Tune a PID controller for the following first$-$order process:

Gain $=1\mathrm{.}1$

Deadtime $=1\mathrm{.}5$ minutes

First time constant $=3\mathrm{.}5$ minutes

Find the PI and PID controller parameters using the four open$-$loop methods $($Ziegler$-$Nichols, CohenCoon, Cohen$-$Coon with constraints, and Fertik$).$ For the Fertik method, tune for a setpoint response.