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Unformatted text preview: ENSC 483 HW#7 Solutions by M. Saif 1 Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems 1. Consider the inverted pendulum mounted on a motor driven cart as shown in the Figure 1. This is a model of the attitude control of a space booster on takeoff, where the objective of the attitude control problem is to keep the space booster in a vertical position. Applying Newtons second law and making some simplifying assumptions (e.g. that the rod is massless, pendulum mass is concentrated at the end, sin , cos 1, and 2 0) we get the following state space representation of the system: x = 1 0 0 M + m Ml g 0 0 0 0 0 1- m M g 0 0 0 x + - 1 Ml 1 M u, x = x x y = 1 0 0 0 0 0 1 0 x Figure 1: Inverted pendulum on a cart (a) Assuming that M = 2 kg,m = 0 . 1 kg and l = 0 . 5 m , investigate if this system is completely controllable and observable. ENSC 483 HW#7 Solutions by M. SaifENSC 483 HW#7 Solutions by M....
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- Spring '07