NO AI PLEASE:

A robotic link is driven by a PM servo$-$motor through a reduction gear with ratio $n=8.$ The motor is energized by an amplifier with a voltage gain $A=100.$ The link has the following parameters: $J_L=4Kg-m^2,B_L=2N-m-sec\frac{.}{r}ad.$ The parameters of the DC motor are $L_a=0,R_a=0\mathrm{.}4,K_a=0\mathrm{.}8N-m\frac{.}{A}.,J_m=0\mathrm{.}06Kg-m^2,$ and $B_m=0\mathrm{.}1Nm-sec\frac{.}{r}ad.$ For the link rotating position control purpose, the input is a target angle ${}_L^d$ and the output is an actual angle ${}_L$ of the link.

a$.$ Draw a block diagram to represent this motor$-$link control system;

b$.$ Find the transfer function $T(s)=\frac{{}_L}{{}_L^d}$;

c$.$ Determine the natural frequency ${}_n$ and the damping ratio $$ of the entire control system;

d$.$ What is the steady$-$state value of the output if the input is a unit$-$step?