ASSIGNMENT

Consider a system described by the transfer function:  where b equals the last two digits of your student number (for example: if your number is 438123456 then b=56).
A) Provide a FULL and comprehensive system analysis of the continues system in both time and frequency domain (unit step time response for k=1: delay time, rise time, settling time, steady state error, maximum overshoot, gain margin, phase margin, etc).

B) Choose a suitable sampling rate (T). Explain why?

C) Obtain the discrete transfer function when the system is preceded by a sampler and zero order hold.

D) Repeat part A) above for the discrete system using bilinear transformation then compare the results of the discrete vs continuous (time and frequency characteristics).

E) Try to improve the speed of the system and the overshoot using the following controllers:
‐phase lag
‐phase lead
‐phase lead‐lag
‐PI
‐PD
‐PID
‐State feedback
‐Output feedback

F) Compare between the performance of the above controllers in terms of time and frequency characteristics.

G) Comment on your results.