ps4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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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 pole-zero plots for four different transfer functions. For each step response, pick the pole-zero 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 real-valued 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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ps4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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