PROCEDURE:

A control system with unity negative feedback and $P-$controller with gain $K$ is shown in Figure $1.$ The plant $G(s)$ are stated in the question below.

$[$Total $50$ marks$]$

Figure $1$: Control system with p$-$controller $($gain K$)$

Q$1$a$.$ The plant $G(s)$ is given below and the controller is P controller with gain$=$K $("$uncompensated$")$

The required $M\frac{p}{?}$ Overshoot is $30\%$ and it has steady state error of about $38\%$ for unit ramp input.

Plant $G(s)=\frac{1}{s(s+4)(s+6)}$;$G_c(s)=K$

Run a simulation $($either using $m$ file or Simulink$)$ with $K=63\mathrm{.}21,$ plot the output signal of the uncompensated case and determine $($by measurement$)$ following;

natural frequency ${}_n$

peak time tp

settle time ts $(5\%)$

steady state error for Unit Ramp signal $R(t)=t**u(t)$

Note:

Plot the root locus plot. Search on the root locus the pole location with Mp$=30\%$ Plot the output signal for unit step input $[10$ marks$]$