Problems of Process Control

Chemical Engineering Department Subject: Process Control for undereducated students Instructor: Dr. Karima Marogi Typical Questions & Answers

Process Control Problems
Problem (1)

Solution
a) Energy balance for the thermocouple,

where m is mass of thermocouple C is heat capacity of thermocouple h is heat transfer coefficient A is surface area of thermocouple t is time in sec Substituting numerical values in (1) and noting that

Taking Laplace transform,

Problem (2)
A thermometer having a time constant of 0.2 min is placed in a temperature bath and after the thermometer comes to equilibrium with the bath, the temperature of the bath is increased linearly with time at the rate of I deg C / min what is the difference between the indicated temperature and bath temperature (a) 0.1 min (b) 10. min after the change in temperature begins. (c) What is the maximum deviation between the indicated temperature and bath temperature and when does it occurs. (d) plot the forcing function and the response on the same graph. After the long enough time buy how many minutes does the response lag the input?

Solution
Consider thermometer to be in equilibrium with temperature bath at temperature

(a) the difference between the indicated temperature and bath temperature

Problem (3)
Determine the transfer function H(s)/Q(s) for the liquid level shown in figure below Resistance R1 and R2 are linear. The flow rate from tank 3 is maintained constant at b by means of a pump; the flow rate from tank 3 is independent of head h. The tanks are non-interacting.

Solution

and balance on tank 3 gives

writing the steady state equation

Subtracting and writing in terms of deviation

Taking Laplace transforms

We have three equations and 4 unknowns (Q(s),H(s),H1(s) and H2(s). So we can express one in terms of other.

From (1)

Combining equation 4,5,6

Problem (4)
Determine Y (4) for the system response expressed by

Problem (5)
Heat transfer