DESIGN of a LEAD COMPENSATOR with MATLAB

For the figure below, $G(s)=\frac{9}{s}(s+0\mathrm{.}5)$

a$)$ For the compensator $G_c(s)=1$ Obtain

Transfer function,

Maximum overshoot and settling time for unit$-$step input

Draw

i$.$ unit step$-$response curve in MATLAB.

ii$.$ unit ramp$-$response curve in MATLAB.

iii. Root$-$ locus curve in MATLAB

Obtain steady state error for unit$-$ramp input

b$)$ Design a lead compensator $G_c(s)$ to shift the poles at new locations of $s_1=-4+j4$ and $s_2=-4-j4$

Obtain new transfer function by calculating $K_c,$ and $G_c(s)$

Draw

i$.$ unit step$-$response curve in MATLAB.

ii$.$ unit ramp$-$response curve in MATLAB.

iii. Root$-$ locus curve in MATLAB

Obtain steady state error for unit$-$ramp input