| Description |
A steady-state pH model developed by Gustaffson, Skrifvars, et. al. (Gustafsson, Tore K Bengt 0 Skrifvars, et al, "Modeling of pH for Control," Ind. Eng. Chern. Res., 1995,34, 850-827.) is tested for use in an IMC adaptive controller for an inline pH mixing apparatus. The model, based on equilibrium and solution neutrality, varies concentrations of hydrochloric acid, hypofluoric acid, and hypochlorous acid to fit titration data. The model is tested against theoretical titration curves, inline titration curves, and benchtop titration curves. The model adequately describes the details of pH titration. Model fitting is performed with a recursive least square algorithm and with Microsoft Excel Solver. Direct substitution iteration successfully solves the model for pH in less than seven iterations with 0.01 pH accuracy. All process non-linearity is assumed to be part of the process gain, as described by the steady-state model. An IMC controller is developed with an inversion-based controller. Both the process model and inversion-based controller are updated during the adaptation. Step testing of the inline-mixing apparatus show that the assumption of nonlinearity only in the process gain is inaccurate. Dead time varies with flow, but process gain and process time vary independent of flow and pH. Also, the steady-state model does not accurately predict the observed process gain. The steady-state model does not describe the process with sufficient accuracy for implementation as an adaptive controller. |
