Q1) Given the feedback control system shown by the diagram below, write a Matlab program that simulates the system and supports investigating the response of the system at the output C(s) to a unity step change at the input R(s). The investigation should cover the following ranges of the proportional and integral (PI) controller gains as specified:

25 ≥ Kcp ≥ 15 with the value of Kcp incremented by steps of 2.5.

80 ≥ Kci ≥ 40 with the value of Kci incremented by steps of 8.

The outcome of the simulation should offer plots of the output C(s) trend with time in response to step change on R(s) for each of the combinations of the proportional and integral gains