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ps8 - 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 8 Due: 11/26/2003 Note: This problem set is due at the beginning of class on Wednesday ! Problem 1 The input to a system with transfer function G ( s ) is r ( t ) = A sin t . Show, by partial fraction expansion and complex number manipulation, that the output in steady-state is: c ss ( t ) = AM ( ) sin( t + ± ( )) where M ( ) = | G ( j ) | and ± ( ) = G ( j ). Problem 2: Nyquist Plots For each of the following open-loop transfer functions, draw a plot of the s -plane showing the poles and zeros of G ( s ) and the Nyquist D-contour. Then sketch (by hand) the Nyquist plot for each system. Label points corresponding to important frequencies (e.g. = 0 , ± ) and use arrows to show the direction of increasing frequency. 1. G ( s ) = K s 2. G ( s ) = s K 2 3. G ( s ) = s K 3 K 4. G ( s ) = s +1 5. G ( s ) = K ( s +2) s +1 6. G ( s ) = K ( s +1) s +2 K 7. G ( s

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ps8 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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