The Application of Extremum Seeking Algorithms in PID Tuning for Continuous Stirred Tank Reactor

One of the most common control algorithms in process control is the Proportional-Integral-Derivative (PID) controller, which could be very efficient if well tuned. The aim of this paper is to discuss the optimal tuning of the PID controller using extremum seeking (ES). Two ES algorithms, Perturbation Based Extremum Seeking (PBES) and Sliding Mode Based Extremum Seeking (SMBES), will be used to tune the PID parameters by searching for the optimal parameters that minimize a certain performance index. The Continuous Stirred Tank Reactor (CSTR), with irreversible first-order reaction, has been considered as a case study. The two algorithms have been implemented with two choices of Performance-Index (PI), Integral Absolute Error (IAE) criteria, and a combination of IAE with the integral of absolute of control signal. With the later choice of PI, both the algorithms show an improvement in the performance over the Internal Mode Control (IMC) tuning method, with good control behavior. The cost in the PBES tuning algorithm has converged to an ultimate bound around the optimal value within a lower number of iteration than the SMBES tuning algorithm. However, the speed of the SMBES algorithm can be increased but with the drawback of increasing the chattering effect produced in the PID parameters.