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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 4 Due: 10/9/2003 Problem 1: Effects of Zeros The first figure below shows four different step responses, and the second figure shows the polezero plots for four different transfer functions. For each step response, pick the polezero plot whose transfer function best matches the response, and explain your decision. Note that the complex poles in (1)(4) are in the same location, and the realvalued pole in (3) and (4) is in the same location. Step Response Amplitude 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 A B D C Time (sec) (1) (2) (3) (4) 1 Problem 2: Matrix Algebra Review 1. Calculate the inverse of each of the following matrices. If the inverse does not exist, explain why. ⎣ ⎤ ⎣ ⎤ ⎣ ⎤ 1 1 3 2 4 A = B = C = 2 − 1 2 8 3 6 2. Calculate the determinant and find the rank of each of the following matrices. Also specify whether or not...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Aeronautics, Astronautics

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