Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can I obtain the time constant of the transfer function of a first order system, such as the example below?

$$ \frac{C(s)}{R(s)} = \frac{2}{s + 3}$$

Where $C(s)$ is the output of the system and $R(s)$ is the input of the system.

I'm not looking for an exact answer, I just would like to be pointed in the right direction as to how to solve for the time constant so that I can solve it myself.

Thanks.

share|improve this question
1  
This doesn't seem to be a first order system, which has a t.f. of the form $K/(\tau s+1)$ and an exponential step response. This one's step response depends on the impulse function $\delta(t)$ –  Ganesh Oct 15 '12 at 19:15
    
@Ganesh: How is this NOT a 1st order system? I really do NOT understand your comment. –  Rod Carvalho Nov 14 '12 at 1:48
    
@Ganesh this is a first order system. If you want to get it in general form, you'll have to divide the top and bottom by 3, in which case you would find τ to be 1/3. –  chilemagic Oct 18 '13 at 3:00
    
Matt: Ah, see the revision history and look at the first revision. Then you'll understand. @RodCarvalho: Now that I see YOUR comment, I DO NOT understand your MANNERS. No need to FLAME. –  Ganesh Oct 18 '13 at 4:35
add comment

1 Answer 1

The LTI system whose transfer function is

$$H (s) = \frac{2}{s + 3}$$

has the impulse response

$$h (t) = 2 \, e^{-3 t} = 2 \, e^{- t / \tau}$$

where $t \geq 0$ and $\tau := \frac{1}{3}$ is the time constant. I am assuming that the system is causal, of course.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.