The response of a system to a unit step change in the input (occurring at time 0) is shown in Fig. E7.11.

(a) Derive a second-order plus time delay model approximation for the system. Provide values for the gain, time constraints, and time delay of the SOPTD model.
(b) Why would a FOPTD model not be as accurate for fitting the data?

1.6 1.4 -1-L--J-L-LJ-1---L --1-1--J- 1.2 H------ ! !! --J- y 0.8 - + ---- + -+ -- 4 - 0.6 ----- -- 0.4 0.2 -----L -I-1-L--J-L-LJ-1-L-L-. - - - -T- " 10 15 20 25 30 Time (s) Figure E7.11