Old spec 3.4 exercise 1 (ENGR5001)

Old spec 3.4 exercise 1Exercise sheetCurrent spec2:28 min

For the system below, find the poles and zeros, plot these on the complex $s$ -plane, determine the stability and sketch the response mode.

$\frac{d^2x}{dt^2} + 8\frac{dx}{dt} + 14x = 2\frac{du}{dt} - u$

Formulas you may need

Laplace with zero initial conditions: $\dot x \to sX$ , $\ddot x \to s^2X$ , $\dot u \to sU$ (learn this)
Poles: roots of the denominator; zeros: roots of the numerator; stable if all poles have negative real parts (learn this)
Dominant pole: the one closest to the imaginary axis (learn this)

zero =

dominant pole =

other pole =