Lecture7

S2 3s 2 0 s1 transfer function g 1 s s 1s

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Unformatted text preview: .1 Zero/pole cancellation. System 1 ODE y + 3y + 2y = u + u ¨ ˙ ˙ Characteristic Equ. s2 + 3s + 2 = 0 s+1 Transfer function G 1 (s ) = (s + 1)(s + 2) Poles −1, −2 Zeros −1 Stability Stable Initial condition y (0) = ε, y (0) = 0 ˙ y ( t ) = ε ( e − t − e − 2 t ) 1( t ) decays System 0 z + 2z = v ˙ s+2=0 G0 (s) = 1 s+2 −2 N/A Stable z (0) = ε z (t) = εe−2t 1(t) decays Impulse response System 2 y + y − 2y = u − u ¨˙ ˙ s2 + s − 2 = 0 s−1 G2 (s) = (s − 1)(s + 2) 1, −2 1 Unstable y (0) = ε, y (0) = 0 ˙ y (t) = 1 ε(et − e−2t ) 1(t) 3 diverges y (t) = e−2t 1(t) y (t) = L−1 [ Response to input 1 U (s)] s+2 While considering the input-output relationship of the systems (...
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