Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

First Order System's Time Constant

  1. Jul 19, 2011 #1
    Hello,
    I have a question on a the units of a first order system's time constant.
    If i have a first order system the basic transfer function will be:
    K/(tau*s+1)
    where K is the Gain, and tau is the system's time constant.
    tau's units, according to what i've learned, are [sec].
    but aren't the s plane's units in [rad/sec] (s=jw+sigma)?
    That means that tau should be given in [sec/rad] to match the "1"-'s units in the transfer function.
    I know that rad can be considered "unitless" but when dealing with actual numbers it matters if the system's time constant is 1 [sec] or 1[sec/rad]= 2*pi [sec].

    My question is specifically about the units of tau in the transfer function,
    not when it is used in the decay rate of e (e^(-t/tau)), there it has to be sec.

    I'll appreciate a clarification.

    Thanks
     
  2. jcsd
  3. Jul 19, 2011 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hello yanaibarr! welcome to pf! :wink:

    tau is always in seconds …

    the difference between radians and (eg) degrees is absorbed into the k :smile:
     
  4. Jul 20, 2011 #3
    Re: welcome to pf!

    No, one may use any unit for tau. For exponential decay, Ae^(-t/tau), the exponent (-t/tau) should be unit-less.
     
    Last edited: Jul 20, 2011
  5. Jul 23, 2011 #4
    Re: welcome to pf!

     
  6. Jul 23, 2011 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    sorry, i don't know, i haven't come across the s-plane :redface:
     
  7. Jul 24, 2011 #6
    Re: welcome to pf!

     
  8. Jul 24, 2011 #7
    The s-plane is what u get after using the Laplace Transform.
     
  9. Jul 24, 2011 #8
    Re: welcome to pf!

     
  10. Oct 23, 2011 #9
    I've stumbled at the same problem. All learning materials seem to expose the concept but none gives example with exact units.

    So, if I want a frequency break at 1 Hz, should I write 1/(s+1) or 1/(s+2Pi)? Second seems more plausible. However, when Laplace-transfromed, it gives e-2pi t meaning that time constant is T = 1/2pi. Yet, I'm customed that periods are measured in seconds rather than seconds per radian. I mean that 2pi is not usually a part of period. But, wikipedia article on time constant does not clarify what are the units.

    https://www.physicsforums.com/showthread.php?t=516891"
     
    Last edited by a moderator: Apr 26, 2017
  11. Oct 24, 2011 #10
    Last edited by a moderator: Apr 26, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook