Problem $1$: Given simplified model of CNC table:

Position control system for this table:

Transfer function of components: $G_A(s)=\frac{48}{s+20}$;$G_M(s)=\frac{90}{s+6\mathrm{.}5}$;$G_T(s)=\frac{1}{16\mathrm{.}8s}$

a$)$ Given PD controller $C(s)=K_p(1+T_{d}s),$ determine controller parameter using magnitude optimum method.

b$)$ Design the given PD controller so that the closed loop system has no overshoot.