PracticeProblemsMidterm_solu

Let a system with input u and output y be represented

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Unformatted text preview: nswer is A, E, F, G 7. Let a system with input u and output y be represented by transfer function P (s). Suppose P (s) = 2 , s+3 u ( t) = 1 + e t . What is y (t)? Solution: U (s) = 1 1 + , s s+1 Y (s) = P (s)U (s) = 2 s+3 ✓ 1 1 + s s+1 ◆ = c1 c2 c3 + + , s s+1 s+3 where c1 = sY (s)|s=0 = 2 , 3 c2 = (s + 1)Y (s)|s= 1 = 1, Taking the inverse Laplace transform of Y (s), we have y ( t) = 1 (2 + 3e 3 t 5e 3t ) 2 c3 = (s + 3)Y (s)|s= 3 = 5 . 3 8. Sketch y (ty (in in the previousSketch y (t) in the previous problem. 8. Sketch ) t) the previous problem. 8. problem. Solution: Solution: Solution: LetLet the three terms in t) t) be denoted byterms and(C), be denoted by A, B , and C , the three terms in y (y ( be Let the threeAABBandy t, denoted by , , , , in C A+B where A is the first term andwhere A islast. first term and C is the last. Then each C is the last. Then each where A is the first term and C is the theThen each y(t) 1 term can sketched as shown on the sketched as term can be be sketched as showncan...
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This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.

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