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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 6 Due: 10/30/2003 Problem 1: Controllability for Systems with Multiple Inputs Determine whether the following systems are controllable: 1. x = 1 1 1 x + 1 1 u 2. 1 1 x = 1 x + u 1 1 Problem 2: Pole Assignment with Full State Feedback 1. For the following system: 1 x = x + 1 u 15 23 9 2 (a) Where are the poles of the open-loop system? (b) Design a full-state feedback controller so that the poles of the closed-loop system are at s = 3 and s = 4 4 j . (The input to the closed-loop system should be in the form u = u c Kx .) 2. In Lecture 9, we looked at the problem of attitude control for a rocket. Neglecting the moment of inertia of the engine, the linearized equation for the rocket attitude is: I = l 1 c n + l 2 T where I is the moment of inertia of the rocket, is the angle...
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