# hw9 - ω gc . (c) Closed-loop Bode plots and the actual...

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ME 475 HOMEWORK #9 Spring 2011 PROBLEM 1 : Given : Find : (a) An analytical expression for the magnitude and the phase for L 1 (s) and L 2 (s). (b) Frequency response plots using MATLAB and expressions in (a). (c) Comment on similarity and differences between frequency response for L 1 (s) and L 2 (s). (d) Can slope of magnitude curve and/or phase information be used to determine relative order for nonminimum phase systems. (e) Gain and phase margins for both systems and use them to assess stability of the closed- loop systems having L 1 (s) and L 2 (s) as loop transfer functions. (f) Using MATLAB, plot the unit step responses for L 1 (s) and L 2 (s). Comment on the similarities and/or differences between the step responses. PROBLEM 2 : Given : A unity-feedback control system with: Find : (a) Open-loop Bode plots and the gain crossover frequency ω gc . (b) Range of frequencies for the closed-loop bandwidth based on your value for

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Unformatted text preview: ω gc . (c) Closed-loop Bode plots and the actual bandwidth frequency. How does it compare with your estimated range in part (b)? (d) The closed-loop system time constant and the 2% settling time. Then, simulate the unit step response and check your predictions. (e) Is the closed-loop system 1 st or 2 nd order dominant? Please explain. PROBLEM 3 : FPE, Prob. 6.39, p. 401. Given : Steering dynamics of a ship: where v is the ship’s lateral velocity in meters per second and δ r is the rudder angle in radians. Find : (a) for K = 0.2 using the MATLAB bode command. (b) Gain crossover frequency and PM, phase crossover frequency and GM on the Bode plot. (c) Is the ship steering system stable with K = 0.2? (d) Value of K for PM = 30º and the corresponding gain crossover frequency....
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hw9 - ω gc . (c) Closed-loop Bode plots and the actual...

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