Consider a plant with a Transfer Function model given by

\[G(s)=\frac{8(s+4)}{s(s+1)(s+10)}\]

Using MATLAB do the following:

(a) Find the discrete-time plant Transfer Function model.

(b) Design the digital PID controller.

(c) Generate the unit-step response to the open-loop discrete-time system.

(d) Generate the unit-step response for the discrete-time feedback system.

(e) Generate the unit-step response for the discrete-time feedback system with a discrete-time PID controller.

(f) Generate the root locus for the discrete-time feedback system.

(g) Generate the root locus for the discrete-time feedback system with a discrete-time PID controller.

(h) Investigate impact of parameter changes on digital control system.