Old spec 2.4 exercise, key points of the first order step responseTutorialOld spec ENGR202Third4 min

ENGR202 (old spec) Control 2.4 Time Response, exercise (slide 11; answer slide 12)

For a unit step input, the output of the first order system τdxdt+x=Ku\tau\dfrac{dx}{dt} + x = Ku (starting from rest) is x(t)=K(1−e−t/τ)x(t) = K\left(1 - e^{-t/\tau}\right) Complete the table: the output x(t)x(t) at t=0t = 0, at t=τt = \tau and as t→∞t \to \infty, as a multiple of KK. Then explain how these points are used to estimate KK and τ\tau from an experimental step response.

Formulas you may need
  • First order unit step response x(t)=K(1−e−t/τ)x(t) = K\left(1 - e^{-t/\tau}\right) (learn this)