(598f) Continuous Stirred Tank Reactor (CSTR) Temperature Control Via Multifractional PID Controller

Vargas, R. D., Universidad de los Andes
Vargas, W. L., Universidad de los Andes

Fractional calculus is the branch of mathematics dedicated to the extension of integral and derivative operations to the real domain (including complex), therefore allowing the possibility of calculating derivatives of , ,  orders among others. There has been an important number of works (Podlubny, 1999 and the references there in) devoted to applications of this mathematical tool in recent years. One of the most relevant areas of the so-called fractional applied analysis is the implementation of fractional order PID controllers.

These types of controllers allows the possibility of incorporating memory in the derivatives by changing the system order which results in changes in the stability regions (Tavazoei and Haeri, 2008). In this work this strategy is implemented on a second order reversible reaction occurring in a CSTR with the purpose of stabilizing the temperature that maximizes the reaction rate velocity. A classical and very important problem in the context of Chemical Reaction Engineering. The controller parameters are tune up via nonlinear optimization methods and comparison are made with implementations based on a classical PID controller.


  1. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999).
  2. M.S. Tavazoei and M. Haeri, Chaos control via simple fractional-order controller, Physics Letters A 372 (2008) 798-807.