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Unformatted text preview: Final Exam, EE3530, Spring 2005 Problem 1 (15 pts) Find the range of K for which all the roots of the following polynomial are
in the open left half plane. s5+5s4+1053+1082+55+K=0 Problem 2 Consider a system shown in Figure 1. The transfer function of the plant is G(s) = fs—STFWIHLQ‘ The transfer function of the controller is 0(8) 2 K, i.e., the controller is a proportional controller with gain K.
a) (15 pts) Determine the range of K so that the system is stable. b) (15 pts) Determine the range of K so that the steady state error is less than 0.01 for
reference signal r(t) ='t1(t). 0 < ,
MS) 263: \f\ Yls) 4 ywxlyd 1- Figure 1: Problem 2 and Problem 3 Problem 3 Consider a system shown in Figure 1. The transfer function of the plant is (1(5) 2 100 K
s+25 ' s+a ' The transfer function of the controller is C(s) =
a) (10 pts) Determine the range of gain K and pole location a so that the system is stable. @(15 pts) Specify the gain K and pole location a so that overall closed-loop response to a
unit—step input has an overshoot of no more than 25%, and a 1% settling time of no more than 0.1 sec. Problem 4 (10 pts) Consider a system with transfer function
A _, ( l ./
C(s)= (W A“ ’“i'fi (s2 + s + 1)(s2 +2003 + 20000 CV L 2 «f
walk/9% ‘\ 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 5 (20 pts) Show that a system with transfer function G(s) = $1; can be imple-
K mented by using an ampliﬁer with constant gain —a—, an ampliﬁer with constant gain —a, an integrator, and a summer. ...
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- Fall '07