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ENGR5001 / Week 2
Old spec 2.4 worked example, axial fan model from a step testTutorialOld spec ENGR2022:28 min

ENGR202 (old spec) Control 2.4 Time Response, axial fan worked example (slides 18-20)

The figure shows a laboratory step test on an axial fan. The input voltage is stepped from 0 to 40 V at about t=5t = 5 s, and the airflow (m3^3/hour) rises from 0 towards a steady value. The fan is to be modelled by the first order system τdxdt+x=Ku(t)\tau\dfrac{dx}{dt} + x = Ku(t), with xx the airflow and uu the input voltage.

Axial fan step test: input voltage steps from 0 to 40 V at about t = 5 s; airflow (m^3/hour) rises to about 60.
Axial fan step test: input voltage steps from 0 to 40 V at about t = 5 s; airflow (m^3/hour) rises to about 60.
Formulas you may need
  • K=x(t→∞)u(t→∞)K = \dfrac{x(t \to \infty)}{u(t \to \infty)} (for a step from zero) (learn this)
  • At t=τt = \tau after the step: x=0.632 x(t→∞)x = 0.632\,x(t \to \infty) (learn this)
  1. (a)
    Estimate the steady state gain KK.
  2. (b)
    Estimate the time constant τ\tau, and write down the model.
  3. (c)
    Using the model, what airflow is expected at steady state for a constant input of 20 V? Sketch the response to a step from 0 to 20 V.