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Exam 1 Fall 2004 (with Solutions)

# Exam 1 Fall 2004 (with Solutions) - ECE 313 Control Systems...

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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 sub-problems. 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‘: , RX LS \, ll Paste 2:) 283 QJMCQ §w1§ach J 3 \ﬂ} {KS\ E733) Hrs , Wm WM :: Bf“ ‘ 5 i " \Aw) 2735M E5113 aways, 23 . 9H :7 . g _ 2k: 2: 33+ 8;) b) Rut? ) ,/ I I» W Gig)” Z(\$2+M:_§+}> f.“ m hammi ~e> mew LC? “:3 ‘3 ‘3 3 W: 0k 9 ? ﬂ *\ 3 A) ‘5?er amgi‘w ‘ \{gjm‘g’} :,,....:..2:...__m: M?» < m > E OX 5 2mm 4“ 2 5-3 "X‘€§?Gﬂ§€ \$3 Q‘Acﬁgi‘rcéqﬁqpegif garb]; { c {33 :3 W T / Zis2~i~ g3+€~> Lop: g“ «: 2 3. r, . 2&1)“ Problem 2. Consider the following block diagram. a) (4 pts) Perform block-diagram 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 813)” 551+ 43%;:342 1‘ 1 b) Wme ohm“ “the RAW Wkwe : Problem 3. Consider the following feedback system. ___2..___ (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 SAU‘UQR : (\$14.39 (Ft; 3 of) Q5 (3“) 1‘ “YRS {‘3 5X SQCe‘ré "‘G‘rtflégr Sﬂgfemm Err slalailiiél ) one neeolS 60L the demoralime teethicieris “Co be pagiiiue : ((+1‘>G/ k+l>o \<>~el F Crave Cara Veer/in at? some WCle§§\QV\ US\$13 @dtlx drab? 7 l “.4 \, . V (PM? 6’ “‘3 Z 2 kg'fkg §9§tﬁwx Q%§&M: kP: Cg+3<>(§fo (I: 598 M, swﬁe *3 HWY E? Yﬁf>tri©uvt) ’Uﬂe Srkkwtj 2 ...
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Exam 1 Fall 2004 (with Solutions) - ECE 313 Control Systems...

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