Perturbation-based pH control systems for buffer and equivalence points

The dynamics of the pH process is well-described by the Wiener model, in which a nonlinear static function follows a linear dynamic subsystem. Gain scheduling applied to the process output, or equivalently to the controller gain, has to be used to keep the pH process at a given set point under the severe static nonlinearity of the titration curve. The present study investigates two control problems of keeping the pH process on the buffer and equivalence points. The proposed method uses extremum seeking control techniques to find the first and second derivatives with continuous process input perturbations. It finds and maintains process operating points where the second derivatives of pH with respect to the process input changes are zero, the local points of minimum and maximum slopes. The performances of the proposed method are verified with simulation and experiment.