Question

Suppose that the zero-state response to the step input for a plant with transfer function G0(s) is given by y0(t) for each t 0. Answer the following questions. Your answers are expected to be expressed in terms of y0.

1) What is the zero-state response to the same plant but for the input given by u(t) = t for each t 0 and u(t) = 0 for each t < 0?

2) Consider now the transfer function G(s) = s2G0(s) What is the zero-state response to the step input for a plant with transfer function G(s)? Hint: Consider G as the series interconnection of systems with transfer functions given by G0 and s.

Answer 1

was 969 190 input in Laplace domain = Urs) Yo(s) = 90). ). output in Laplace domain = Yo (6) Cos 12 step response U=1 ; u(t)=1 YOG)- 90). Ś by in vertic Laploce Solo = '(3.00) Cose di if. wlt=6 = Usaha Then yo(s) = 1496) You) = $ (490) e cosc (1) output in conversion of Laplace to troc domain s a Ś fdt .. (Polina 9 yoxle) dot .: Integra hon of step response will give Yomp response.

shaols) Transfer finchon Y9) - Gw) = () step reponse Yo = ĝi gols).vo) = 3! Goes). } YU = g. GoC) Similar y(t)= yolf) Ssan if Go(s) is step response Then SGCO) will gnc impuler response.