Consider a process model:

For a step input, show that:
(a) y(t) can exhibit an extremum (maximum or minimum value) in the step response only if

(b) Overshoot occurs only for Ï„_a/Ï„₁ > 1.

(c) Inverse response occurs only for Ï„_a < 0.

(d) If an extremum in y exists, the time at which it occurs can be found analytically. What is it?

Transcribed Image Text:

K(t,s+1) Y(s) (т > т) X (s) (т,5 + 1)(т,s + 1) 1- t,/t, Ta/T, 1- T,/T,