Midterm Exam with Resolution - Control Systems | ME 451, Exams of Control Systems

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Name: ID# Solutions ___ME4S51 — Mid Term | Grade: 1. (25) Given the system transfer function G(s 2). -_S@8+5) Us) s((s +1)? +27) a) (10) Find the corresponding differential equation in the form of AVE) + aH) + ap + a, y(t) = bu(t) + byu(t) b) (15) Find the time response (1) (¢ >= 0) when the input (7) is an impulse function (Z[S(7)]=1) Hint: £7 la] =e" cosat. Sta) +@ QA) YsysTs?+25 4644) = U)Cios +25) = HO) +24) +54) = 10 dct) + 25Ult) b) UGre 4 “Ss (astsy) ae Yis) = = A + Bs SLG+r4 25] 8 CSP 42° loS +QS5 = = AS*+2A8 445A + BS74CS =7 At+BR=0, BPAtC =10, SA= AS , A=5,c=o0 > , B=-5 Yoo = S_ _S8 2 5_ 56), 8 s Csay2422 S cory r2* Gry? L'LYCN SY (4) = 5-5 e” “(cos ot--psin2t) February 25, 2009 Dr. Zhu ME4S1 Mid Term! — Spring 2009 Page |