【作者】 翟龙余；

【导师】 徐保国； 周忠旺；

【作者基本信息】 江南大学 ， 控制工程， 2008， 硕士

【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。更多还原

【Abstract】 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.更多还原