as well as the state-space equation of inverted pendulum is deduced.
2) Take a research on mathematical fundament and methods of fuzzy control theory:Fuzzy subset,fuzzy relations,as well as fuzzy reasoning,other related knowledge is introduced.Based on that further study on the structure and component of controller of single inverted pendulum are made and the precise amount of fuzzy,the design method of fuzzy control algorithm and fuzzy output ruling are introduced.
3) The simulation of fuzzy control of inverted pendulum system.It is introduced how to realize the simulation of the inverted pendulum system by the SIMULINK toolbox.Especially the MASK packaging function enables the simulation model flexibility,which facilitates the simulation work.
4) Design and simulation for controller of single inverted pendulum:considering simultaneous control four state variables x,x,θ,θdefinitely makes fuzzy control rules complicated and huge(the so-called rules explosion).Two fuzzy control design,that is location fuzzy controller and angle fuzzy controller,in tandem control.Take the output of the location fuzzy controller as a virtual angle plus a parameter which adds to the real angle of the swing pole to form a generalized angle. Take the generalized angle and the angular velocity as the input into the angle fuzzy controller to control the angle of the swing pole.Simulation experiment of the fuzzy control of inverted pendulum is very well implemented by using MATLAB SIMULINK.The result shows that it not only has quite good stability,but also is able to make the cart of the pendulum moving to the place where it is appointed by us in advance,along the orbit.
5) The idea of layered fuzzy control solves the problem of rules explosion on double inverted pendulum.Simulation results show the better control effect.
本文围绕一级倒立摆系统,采用模糊控制理论研究了倒立摆的控制系统仿真问题。仿真的成功证明了本文设计的模糊控制器有很好的稳定性。主要研究工作如下:
1)使用了牛顿力学和Lagrange方程对倒立摆进行数学建模,推导出倒立摆系统传递函数和状态空间方程。
2)分析了模糊控制理论的数学基础,对模糊控制的方法进行了研究:介绍了模糊子集、模糊关系和模糊推理等相关知识,在此基础上进一步分析了模糊控制器的结构与组成,对精确量的模糊化、模糊控制算法设计方法以及输出信息的模糊判决作了进一步的介绍。
3)介绍了如何利用Simulikn建立倒立摆系统模型,特别是利用Mask封装功能,使模型更具灵活性,给仿真带来很大方便。
4)一级倒立摆系统的控制器设计与仿真:考虑到同时控制倒立摆的四个状态变量x,(?),θ,(?),必然会使模糊控制规则复杂并且数目庞大(即所谓的规则爆炸),本文设计了两个模糊控制器即位置模糊控制器和角度模糊控制器,用这两个模糊控制器进行串联控制,并把位置模糊控制器控制输出作为一个虚拟角度乘以一个系数与摆杆的实际角度叠加形成一个广义角,以这个广义角和摆杆的角速度作为输入量输入给角度模糊控制器对摆杆的角度进行控制;通过matlab的Simulikn实现了倒立摆模糊控制系统的仿真,仿真结果证明:模糊控制器不仅可以稳定倒立摆系统,还可以使小车定位在特定位置。
5)对于二级倒立摆采用了分层模糊控制的思想,解决了规则爆炸问题,仿真结果显示对摆杆的控制效果较好。
Inverted pendulum system is a typical multivariable,nonlinear,strong-coupling with fast motion and natural instability system.So the research of inverted pendulum has many important realistic meaning in the areas such as,the walking of biped robot,the posture adjustment in launching process of rocket,and the flying control of helicopter.Many correlative productions have applications in many fields of technology of spaceflight and subject of robot.
Fuzzy control theory is introduced to study simulation and the simulation and the controlling problem in inverted pendulum in this paper.Success of simulation proves that the designed fuzzy controller has very good stability.Main research work is declared below:
1) The Newton's mechanics and Lagrange Equation is used to drive the mathematical model of inverted pendulum and the transfer function as well as the state-space equation of inverted pendulum is deduced.
2) Take a research on mathematical fundament and methods of fuzzy control theory:Fuzzy subset,fuzzy relations,as well as fuzzy reasoning,other related knowledge is introduced.Based on that further study on the structure and component of controller of single inverted pendulum are made and the precise amount of fuzzy,the design method of fuzzy control algorithm and fuzzy output ruling are introduced.
3) The simulation of fuzzy control of inverted pendulum system.It is introduced how to realize the simulation of the inverted pendulum system by the SIMULINK toolbox.Especially the MASK packaging function enables the simulation model flexibility,which facilitates the simulation work.
4) Design and simulation for controller of single inverted pendulum:considering simultaneous control four state variables x,x,θ,θdefinitely makes fuzzy control rules complicated and huge(the so-called rules explosion).Two fuzzy control design,that is location fuzzy controller and angle fuzzy controller,in tandem control.Take the output of the location fuzzy controller as a virtual angle plus a parameter which adds to the real angle of the swing pole to form a generalized angle. Take the generalized angle and the angular velocity as the input into the angle fuzzy controller to control the angle of the swing pole.Simulation experiment of the fuzzy control of inverted pendulum is very well implemented by using MATLAB SIMULINK.The result shows that it not only has quite good stability,but also is able to make the cart of the pendulum moving to the place where it is appointed by us in advance,along the orbit.
5) The idea of layered fuzzy control solves the problem of rules explosion on double inverted pendulum.Simulation results show the better control effect.
