Q$1.$ Figure $1$ shows a typical application for a digital controller, having an existing piece of plant which has the transfer function P$($s$)$; this operates in the continuous domain. As an engineer, your company wanted to add a controller operating in a microprocessor which will improve the running of the existing plant. The parameters of the system is define as follows

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a$)$ Determine a discrete equivalent of the continuous system P$($s$).$

b$)$ Determine the Z$-$transform of the overall feedback system.

c$)$ Write a program in Matlab which calculates the Z transfer function of the feedback system and determine the response of the system to a unit step input.

d$)$ Compare the result of $($b$)$ to that obtained in Matlab in $($c$)$