毕业设计（论文）外文参考
资料及译文
译文题目：Inverted Pendulum
学生姓名：徐飞马学号： 0704111030 专业： 07自动化
所在学院：机电学院
指导教师：陈丽换
职称：讲师
2011 年 2月 24日
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The inverted pendulum
Key words: inverted pendulum, modeling, PID controllers,
LQRcontrollers
What is an Inverted Pendulum? Remember when you were a child and you tried to balance a broom-stick or baseball bat on your index finger or the palm of your hand ? You had to constantly adjust the position of your hand to keep the object upright. An Inverted Pendulum does basically the same thing. However, it is limited in that it onl y moves in one dimension, while your hand could move up, down, sideways, etc. Che ck out the video provided to see exactly how the Inverted Pendulum works.
An inverted pendulum is a physical device consisting in a cylindrical bar (usually o f aluminum) free to oscillate around a fixed pivot. The pivot is mounted on a carriage, which in its turn can move on a horizontal direction. The carriage is driven by a moto r, which can exert on it a variable force. The bar would naturally tend to fall down fro m the top vertical position, which is a position of unsteady equilibrium.
The goal of the experiment is to stabilize the pendulum (bar) on the top vertical pos ition. This is possible by exerting on the carriage through the motor a force which ten ds to contrast the 'free' pendulum dynamics. The correct force has to be calculated me asuring the instant values of the horizontal position and the pendulum angle (obtained e.g. through two potentiometers).
The system pendulum+cart+motor can be modeled as a linear system if all the para meters are known (masses, lengths, etc.), in order to find a controller to stabilize it. If not all the parameters are known, one can however try to 'reconstruct' the system para meters using measured data on the dynamics of the pendulum.
The inverted pendulum is a traditional example (neither difficult nor trivial) of a co ntrolled system. Thus it is used in simulations and experiments to show the performan ce of different controllers (e.g. PID controllers, state space controllers, fuzzy controlle rs....).
The Real-Time Inverted Pendulum is used as a benchmark, to test the validity and t
he performance of the software underlying the state-space controller algorithm, i.e. th e used operating system. Actually the algorithm is implement form the numerical poin t of view as a set of mutually co-operating tasks, which are periodically activated by t he kernel, and which perform different calculations. The way how these tasks are acti vated (e.g. the activation order) is called scheduling of the tasks. It is obvious that a co rrect scheduling of each task is crucial for a good performance of the controller, and h ence for an effective pendulum stabilization. Thus the inverted pendulum is very usef ul in determining whether a particular scheduling choice is better than another one, in which cases, to which extent, and so on.
Modeling an inverted pendulum.Generally the inverted pendulum system is modele d as a linear system, and hence the modeling is valid only for small oscillations of the pendulum.
With the use of trapezoidal input membership functions and appropriate compositio n and inference methods, it will be shown that it is possible to obtain rule membership functions which are region-wise affine functions of the controller input variable. We propose a linear defuzzification algorithm that keeps this region-wise affine structure and yields a piece-wise affine controller. A particular and systematic parameter tuning method will be given which allows turning this controller into a variable structure-like controller. We will compare this region-wise affine controller with a Fuzzy and Varia ble Structure Controller through the application to an inverted pendulum control. We will begin with system design; analyzing control behavior of a two-stage invert ed pendulum. We will then show how to design a fuzzy controller for the system. We will describe a control curve and how it differs from that of conventional controllers when using a fuzzy controller. Finally, we will discuss how to use this curve to define labels and membership functions for variables, as well as how to create rules for the c ontroller.
In the formulation of any control problem there will typically be discrepancies betw een the actual plant and the mathematical model developed for controller design.This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of complex plant behavior by a straightforward model.The engineer