引文
1 汪雪琴.倒立摆系统的模糊智能控制研究[D]:[硕士学位论文].北京:北京化工大学,2004
2 Mori Shozo,H.Nishihara and K.Furuta.Control of unstable mechanical system:Control of pendulum[J].Int.J.of Control 1976,23(8):673-692.
3 K.Furuta,Katsuhisa,H.Kajiwara and K.Kosuge.Digital control of a double inverted pendulum on an inclined rail[J].Int.J.of Control 1980,32(8):907-924.
4 K.Furuta,Katsuhisa,T.Ochia and N.Ono.Attitude control of a triple inverted pendulum[J].Int.J.of Control 1984,39(6):1351-1365.
5 J.W.Watts.Control of an inverted pendulum.ASEE Annual Conference,session 2827,1984,706-710.
6 李洪兴,苗志宏,王加银.四级倒立摆系统的变论域自适应模糊控制[J].中国科学E 辑,2002,32(1):65-75
7 张飞舟、沈程智、范跃祖.拟人智能控制三级倒立摆[J].计算机工程与应用,2000,2:17-20
8 李德毅.三级倒立摆的云控制方法及动平衡模式[J].中国工程科学,1999,1(2):41-46
9 薛安克,王惠姣.基于鲁棒LQ控制的倒立摆系统分析和设计[J].上海交通大学学报,2002,36(增刊):1-7
10 固高科技(深圳)有限公司等编著.固高摆系统与自动控制实验(实验教程).2002,42-48
11 章卫国,杨向忠.模糊控制理论与应用[M].西安:西北工业大学出版社,2004,1-100
12 洪旭.倒立摆系统模糊控制算法研究[D]:[硕士学位论文].西安:西安电子科技大学,2005
13 王正林、王胜开、陈国顺.MATLAB/Simulink与控制系统仿真[M],2005.7:30-150
14 刘叔军、盖晓华、樊京等.MATLAB7.0控制系统应用与实例[M],2006.1:85-120
15 李志鸿.倒立摆系统的模糊控制[D]:[硕士学位论文].西安:西安建筑科技大学,2007
16 严雪莉,江汉红.单级倒立摆方法的仿真对比研究[J].测控技术,2005,7:37-39
17 李丽娟,赵英凯,胡盛祥.两种简化规则的模糊控制系统的分析比较[J],计算机仿真,2006,4:157-159
18 罗晶,陈平.一阶倒立摆的PID控制[J].实验室研究与探索,2005.11:26-28
19 杨平,徐春梅,曾婧婧,等.PID控制在倒立摆实时控制系统中的应用[J].微计算机信息,2006.7-1:83-85
20 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(自然科学版),2006,33(1),111-115
21 沈艳霞,纪志成,姜建国.二级倒立摆新型模糊控制策略的研究[J].中国矿业大学学报.2004,33(3),327-331.
2 Mori Shozo,H.Nishihara and K.Furuta.Control of unstable mechanical system:Control of pendulum[J].Int.J.of Control 1976,23(8):673-692.
3 K.Furuta,Katsuhisa,H.Kajiwara and K.Kosuge.Digital control of a double inverted pendulum on an inclined rail[J].Int.J.of Control 1980,32(8):907-924.
4 K.Furuta,Katsuhisa,T.Ochia and N.Ono.Attitude control of a triple inverted pendulum[J].Int.J.of Control 1984,39(6):1351-1365.
5 J.W.Watts.Control of an inverted pendulum.ASEE Annual Conference,session 2827,1984,706-710.
6 李洪兴,苗志宏,王加银.四级倒立摆系统的变论域自适应模糊控制[J].中国科学E 辑,2002,32(1):65-75
7 张飞舟、沈程智、范跃祖.拟人智能控制三级倒立摆[J].计算机工程与应用,2000,2:17-20
8 李德毅.三级倒立摆的云控制方法及动平衡模式[J].中国工程科学,1999,1(2):41-46
9 薛安克,王惠姣.基于鲁棒LQ控制的倒立摆系统分析和设计[J].上海交通大学学报,2002,36(增刊):1-7
10 固高科技(深圳)有限公司等编著.固高摆系统与自动控制实验(实验教程).2002,42-48
11 章卫国,杨向忠.模糊控制理论与应用[M].西安:西北工业大学出版社,2004,1-100
12 洪旭.倒立摆系统模糊控制算法研究[D]:[硕士学位论文].西安:西安电子科技大学,2005
13 王正林、王胜开、陈国顺.MATLAB/Simulink与控制系统仿真[M],2005.7:30-150
14 刘叔军、盖晓华、樊京等.MATLAB7.0控制系统应用与实例[M],2006.1:85-120
15 李志鸿.倒立摆系统的模糊控制[D]:[硕士学位论文].西安:西安建筑科技大学,2007
16 严雪莉,江汉红.单级倒立摆方法的仿真对比研究[J].测控技术,2005,7:37-39
17 李丽娟,赵英凯,胡盛祥.两种简化规则的模糊控制系统的分析比较[J],计算机仿真,2006,4:157-159
18 罗晶,陈平.一阶倒立摆的PID控制[J].实验室研究与探索,2005.11:26-28
19 杨平,徐春梅,曾婧婧,等.PID控制在倒立摆实时控制系统中的应用[J].微计算机信息,2006.7-1:83-85
20 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(自然科学版),2006,33(1),111-115
21 沈艳霞,纪志成,姜建国.二级倒立摆新型模糊控制策略的研究[J].中国矿业大学学报.2004,33(3),327-331.