Old spec 5.3 exercise (ENGR5001) - Revisica

Old spec 5.3 exerciseExercise sheetCurrent spec2:212 min

ENGR202 (old spec) Control 5.3 Frequency Response Revisited, exercise

Determine the frequency response of the following 3rd order system i.e. magnitude and phase

$G(s) = \frac{1}{(s + 4)(s + 5)(s + 7)}$

Work out the values of magnitude and phase for the following frequencies: 0, 1, 3, 10, infinity.

Formulas you may need

Frequency response: $M = |G(j\omega)|$ , $\phi = \mathrm{Arg}\,G(j\omega)$ (learn this)
$|j\omega + a| = \sqrt{\omega^2 + a^2}$ , $\mathrm{Arg}(j\omega + a) = \tan^{-1}(\omega/a)$ (learn this)
Arguments of a product add; of a quotient subtract (learn this)

M at omega = 0 =

M at omega = 1 =

phase at omega = 1 =deg

M at omega = 3 =

phase at omega = 3 =deg

M at omega = 10 =

phase at omega = 10 =deg

Related questions

Old spec 3.4 example, third order system with poles on the imaginary axis poles-stability, marginal-stability, dominant-poles, third-order
Old spec 5.3 worked example, first order response to a harmonic input by Laplace frequency-response, laplace-tf, partial-fractions, magnitude-phase
Old spec 5.3 numerical example, Bode diagram of a first order system frequency-response, bode-diagram, magnitude-phase
Old spec 5.4 example, closed-loop stability from the Bode diagram frequency-design, bode-diagram, gain-margin, phase-margin, poles-stability
Old spec 5.4 example, Nyquist stability and Hurwitz limit for a third order loop frequency-design, nyquist, hurwitz, gain-margin, phase-margin
ENGR201 2019 B3 laplace-tf, partial-fractions, modelling, frequency-response, time-response, time-constant
ENGR202 2017 Q A1 laplace-tf, generalised-forms, poles-stability, frequency-response, controller-design, time-constant, pole-placement, oil-fractionator
ENGR202 2017 Q A3 poles-stability, block-diagrams, pid-actions, feedback-objectives, frequency-design, pv-control, stability-shortcuts, heating-control