(Solved): Consider the feedback control system shown in Figure 4 below. Here G(s)=(s+1)41 and K(s) is a co ...

Consider the feedback control system shown in Figure 4 below. Here $G(s)=\frac{1}{(s+1{)}^4}$ and $K(s)$ is a compensator. a) Sketch the Nyquist diagram of $G(s)$ indicating (i) where the frequency $?$ is zero and (ii) where it is infinite. Also calculate the real-axis intercepts. b) Show that the closed-loop is stable and determine the gain and phase margins. c) Comment on the stability and performance properties of the closed-loop. Your answer should include analysis of tracking disturbance and noise attenuation. d) Explain what is meant by a phase-lag compensator. Your answer should include an expression for such a compensator and a description of its frequency response. e) Without doing any actual design calculations, describe how a phase-lag compensator would affect the stability margin and the steady state tracking properties of the loop. Figure 4