Fig. P1.1 shows the block diagram of a control system. The system in block A has an impulse response \(h_{\mathrm{A}}(t)=e^{-t} u(t)\). The system in block B has an impulse response \(h_{\mathrm{B}}(t)=e^{-2 t} u(t)\). The block ' \(k\) ' amplifies its input by a factor \(k\). For the overall system with input \(x(t)\) and output \(y(t)\), find

(a) the transfer function \(\frac{\mathrm{Y}(s)}{\mathrm{X}(s)}\) when \(k=1\)
(b) the impulse response when \(k=0\).

Transcribed Image Text:

x(1) + A k B y(t)