Derive the output responses for all parts of Figure 4.7. System Pole-zero plot Response G(s) R(s) =

Derive the output responses for all parts of Figure 4.7.

Transcribed Image Text:

System Pole-zero plot Response G(s) R(s) = C(s) s2+ as + b General c(1) c(t) = 1 +0.17le 7854 1.0 ja 1.17leL146t G(s) S-plane R(s) =3 (b) C(s) 9 0.5 2+ 9s +9 -7.854 -1.146 Overdamped 2 3 4 5 c(1) c(1) = 1-e(cosv8r + sinv8r) =1-1.06e cos8t-19.47") ja s-plane 1.4 1.2 G(3) 1.0 R(s) = 9 C(s) 0.8 0.6 -1 0.4 6+ 57 + Underdamped 0.2 3. c(t) C1) =1- cos 3t ja s-plane G(s) * j3 R(s) =; C(s) Undamped * -3 0 1 2 4 c(1) ja S-plane c() = 1- 3te 3 e3 1.0 G(s) R(S) = C(s) 9 0.8 s2+ 68 + 9 0.6 -3 0.4 FIGURE 4.7 Second-order Critically damped 0.2 systems, pole plots, and step responses 4208 642