Old spec 3.4 example, effect of a zero (ENGR5001)

Old spec 3.4 example, effect of a zeroTutorialOld spec ENGR2022:28 min

Consider $X = \frac{8(1 + as)}{s^2 + 2s + 8}U$

Formulas you may need

Zeros do not affect stability; a zero with positive real part makes the system non-minimum phase (learn this)
Unit impulse $\delta(t)$ is the derivative of the unit step (learn this)

(a)
Find the poles, the zero (in terms of $a$ ) and the steady state gain.
imaginary part of poles (+) =
steady state gain =
(b)
Show that the numerator acts as a modified input, and describe this modified input when $u$ is a unit step. Hence explain how $a$ changes the step response. When is the system non-minimum phase?