Use the MATLAB pidtool to design a PID controller for the system of Problem 8.6-5. Start with these parameters, then try to improve the design \(\left(G_{p}=20 /\left(s^{2}+6 sight), H=1, T=0.05, P_{m}=45, \omega_{w 1}=20.0ight)\).

Problem 8.6-5

Consider the block diagram of an antenna control system shown in Fig. P8.6-5. This system is described in Section 1.5. Let \(T=0.05\) and the sensor gain be unity \((H=1)\). It was shown in Problem 7.5-5 that

\[ G(z)=\frac{z-1}{z} z\left[\frac{20}{s^{2}(s+6)}ight]=\frac{0.02268 z+0.02052}{(z-1)(z-0.7408)} \]

Fig. P8.6-5

Computer Digital controller Amplifier Motor. gears, and pedestal R(z) M(s) 20 O(s) + D(z) DIA K +68 0(t) r(k) Sensor V(z) 0.4 T Binary data