Comparison of linear and nonlinear adaptive control of a pH-process

Physical inspection leads to the modeling of a pH-reactor by a linear dynamic flow and mixing process followed by a static nonlinearity. In this paper, a pH process very difficult to control is simulated for testing different types of adaptive algorithms. In one scheme, the flow and mixing model is assumed to be known. The nonlinear adaptive controller is constructed based on a combination of a pole-placement design method with a piecewise-polynomial approximation of a titration function, the coefficients of which are estimated from pH measurements. In another scheme, an inverse overall process model is obtained by the combination of the flow and mixing model with a piecewise-polynomial approximation of the titration curve. This model is applied to the development of a nonlinear controller based on the model reference adaptive technique. Both methods are applied for tracking a given pH-variable and for regulation. The effectiveness of linear and nonlinear adaptive controllers, obtained using the linear or non-linear approximation of the titration curve, respectively, is examined and compared for different process solutions and different applications.