Old spec 2.4 numerical example, first order impulse response (ENGR5001) - Revisica

Old spec 2.4 numerical example, first order impulse responseTutorialOld spec ENGR202Third5 min

ENGR202 (old spec) Control 2.4 Time Response, numerical example (slides 5-8)

A first order system $\tau\dfrac{dx}{dt} + x = Ku(t)$ has a time constant of 2 s and unity steady state gain. It starts at rest and a unit impulse is applied at $t = 0$ .

Formulas you may need

Unit impulse response of $\tau\dot x + x = Ku$ (zero initial conditions): $x(t) = \dfrac{K}{\tau}e^{-t/\tau}$ (learn this)

(a)
Write down the model and its unit impulse response $x(t)$ .
(b)
Find $x(0^+)$ and $x$ at $t = 2$ s, and sketch the response.
x(0+) =
x(2 s) =

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