Consider a transfer function of the form below.

$G(s)=\frac{(5s+1)e^{-4s}}{(s-2)(s+5)}$

Apply $\frac{1}{1}$ pade approximation to time delay and answer the following with proper reasonings. Show all steps

a$)$ Estimate gain, pole$($s$)$ and zero$($s$)$ of the transfer function. $[10$ pts$]$

b$)$ Describe the nature of the step response for the process after applying Pade approximation $[10$ pts$]$

c$)$ Derive a first order plus time delay model, starting from the original model, using Skogestad's half rule. $[10$ pts$]$