Assignment #21 ECSE-2410 Signals & Systems - Fall 2006 Tue 12/5/06 1(30). Using Nyquist and Bode plots and Bode approximations, find gain constant K at which the feedback systems shown are just on the verge of instability. Sketch the Nyquist and Bode (straight line magnitude and smooth phase) diagrams. (a) () 3 1 ) ( + = s K s G (b) () 2 1 ) ( + = s s K s G-+ ) ( s G X ( s ) (c) () 1 ) ( 5 + = − s s Ke s G s 2(20). Using the feedback block diagram above where ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 100 1 10 1 1 1 ) ( s s s K s G , (a) Sketch both the Bode straight line magnitude and the smooth phase diagrams. (b) Calculate the approximate gain and phase margins using Bode approximations. (c) Sketch the Nyquist diagram. (d) Use MATLAB to plot the exact Bode diagrams, the Nyquist plot (scale so the diagram around the -1 point is clearly visible), and using the Margin command calculate the exact gain and phase margins. 3(20). A boat is being steered automatically by the following means:
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