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# controls - PROBLEM#1 a P1=conv[1 3-1 8[0 1 2 3 P1 = 0 1 5 8...

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Sheet1 Page 1 PROBLEM #1 a) P1=conv([1 3 -1 8],[0 1 2 3]) P1 = 0 1 5 8 15 13 24 b) >> P2=conv([1 -1 1 -1 0 0],[1 0 0 0 1 -1]) P2 = 1 -1 1 -1 1 -2 2 -2 1 0 0 PROBLEM 3 a) >> syms a b c t x >> g4=exp(-5*t)* 5*t g4 = 5 t exp(-5 t) >> G4=laplace(g4) G4 = 5 -------- 2 (s + 5) b) >> g5=t*sin(2*t)+ exp(-2*t) g5 = sin(2 t) t + exp(-2 t) >> G5=laplace(g5) G5 = s 1 4 --------- + -----

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Sheet1 Page 2 2 2 s + 2 (s + 4) PROBLEM 4 >> G6=1/(s+3)*(s+3) ??? Undefined function or variable 's'. >> syms s >> G6= 1/(S+3)*(S+3) ??? Undefined function or variable 'S'. >> G6=1/(s+3)*(s+3) G6 = 1 >> g6=ilaplace(G6) g6 = dirac(t) >> G6=1/(s+3)^2 G6 = 1 -------- 2 (s + 3) >> g6=ilaplace(G6) g6 = t exp(-3 t) >> G7=s^3+4*s^2+6*s+5/(s+8)*(s^2 +8*s+3)*(s^2+5*s+7) G7 = 2 2 3 2 (s + 5 s + 7) (s + 8 s + 3) s + 4 s + 6 s + 5 ----------------------------- s + 8 >> G7=s^3+4*s^2+6*s+5/((s+8)*(s^2 +8*s+3)*(s^2+5*s+7)) G7 = 3 2 5 s + 4 s + 6 s + ------------------------------------- 2 2 (s + 5 s + 7) (s + 8 s + 3) (s + 8) >> G7=(s^3+4*s^2+6*s+5)/(s+8)*(s^2 +8*s+3)*(s^2+5*s+7)
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## This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Winter '11 term at Ryerson.

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controls - PROBLEM#1 a P1=conv[1 3-1 8[0 1 2 3 P1 = 0 1 5 8...

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