Question


1 Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s). Determine the phase margin, gain-crossover frequency, gain margin and phase-crossover frequency, (Sketch the bode diagram by hand) 

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2 Consider the system shown as below. Use MATLAB to draw a bode diagram of the open-loop transfer function G(s). Show the gain-crossover frequency and phase-crossover frequency in the Bode diagram and determine the phase margin and gain margin. 

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3. Consider the system shown as below. Design a lead compensator such that the dominant closed-loop poles are located at s=2±j3.464. Plot the unit-step and nit-ramp response curves of the compensated system with MATLAB. 

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4. Referring to the closed-loop system shown as below, design a lead compensator Ge(s) such that the phase-margin is 45°, gain margin is not less than 8dB, and the static velocity error constant K, is 4.0 sec-1. Plot unit-step and unit-ramp response curves of the compensated system with MATLAB.

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