Control Finals

Control Finals - Final Exam, EE3530, Spring 2002 PyMe/rl; 1...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Final Exam, EE3530, Spring 2002 PyMe/rl; 1 (10 pts). Design .Qntroller using quarter ratio method for syétem with the following step response. RT '.' (I ' \J,‘ . 1B ‘ . > ‘ ' , A V x V ; . i ‘ Figure 1: Problem 1 —— Déaign PI Controller ' , 5 gr ' ‘ ' k. - M: W 2 (15 pts) Find the range of which all the rodts of the followipg polynomial are in the ogen'lefthaliplanem; h ‘ I " I 3/" .\ "'x‘ , ,'\ sflwfi+mfi+mfi+a+f=a‘g ,. -- ‘ > , ‘ . V..,..'.,.. _-.. .._~... - :_. I L117 CE a?- a QL-f 71) w""' H Pym: 3 Consgder a. systemlshown in Figure 2. 1'Ii‘hei transfer, funfliqufjcfie plant is 9(8) = I) ' _ , . m. ..._.- , . "1 v .m- V... _ ‘ (I s; $1.156 . The transfer function of the-Eélifmlier (s) = .K‘, Le” the Cami-0115; is at”? M“ proportional controller with gain K. . ‘ _ W Q a) (15 pts) Detergfine the range of K so that; the 3313mm is stable. L b) (15 pts) Determine the range of. v 90 the' steady-state error Mess-Shir: 2101 for ‘9 reference sipal 9‘0?) = t1 ‘ I gigglefii'é'Cofisider a system shown in'Figm:e ZMagfer funcfgioxx of tfle plagg is G (a ..—...._V .—~ .-. ~ ~ - ) . _ - p:- r _...-,. a: The tramsferfgflgtion of the controller is _ ' ‘ ' . - V. V . , a) (10 pts) Determine the range~ofigaipggandpole location a so that the system is stable. w v -- . . . v . --__— ———— ~- , / b) C 15 P138) Specifi' the gain K and pole location a so that overall cloaed-ioop response to a 'a— 4.2..‘__ unit-step input haa'an overshoot of do more {him 25%, ade a 1% Settling time of no more than 0.1 see. > «- RM Figure 2: Problem 3 29nd Problem 4 1/," ;- ‘ . ' Richly/é 10 ] Causidez-a_ system with transfer function g I [/f ‘ ’ . V ' 6(5) = (ad—gOOO) Compute the the overshoot andf\se£flir!1g time of the step response of. the system. (Hint: Truncate the system 33 a aegfind order system by éfiminafing non-domjnwé poles and zeros.) ‘ Problem 6 (1 pts) Show that a. systém with transfer function 6(5) I I > K an amplifier with confirm W __._.... -. x---- ‘ w " Final Emm, EE3530, 173112003 '/I:;oblem 1 (15/ pts) Let. G be a linear ntabla system with frequency response shown by Figure / \\ input be yfipsinfi) + 3cos(10t)]1(t). Determine the steady state. response Mt). Bo'du Dingmmc From U11) qumflmdhflt) Figure: 1: Problem 1 — Frequency Response Problem 2 (20 ' 5) Consider the feedback system shown by Figure 2. Derive the aarwitivitjr function with gmfiect to the variation of plant. model G. What. is the significanne of atudyizig the 3W function? Problem 3 (15 pts] Consider a systém with transfer function x" a - 1 a = ———~——___._ V’m 85+34+33+23,2+75+K ' where K is a parameter. Is it. possible to find parameter K so thaw the system in stable? Justify your answer or determine the range of K that. guarantees ahabflity. V ji Problem 4 (20 pie) Consider a. feedback system shown in Figure 2- T he transfer fimcim 0f the-p13, 13 0(3) = F—i; Where p is a negative uncertain parameter. The transfer function of the controller is 0(a) = if . Detormine the condltion for K so that the feedhadc system. is stable for ANY value of the uncertain parameter 3:. GI!) YM Figure 2: Problem 2. Problem 4 mid-Problem 5 r' Problem 5 .1 Consider a feedback system shown in Figure 2. The transfer fundan of His plant is G'(s) = m .- ' V . 1:;1'3117 ‘ (a) (15 pts) Suppose that; the reference input signal in r(t) = 1(t‘)iand that C(o) = K is a. proportional controller with gain K. Can the steady state error be arbitrarily decreased by increasing the controller gain K? Justify your answer. (13) (15 pta) Suppose that the reference. input signal is r(t) = t 105) and that 0(3) = § is an integral controller with. gain X: What is the smallest: error (an be whiéved by increasing the controller gain K Justify yoiir mower. Zl+=i_=0. (a) (15 pts) Ugfihismndeuo find the transfer function T(s) = the amplification circuit shown by Figure 1. A: ~—---— — / @15 pts) Compute the sensWioa Si. (Hint: 3'}; = limAqu‘ I?! = jig) Figure 1': Problem 1 - Amplification Circuit Problem 2 (15 pts) Consider 5, system with transfer function . J 6(8); 3+1 r” . ‘55+‘s4+s3+252+73+K / K/where K is a parameter. Is it. possible to find parameter K 50 that (he system is stable-Y Justify. your answer or detemline the range of X that. guarantees stability. ' ' I I I ’ 'I i 1 Proplem 3 (20 pts) Consider a feedback system ‘shown in Figue 2._ The tramsfer function of the plant is' G'(s) = where dais-an: uncertain parameter, The 'trailsfer funC'fiOn 0f the f, I - > _ M ‘ V _ I controller is C(s) = éf-fshow that. the feedback system is stable for positive a (Hint: \r / If Apply Rout}: stability criterion). Problem 4 Consider a "system shown in Figure 2, The'tmfisfer functiofi o:£ the plant is 9(3) = $4 The transfer functiofief like, Egntrol-ler is 0(a) = {1%. ,( 15 pts)‘ Determine the range of gain. K endjpole location}: so thatithe s§retem is stable. .1' ‘ Figure 2: Problem 3 and Problem 4 b) (20 1)sz Specify the gain K and pole logation 32 so that overall closed-loop réépbnse to a. 1-46-12 input has an' overshoot of no more than 25%, and a 1% settling {time of no more \j ' than 0.1 sec. ...
View Full Document

Page1 / 6

Control Finals - Final Exam, EE3530, Spring 2002 PyMe/rl; 1...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online