(Solved): Consider the block diagram of an antenna control system shown in Figure P8-20. rigure ro-zv siock d ...

Consider the block diagram of an antenna control system shown in Figure P8-20. rigure ro-zv siock diagram tor an antenna conuro system. \[ T=0.05 \text { sec } \] (a) Find the system phase margin with \( K=1 \) and \( D(z)=1 \). (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) Simulate the compensated system in part b using Matlab. (d) Design a unity-dc-gain phase-lead controller, with \( K=5 \), that yields a system phase margin of \( 45^{\circ} \). (f) Simulate the compensated system in part d using Matlab. \begin{tabular}{ccccc} \hline\( \omega \) & \( \omega \) & \( \left|G\left(j \omega_{\mu}\right)\right| \) & \( \left|G\left(j \omega_{\mu}\right)\right| \omega^{\prime} \) & \( \left\langle G\left(/ \omega_{-}\right)\right. \) \\ \hline \( 0.1 \) & \( 0.100 \) & \( 33.32874 \) & \( 0.00 \) & \( -91.09 \) \\ \( 0.2 \) & \( 0.200 \) & \( 16.65748 \) & \( 0.00 \) & \( -92.19 \) \\ \( 0.3 \) & \( 0.300 \) & \( 11.09735 \) & \( 0.00 \) & \( -93.29 \) \\ \( 0.4 \) & \( 0.400 \) & \( 8.31502 \) & \( 0.01 \) & \( -94.38 \) \\ \( 0.5 \) & \( 0.500 \) & \( 6.64381 \) & \( 0.02 \) & \( -95.47 \) \\ \( 0.6 \) & \( 0.600 \) & \( 5.52819 \) & \( 0.03 \) & \( -96.56 \) \\ \( 0.7 \) & \( 0.699 \) & \( 4.73007 \) & \( 0.05 \) & \( -97.65 \) \\ \( 0.8 \) & \( 0.799 \) & \( 4.13040 \) & \( 0.06 \) & \( -98.73 \) \\ \( 0.9 \) & \( 0.899 \) & \( 3.66305 \) & \( 0.08 \) & \( -99.81 \) \\ \( 1.0 \) & \( 0.999 \) & \( 3.28834 \) & \( 0.09 \) & \( -100.89 \) \\ \( 2.0 \) & \( 1.998 \) & \( 1.58193 \) & \( 0.26 \) & \( -111.28 \) \\ \( 3.0 \) & \( 2.994 \) & \( 0.99511 \) & \( 0.08 \) & \( -120.81 \) \\ \( 4.0 \) & \( 3.986 \) & \( 0.69524 \) & \( -0.95 \) & \( -129.31 \) \\ \( 5.0 \) & \( 4.974 \) & \( 0.51456 \) & \( -2.88 \) & \( -136.78 \) \\ \( 6.0 \) & \( 5.955 \) & \( 0.39576 \) & \( -5.22 \) & \( -143.31 \) \\ \( 7.0 \) & \( 6.929 \) & \( 0.31327 \) & \( -7.57 \) & \( -149.03 \) \\ \( 8.0 \) & \( 7.895 \) & \( 0.25375 \) & \( -9.75 \) & \( -154.07 \) \\ \( 9.0 \) & \( 8.852 \) & \( 0.20951 \) & \( -11.73 \) & \( -158.54 \) \\ \( 10.0 \) & \( 9.799 \) & \( 0.17582 \) & \( -13.52 \) & \( -162.54 \) \\ \( 20.0 \) & \( 18.546 \) & \( 0.05320 \) & \( -25.01 \) & \( -188.55 \) \\ \( 30.0 \) & \( 25.740 \) & \( 0.02706 \) & \( -31.13 \) & \( -203.49 \) \\ \( 40.0 \) & \( 31.416 \) & \( 0.01738 \) & \( -35.07 \) & \( -213.67 \) \\ \hline \end{tabular}