Lecture7

Lecture7

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Unformatted text preview: with zero initial condition), G1 (s) = G0 (s), G2 (s) = G0 (s). However, while considering the stability of the systems, G1 (s) = G0 (s), G2 (s) = G0 (s). Transfer function: s+1 1 = (s + 1)(s + 2) s+2 s−1 1 = (s − 1)(s + 2) s+2 (for stability analysis) Unstable zero/pole cancellation is not allowed. 1 2 Zeros and poles of cascaded systems G1 (s) = G(s) = a(s) , b (s ) G2 (s ) = c (s ) . d(s) Y (s ) a (s ) c (s ) = G 2 (s )G 1 (s ) = R (s ) b(s)d(s) Characteristic equation: b(s)d(s) = 0. Poles: b(s)d(s) = 0. Zeros: a(s)c(s) = 0. The system is stable, if all poles are on LHP. Example 2.1 . (1) G1 (s) = Zeros: 1, −3. s−1 s+3 , G2 (s ) = s+2 s−4 Poles: −2, 4. s+1 1 (2) G1 (s) = , G2 (s ) = , s+2 s+1 Zeros: −1. Poles: −1, −2. [ u + 2u = r + r, ˙ ˙ (3) ⇒ s−1 1 , G2 (s ) = s+2 s−1 Poles: 1, −2. G1 (s) = Zeros: 1. [ u + 2u = r − r, ˙ ˙ 3 y+y =u ˙ y−y =u ˙ ⇒ ⇒ ⇒ G(s) = G1 (s)G2 (s) = (s − 1)(s + 3) (s + 2)(s − 4) s+1 G(s) = G1 (s)G2 (s) = (s + 1)(s + 2) y + 3y + 2y = r + r ] ¨ ˙ ˙ ⇒ G(s) = G1 (s)G2 (s) = y + y − 2y = r − r ] ¨˙ ˙ Framework of Control Systems Open Loop Control Feedback Control (Closed-loop Co...
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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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