1) Take the following TF: (1 - 5)(1 - 2s) e-0.5 G(s) = (12s + 1)(6s + 1)(0.3s +1) Equation [1] All the step responses (from a to e) must be in single plot with proper color, line style (solid, dash, dash dot and dot) with legends. All pole zero plots (from a to e) must appear in one page so that the comparison can be made easily. a. Plot the pole zero diagram of G(s). plot the step response in time domain, (use 60 seconds as final time for plotting) Comparison of Egn. 1 to the FOPTD b. Use taylor series approximation to get FOPTD model. Compare the step response to the full model. Plot pole zero diagram. C. Use Skogestad method to get FOPTD model. Compare the step response to the full model. Plot pole zero diagram. d. Use the inflection point method to derive FOPTD model (use t=14 as inflection point). Compare the step response to the full model. Plot pole zero diagram. e. Use the method described in the lecture (excel minimization) to derive the FOPTD model (obtain 6 and ) by minimizing the sum of squared error between full solution derived in part a and the FOPTD model (use tfinal as 60 s). You can also use other softwares. Copy paste the code in case you use Matlab/python. In case you use excel, copy paste the screenshot of the excel sheet. Compare the time domain response. Plot pole zero diagram