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1、电子与信息工程学院本科毕业设计本科毕业设计外 文 文 献 翻 译论文题目论文题目 直线式倒立摆控制系统直线式倒立摆控制系统 学生姓名学生姓名 包雷包雷 专专 业业 电气工程及其自动化电气工程及其自动化 指导教师指导教师 李李 东东 京京 2011 年 11 月The inverted pendulumKey words: inverted pendulum, modeling, PID controllers, Fuzzy controllers, state space controllersWhat is an Inverted Pendulum? Remember when you we
2、re 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 t he same thing. However, it is limited in that it only moves in one
3、 dimension, while your hand coul d move up, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pe ndulum works.倒立摆是什么？还记得当你是个孩子时你曾用你的食指或者掌心设法去平 衡一把扫帚柄或者棒球棍吗？你必须不断地调整你 的手的位置以保持对象的垂 直。一个倒立摆在本质上就是做相同的事情。然而，它会受限制因为它只能在 一 定范围内移动，虽然你的手可以上升、下降、斜向一边等等。检查录象提供 的画面来观察倒立摆是如何确切 地工作
4、的。An inverted pendulum is a physical device consisting in a cylindrical bar (usually of aluminum) free to oscillate around a fixed pivot. The pivot is mounted on a carriage, which in its turn can mo ve on a horizontal direction. The carriage is driven by a motor, which can exert on it a variable for
5、 ce. The bar would naturally tend to fall down from the top vertical position,which is a position of unsteady equilibrium.一个倒立摆是个物理设备它包括一个圆柱体的棒子（通常是铝的）可以在一 个支点周围振荡。这个支点是安在一个车架上，它的转动方向是水平的偏转。小 车是由一个马达控制的，它可以运用于一个变力。棒子会有自然的趋势从最高的 竖直位置下落，那是一个不稳定的平衡位置。The goal of the experiment is to stabilize the pendu
6、lum (bar) on the top vertical position. This is possible by exerting on the carriage through the motor a force which tends to contrast the free pe ndulum dynamics. The correct force has to be calculated measuring the instant values of the horiz ontal position and the pendulum angle (obtained e.g. th
7、rough two potentiometers).实验的目标是使摆（棒子）稳定在最高的竖直位置。这是有可能的只要运用 通过马达的小车一个力该力可以与“自由”摆的动力学抵消。 这个正确的力必须 通过计算测量水平偏转的瞬时值和摆的角度（获得两个电位计） 。The system pendulum+cart+motor can be modeled as a linear system if all the parameters are k nown (masses, lengths, etc.), in order to find a controller to stabilize it. If
8、not all the parameters ar e known, one can however try to reconstruct the system parameters using measured data on the d ynamics of the pendulum.系统摆+车+马达可以建模成一个线形系统如果所有的参数都是已知的（质 量、长度等） ，为了寻找一个控制 器去稳定住它。如果不是所有的参数都已知， 可以用多种方法去“推想”系统参数像用摆的动力学的测量数据。What is it used for?Just like the broom-stick, an Inve
9、rted Pendulum is an inherently unstable sys tem. Force must be properly applied to keep the system intact. To achieve this, proper control theo ry is required. The Inverted Pendulum is essential in the evaluating and comparing of various cont rol theories.倒立摆是干什么的？就好象扫帚柄，一个倒立摆是一个天生的不稳定系统。 力度必须被严格地应用
10、以保持系统的完整性。为了实现它，严格的控制理论是必须的。倒立摆在求数值和各种控制理论的比较中是必要的。The inverted pendulum is a traditional example (neither difficult nor trivial) of a controlled syst em. Thus it is used in simulations and experiments to show the performance of different controller s (e.g. PID controllers, state space controllers,
11、fuzzy controllers).倒立摆是一个控制器系统中的一个传统的例子 （既不困难也不是没有价值） 。 尽管它是仿真和实验来显示不同控制器的性能（举例来说 PID 控制器，状态空间 控制器，模糊控制器） 。The Real-Time Inverted Pendulum is used as a benchmark, to test the validity and the performa nce of the software underlying the state-space controller algorithm, i.e. the used operating system
12、. Actually the algorithm is implement form the numerical point of view as a set of mutually co-oper ating tasks, which are periodically activated by the kernel, and which perform different calculation s. The way how these tasks are activated (e.g. the activation order) is called scheduling of the ta
13、sks . It is obvious that a correct scheduling of each task is crucial for a good performance of the contro ller, and hence for an effective pendulum stabilization. Thus the inverted pendulum is very useful i n determining whether a particular scheduling choice is better than another one, in which ca
14、ses, to which extent, and so on.实时倒立摆被作为一个基准， 去测试软件在状态空间控制器运算法则下的有 效性和性能，也就是实用的操作系统。事实上运算法则是通过数值点实现的该数 值点看作一组互助的协同操作的任务，它是周期性的通过核心的活动，它执行不 同的计算。这些任务如何活动的方法（举例来说激活命令）被称作任务的时序安 排。很明显每个任务的时序安排对控制器的一个好的性能是至关紧要的，因此对 一个摆的稳定性是有效的。 如此倒立摆是非常有用的在决定是否一个特殊的时序 安排的选择比另一个好，在哪个情形下，在什么程度内等等。Modeling an inverted pend
15、ulum.Generally the inverted pendulum system is modeled as a linear system, and hence the modeling is valid only for small oscillations of the pendulum.为倒立摆建模。通常倒立摆系统建模成一个线形系统，因此模型只对小幅度 摆动的摆才有效。Prescribed trajectory tracking with certain accuracy is a main task of robotic control. The contr ol is oft
16、en based on a mathematical model of the system. This model is never an exact representati on of reality, since modeling errors are inevitable. Moreover, one can use a simplified model on pu rpose. In this paper, the structured and unstructured uncertainties are of primary interest, i.e., the m odeling error due to the parameters variation and unmodeled modes, especially the friction and sen sor dynamics, neglected time del
