A new suspended, mobile, remote-controlled videocamera system to bring three-dimensional mobility to professional NFL football is shown in Figure P12.2(a) [24]. The camera can be moved over the field, as well as up and down. The motor control on each pulley is represented by the system in Figure P12.2(b), where $\tau_1=20 \mathrm{~ms}$ and $\tau_2=2 \mathrm{~ms}$.
(a) Select $K$ so that $M_{p \omega}=1.84$. (b) Plot $20 \log |T|$ and $20 \log \left|S_K^T\right|$ on one Bode diagram. (c) Evaluate $\left|S_K^T\right|$ at $\omega_B, \omega_{B / 2}$, and $\omega_{B / 4 \cdot}$ (d) Let $R(s)=0$ and determine the effect of $T_d(s)=1 / s$ for the gain $K$ of part (a) by plotting $y(t)$.