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1、TheinvertedpendulumKeywords:inverted pendulum,modeling,PID controllers, Fuzzy controllers, state space controllersWhat 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
2、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 only moves in one dimension, while your hand could move up, down, sideways, etc. Check out the video provided to see
3、 exactly how the Inverted Pendulum 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 地工作的。 An inverted pendulum is a physical device consisting in a cylindrical bar (usually
4、of 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 motor, which can exert on it a variable force. The bar would naturally tend to fall down from the top vertical
5、 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 pendulum (bar) on the top vertical position. This is po
6、ssible by exerting on the carriage through the motor a force which tends to contrast the 'free' pendulum dynamics. The correct force has to be calculated measuring the instant values of the horizontal position and the pendulum angle (obtained e.g. through two potentiometers).
7、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 known (masses, lengths, etc.), in order to find a controller to stabilize it. If not all the
8、parameters are known, one can how
