# Control System - First order system

#### kloong

Q:
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?

thanks.

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#### CEL

You got the first part right.The time constant is 15s.
For the second part, your system is of the form $$G(s)=\frac{k}{s+a}$$.
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 $$\frac{A}{s^2}$$?
A = 10/60 degrees/s.

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