Consider the conventional feedback control system:

with the following transfer functions,

$G_c=K_c,K_m=5,G_v=\frac{2}{s+1},G_p=\frac{1}{s^2+s+1},G_m=0\mathrm{.}5$

Using Simulink and continuous cycling method $($Ziegler$-$Nichols setting$)$:

Determine the value of the ultimate gain $(K_{cu})$ for the controller, show the plots at $K_{cu}$

Design P$-$controller, PI$-$controller and PID$-$controller. Show parameters and plot the output responses of three controllers then compare them.

Use Auto$-$tuning feature $($PID$-$Controller case$)$ and determine new design values and compare plots and parameters with the PID$-$controller design in part $2.$