Consider the system of Fig. P8.2-2 with T = 1 T = 1 s. The plant frequency

Consider the system of Fig. P8.2-2 with $T=1$ s. The plant frequency response $\text{Extra close brace or missing open brace}$ is given in Table P8.4-1.
(a) Let $D\left(z\right)=1$. If the system is stable, find its phase margin.
(b) Let the digital controller realize a gain $K$, that is, $D\left(z\right)=K$. Find $K$ such that the system phase margin is ${45}^{\circ }$.
(c) Obtain the system step response of part (b) using MATLAB, and find the rise time ${}_{t_r}$, and the percent overshoot.
(d) Design a unity-dc-gain phase-lag compensator that yields a phase margin of approximately ${45}^{\circ }$.
(e) Obtain the system step response of part (d) using MATLAB, and find the rise time ${}_{t_r}$, and the percent overshoot.

Fig. P8.2-2

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