EE_302_2010_HW6

# EE_302_2010_HW6 - Problem 3 Consider a unity feedback...

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EE 302 Home work 6 Due April 29, 2010 Problem 1 a) Consider the following circuit. Draw the Nyquist plot for i) R 1 C 1 > R 2 C 2 and for ii) R 1 C 1 < R 2 C 2 . For each of these to cases in i) and ii) answer the following question analytically : what is the contribution of this circuit to any plant if used in cascade with it? What type of controller would this be? b) Prove that the Nyquist plot of the transfer function s/[1+s] 0 s= j ω ≤∞ is a semicircle. Find the center and the radius of this circle. Problem 2 The stability of a closed loop system with the following open loop transfer function G(s)H(s)= K ( T 2 s+ 1)/ [ s 2 ( T 1 s + 1)] depends on the relative magnitudes of T1 and T2. Draw the Nyquist plots for T 1 <T 2 , T 1 =T 2 , and for T 1 >T 2 . Analyze stability for each case.

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Unformatted text preview: Problem 3 Consider a unity feedback system with open loop transfer function being G(s)= K (e- 0.8 s ) / (s+1). Draw the Nyquist plot. Find the value of K for achieving stability. Problem 4 Consider a lead compensator Gc1(s) in cascade with a lag compensator Gc2(s) such that the open loop is Gc1(s) Gc2(s). Draw the Nyquist plot of this system. Compare this plot with the Nyquist plot of a PD and that of a PI controller for very small ω and for very large ω when applicable. Problem 5 Consider a unity feedback control system with open loop TF: G(s)= k/ [ s( s 2 + s + 4) ] Determine the value of gain K such that the phase margin is 50 o . What is the gain margin for this K? show all your work....
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