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?

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