ps10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 10 This problem set is for practice only! Problem 1: Sketching Bode Plots Sketch (by hand) the Bode plot for each of the following systems. Hint : first rewrite each transfer function in Bode (standard) form. 1. G ( s ) = 1 s +1 2. G ( s ) = s ( s 1 +1) 10 3. G ( s ) = s 2 + s +10 4. G ( s ) = s +10 s +1 5. G ( s ) = s +1 s +10 1000(0 . 1 s +1) 6. G ( s ) = s ( s +1)( s 2 +10 s +100) Problem 2: Bode Plots and Polar Plots As you probably have noticed already, Bode plots and polar plots represent the same information. (Recall that the polar plot of a transfer function is just the Nyquist plot for 0 < � < .) Nyquist plots are essential for evaluating the stability of the closed-loop system when the open-loop transfer function has poles in the right half plane. Bode plots are useful for designing controllers because they can be sketched quickly and accurately by hand, without diﬃcult calculations.

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