Question

The level in a tank responds as a first order system with changes in the inlet flow. The following level vs. time data were gathered after the inlet flow was increased quickly from 1.5 gal/min to 4.8 gal/min. Determine the transfer function that relates the height in the tank to the inlet flow. Be sure to use deviation variables and include units on the steady state gain and the time constant. Time (min) Level (ft) 0.0 10.4 0.25 12.0 0.50 13.5 0.75 15.1 1.00 16.8 1.25 18.1 1.50 19.2 1.75 20.3 2.00 21.5 2.25 22.1 2.50 22.9 2.75 23.7 15.0 30.7 (steady-state)

Answer 1

Solution:

The plot for the given data is shown below,

from the above plot the height occurs at

The transfer function for the system is,

by plugging the values we get,

The equations are,

Among them H(s) and Q(s) are deviation variables.