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What is the transient and steady-state response in the next equation:

$$2 + 5t + 3\exp(-0.1t)$$

I am looking to understand how to identify both responses just looking the equations....Please Help me!

Antonio Vargas
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Arturo Ortiz
  • 13

1 Answers1

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A transient term is the one that dies off (goes to zero) as $ t \to \infty $

so for your example:

$$\lim_{t\to \infty} 3e^{-0.1t} = 0$$

so that can be classified as the transient term in your equation.

A steady-state function is a function that does not change as $ t \to \infty $.

An example of a steady-state function would be trigonometric function like $sin(t)$ which oscillates within a boundary as t grows larger.

For your example, the steady-state would be

$$ 2 + 5t $$

Another example would be;

let $f(t) = g(t) + h(t)$

if $$\lim_{t\to \infty} g(t) = 0$$ and $$\lim_{t\to \infty} h(t) \neq 0$$

$h(t)$ is the steady-state and $g(t)$ is the transient term

JLL
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  • Otherwise, if x is different from 0, is it a Steady state? @Jean Ferreira – Arturo Ortiz Sep 27 '14 at 20:55
  • yes, so when you have a function that has a transient term in it, the steady-state can be classified as the same function but without the term that goes to zero. check out the edit on the answer. – JLL Sep 27 '14 at 21:01
  • Your answer was a great relief, Thanks!! I owe you one! – Arturo Ortiz Sep 27 '14 at 21:16