Consider the block diagram of an antenna control system shown in Fig. P8.6-5. Let $T=0.05$ and the sensor gain be unity $(H=1)$.$$\text{Extra left or missing right}$$The frequency response for $G\left(z\right)$.

(a) Find the system phase margin with $K=1$ and $D\left(z\right)=1$.
(b) To reduce steady-state errors, $K$ is increased to 5 . Design a unity-dc-gain phase-lag controller that yields a system phase margin of ${45}^{\circ }$.
(c) Design a unity-dc-gain phase-lead controller, with $K=5$, that yields a system phase margin of ${45}^{\circ }$.
(d) Using MATLAB, find the unit step response for the systems of parts (b) and (c). Compare the rise times and the percent overshoot for the two systems.

Transcribed Image Text:

G(z) = Z. - 1 2 20 s (s + 6). 0.02268z+0.02052 (z 1)(z 0.7408)