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Control System - First order system

  1. Jul 21, 2009 #1
    1) A thermometer requires 1min to indicate 98% of the response to be a step input. Assuming the thermometer to be a first order system, find the time constant.

    2)If the thermometer is placed in a bath, the temperature of which is changing linearly at a rate of 10degrees/min, how much error does the thermometer show?

    for the first part, i think that it takes 4 time constant tor for the system to reach 98%. So im thinking that if i divide the 1min by 4 (i.e, 1min/4), id get the time constant, T. is this correct?

    and for the second part, im not sure how should i tackle it. can you give me an outline of what i should do?

  2. jcsd
  3. Jul 22, 2009 #2


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    You got the first part right.The time constant is 15s.
    For the second part, your system is of the form [tex]G(s)=\frac{k}{s+a}[/tex].
    You can calculate a from the time constant. K can be determined requiring that the termometer has no steady state error.
    Now, what is the response of your system to an input [tex]\frac{A}{s^2}[/tex]?
    A = 10/60 degrees/s.
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