Consider a process model:
\frac{Y(s)}{X(s)}=\frac{K\left(\tau_{a} s+1\right)}{\left(\tau_{1} s+1\right)\left(\tau_{2} s+1\right)}\left(\tau_{1}>\tau_{2}\right)
For a step input, show that:
(a) y(t) can exhibit an extremum (maximum or minimum value) in the step response only if
\frac{1-\tau_{a} / \tau_{2}}{1-\tau_{a} / \tau_{1}}>1
(b) Overshoot occurs only for \tau_{a} / \tau_{1}>1.
(c) Inverse response occurs only for \tau_{a}<0.
(d) If an extremum in y exists, the time at which it occurs can be found analytically. What is it?