We would like to rise water temperature with a heater. Oulet temperature must be equal to the set point temperature (80°C). Proportional (P), Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) control are used and the respective results are compared. Inlet water temperature is equal to 20°C. Water flow is equal to 10 m3/hr. Tank volume is equal to 100 m3. Water density and heat capacity are 1 Kg/m3 and 4.19 KJ/(Kg °C). The heater and the temperature measurement device have a first order delay with a time constant equal to respectively TauQ and TauSens. Initial heat input and tank temperature are equal to 2500 KJ/hr and 20°C. This problem is solved using Berkeley-Madonna in Chemical Engineering Dynamics by J. Ingham et al. (second edition, Wiley-VCH, 2000). The solution using MatLab is present in this page. Sensor temperature lags slightly behind tank temperature. P control gives a small characteristic offset, PI control shows oscillations and PID control gives best control with no offset and quickly damped oscillations.
A similar program using Mathematica 6.0 is available at the following link:
Please also visit an earlier version using Mathematica 5.0 available at the Wolfram Library Archive: