Dynamics of a Heated Tank with Proportional Integral Differential (PID) Control and Outlet Flow Time Delay

This Demonstration simulates the dynamics of a continuous process system consisting of a well-stirred tank, heater, and PID temperature controller. The liquid feed stream flows into a constant-volume heated tank at a constant rate. The outlet stream is heated to a higher set point temperature. The outlet temperature is measured by a thermocouple, while a PID temperature controller adjusts the required heater input. The objective is to maintain the outlet temperature equal to the set point whatever the change in inlet temperature. The thermocouple in the outlet stream is described by a first-order system plus dead time for the output flow to reach the measurement point.
The system is modeled by a system of delay ordinary differential equations. Details of the equations and parameter values used are given in reference [1]. Initially the system is operating at steady state with an inlet temperature 60 degrees; at time 10, the inlet temperature is decreased to 40 degrees. You can vary the control variables and choose three different types of controllers to study the response of the system.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[1] M. B. Cutlip, J. J. Hwalek, H. E. Nuttall, M. Shacham, J. Brule, J. Widmann, T. Han, B. Finlayson, E. M. Rosen, and R. Taylor, "A Collection of 10 Numerical Problems in Chemical Engineering Solved by Various Mathematical Software Packages," Computer Applications in Engineering Education, 6(3), 1998 pp. 169–180. doi:10.1002/(SICI)1099-0542(1998)6:3<169::AID-CAE6>3.0.CO;2-B. ftp://ftp.bgu.ac.il/shacham/publ_papers/CAEE_6_169_98.pdf.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.