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Unformatted text preview: ECE 313 Control Systems, Fall 2004
Midterm Exam I ( S9 ludtt on 3 >
October ll, 2004
NOTE: This is a closed~book exam. You may bring one sheet (front & back, Letter
size) of written formulas for your own reference during the exam. You are not
allowed to use calculators, books, lecture notes, homework sets, or any other materials. The exam lasts 50 minutes. You should stop writing once the time is up. There are 3 problems, and each consists of two or three subproblems. The total points
are 25 for this exam. Please make sure that you write down your name, PID and sign below before
working on the problems. Write legibly and cleanly —— this will get you all the deserving points for your effort.
Keep important intermediate steps of your calculation. Good luck! Prof. Xiaobo Tan Student Name:
PID: Signature: (eager; Problem 1. Consider the following circuit. R1 L=2H a) (4 pts) Consider vi (t) as the input and va(t) as the output. Find the transfer
ﬁmction G(s)= V0(s)/ Vi(s). Note that G(s) should be expressed in terms of the parameter R]. b) (3 pts) Determine the types of step response (namely, overdamped, critically
damped, underdamped, or undamped) when R1=1§2, and R1=7Q, respectively. whim : CK); Kgclmbl “the Ci‘rtuiﬁ in terms \Kaapeddhéﬂ‘:
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2&1)“ Problem 2. Consider the following block diagram. a) (4 pts) Perform blockdiagram reduction step by step and ﬁnd G(s)=Y(s)/R(s). b) (4 pts) Determine whether the system G(s) is stable. S New {Q
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(S+K)(s+1) a) (3 pts) Find the range of the parameter K that guarantees the stability of the
closed~loop system Gc(s)=Y(s)/R(s). b) (4 pts) For what value of K, the steady~state error Will be 5 when the input
r(t)=10u(t)? And for this K, what will be the steady state error if r(t)=4tu(t)? c) (4 pts) For the value of K found in Part b), what will be the peak time T p and
the percent overshoot 08% of the step response of the closed—loop system? 2
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 Gokcek,C
 pts, following block diagram, Prof. Xiaobo Tan, blockdiagram reduction step

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