Question

Y(s) a) Thefolowing sne tandfer funtions X(s) whout finding the sresonie loutputrom unit step input), find y(0) and y(oo), if exist. Indicate the reasons b) Invert the transfer functions, show steps

Answer 1

Consider x(t) and y(t) are a system with input and output and Given that the transfer function H(s) = y(s)/x(s) y(s) = x(s) H(s) This is the output with initial condition is zero Thus, the unit step response Y_u (s) is Y_4(s) = 1/s H(s) Therefore L'[1] = 1/s Now to find a two characteristics of the unit step response of the initial and find value by using initial and find value theorem lim_t rightarrow 0^+ y_u(t) = lim_s rightarrow infinity s. 1/s H(s) by using initial value theorem = lim_s rightarrow H(s) lim_l rightarrow y_u(t) = lim_s rightarrow s. y_u(s) = lim_s rightarrow s . 1/s H(s) by using initial value theorem lim_s rightarrow H(s) Therefore y_u(0*) = H(infinity) y_u = H(0) F(s) = S + c/(S + a) (S + b)^2 L^- 1 [F(s)] = L^- 1 [S + c/(S + a)