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ENGR5001 / Week 3
Old spec 3.4 example, poles and zeros of a second order systemTutorialOld spec ENGR2022:26 min

ENGR202 (old spec) Control 3.4 Poles, Zeros and Stability, second order example (slides 15-17)

Find the poles and zeros, plot the poles on the complex ss-plane, determine the stability and sketch the response mode. d2xdt2−dxdt+0.5x=dudt+2u\frac{d^2x}{dt^2} - \frac{dx}{dt} + 0.5x = \frac{du}{dt} + 2u

Formulas you may need
  • Zeros: roots of the numerator; poles: roots of the denominator (learn this)
  • Quadratic formula s=−b±b2−4ac2as = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} (learn this)
  • Complex poles σ±jω\sigma \pm j\omega give a mode eσtsin⁡(ωt+ϕ)e^{\sigma t}\sin(\omega t + \phi) (learn this)