Let H(s) = Y(s)/X(s) be the transfer function of the feedback system in Figure 6.22. The impulse response of the plant (with transfer function H_p(s)) is h_p(t) = sin(t) u(t).

(a) If we want the impulse response of the feedback system (with input x(t) and output y(t)) to be h(t) = h_p(t)e^ˆ’tu(t), what should be the transfer function H_c(s) of the controller?

(b) Find the unit-step response s(t) of the feedback system.

Figure 6.22:

y(t) Н, (8) x(t) + Н (8)