Question: 4. Consder the following second order system with an extra pole. H(s) (s+p)(s +2Cwns+w) (a) Show that the unit-step response can be expressed as

4. Consder the following second order system with an extra pole. H(s)

4. Consder the following second order system with an extra pole. H(s) (s+p)(s +2Cwns+w) (a) Show that the unit-step response can be expressed as v(t) = 1+ Ae pt + Be-ot cos (wt + 0) where A = w - 2pwn + p 2 B = V1- 5?. Jw - 2pCwn + p -1 p- SWn 0 = tan + tan (b) Assuming wn = 1 and ( = 0.5, plot the step response for p = 0.1, p = 1 and p = -10. What is the effect of an extra pole when the extra pole is near the real part of the complex poles? What happens as the extra pole moves away from the real part of the complex poles?

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