An industrial grinding process is given by the transfer function [15]

The objective is to use a digital computer to improve the performance, where the transfer function of the computer is represented by D(z). The design specifications are (1) phase margin greater than 45°, and (2) settling time (with a 2% criterion) less than 1 second.
(a) Design a controller

to meet the design specifications, (b) Assuming a sampling time of T = 0.02 s, convert Gc(s) to D(z).
(c) Simulate the continuous-time, closed-loop system with a unit step input, (d) Simulate the sampled- data, closed-loop system with a unit step input.
(e) Compare the results in parts (c) and (d) and comment.

10 (s 5) s + a