Test 2 Fall 04 with solutions

Test 2 Fall 04 with solutions - Test (II), EE3530, Fall...

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Unformatted text preview: Test (II), EE3530, Fall 2004 Problem 1 (20 pts): Find the transfer function T(s) 2: gig of the system shown in Figure 1. Figure 1: Problem 1 Problem 2 (15 pts). Design a PID controller using quarter decay ratio method for a system with the following step response. ~ O i 5 1 O 1 5 2‘1 25 3O 35 *46' 45 Figure 2: Problem 2 — Design PID Controller Problem 3 (15 pts) Consider a system with transfer function (3 + 3000) 0(3) = (32 + s + 1)(3 + rqoooy Compute the the overshoot and settling time of the step response of the system. (Hint: Truncate the system as a second order system by eliminating non-dominant poles and zeros.) Problem 4 Consider the unit feedback system shown in Figure 3. Suppose that the controller is a proportional controller with gain K. Let G(s) == (a) (10 pts). Show that feedback system is stable if K is positive. LM <27? 5Q [/wa l4 \ 9/7 0 F G- / UM \L w W" (b) (10 pts). Let 7'(t) = (1 + 2t) 1(t). Determine controller gain K so that the steady state error is less that 0.001'.7 ‘ (c) (10 pts). Let 7'(t) = e t2 1(t). Show that, for arbitrary small 6 > 0, it is not possible to specify K so that the steady state error is finite; R‘s) + ' Ylsl Sum 6(5) 1____J Figure 3: Problem 4 'Problem 5 (20 pts). Consider a system shown in Figure 4. Show that E(s) = HICGR — fiD where R, D are the Laplace transfoer 7‘(t), d(t) respectively. 0(5) Figure 4: Problem 5 WLL k 'ELL MuiQ/KJK E. :v 2’7 7‘» LC? *9) Q MM 9; 2 —~ CQE +9) Cr] C v y R I Q .1) b’LSW _ m v lécfl‘a— D ' ...
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Test 2 Fall 04 with solutions - Test (II), EE3530, Fall...

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