An open$-$loop process has a unit step input change made to the controller output, and the

resulting process response can be modeled by the transfer function:

$G(s)=\frac{5e^{-3s}}{4s+1}$

a$)(20$ points$)$ Design PI and PID controllers using the Ziegler$-$Nichols method for initial

tuning parameters.

b$)(20$ points$)$ Simulate this system using MATLAB. Does the addition of derivative action

improve the control response to the unit step change in setpoint? Assume that the

measurement transfer function is $K_m=1.$