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e483h7_07 - Simon Fraser University School of Engineering...

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Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems Spring 2007–Assignment 7 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 Newton’s second law and making some simplifying assumptions (e.g. that the rod is massless, pendulum mass is concentrated at the end, sin θ θ, cos θ 1, and θ ˙ θ 2 0) we get the following state space representation of the system: ˙ x = 0 1 0 0 M + m Ml g 0 0 0 0 0 0 1 - m M g 0 0 0 x + 0 - 1 Ml 0 1 M u, x = θ ˙ θ x ˙ x y = ˆ 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 com- pletely controllable and observable.
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