# hw12 - MEEN 364 Fall 2004 Homework Set 12 Due 5:00 PM(1...

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MEEN 364 Homework Set 12 Fall 2004 November 22, 2004 1 Homework Set 12 – Due November 29, 2004 @ 5:00 PM (1) a) Determine the Gain Margin (GM) and the Phase Margin (PM) of the following transfer function, (do not use MATLAB): () 100 4 Gs ss = + b) For the transfer function given, determine the gain margin and phase margin using MATLAB. Also determine whether the negative-feedback system with a unity controller gain is stable or unstable. Justify your answer. (2) Consider the open loop transfer function 4 k = + a) Determine the gain k such that the phase margin of the Closed-Loop System with Unity Negative Feedback and the above open loop transfer function is 30 ° . ( Hint : Consider only positive k ) b) What is the gain margin in this case? ( Note : Do not use MATLAB. Show the details of your work for full credit) (3) For the lead compensator 1 1 Ts Ds Ts α + = + , where 1 < . a) Show that the phase of the lead compensator is given by 11 tan ( ) tan ( ) TT φ ωα ω −−

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hw12 - MEEN 364 Fall 2004 Homework Set 12 Due 5:00 PM(1...

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