The process $($including the sensor and control valve$)$ can be modelled by the following transfer function;

$G(s)=\frac{K_p{e}^{-s}}{s+1}=\frac{4\mathrm{.}5e^{-0\mathrm{.}68}}{0\mathrm{.}13s+1}$

Obtain the PID tuning parameters using;

IMC relations for the time delay processes where dead time is approximated using the first order Pade

approximation.

$f(s)=\frac{1}{{}_{c}s+1},$ where $=$ the parameter for filter tuning

Tyreus$-$Luyben $($T$-$L$)$ settings.