Use the MATLAB pidtool to design a PID controller for the system of Problem 8.6-6. Start with these parameters, then try to improve the design \(\left(G_{p}=10 / s^{2}, H=0.02, T=0.1, P_{m}=45, \omega_{w 1}=1.0ight)\).

Problem 8.6-6

Consider the block diagram of a satellite control system shown in Fig. P8.6-6. This system is described in Problem 1.4-1. Let \(T=0.1 \mathrm{~s}, K=1, J=0.1\), and \(H_{k}=0.02\). It was shown in Problem 7.5-6 that

\[ G(z)=\frac{z-1}{z} z\left[\frac{10}{s^{3}}ight]=\frac{0.05(z+1)}{(z-1)^{2}} \]

Fig. P8.6-6

Digital controller Amplifier and thrusters Satellite R(s) M(s) T(s) O(s) A/D D(z) DIA K n(t) Torque Js 0(t) Sensor H