Nonlinear and adaptive control of pH

Methods for continuous control of pH in process streams are treated.Nonlinear models for pH, valid for acid-base reactions in water solutions, are derived from first principles, and a nonparam- etrized model is introduced for processes with unknown composition.The two basic choices for continuous in-line feedback control of pH are between linear and nonlinear control and between fixed-parameter and adaptive control.A detailed simulation example illustrates properties of pH-control systems in oscillating mode, a common phenomenon in, e.g., wastewater pH-control systems.Use of a proper nonlinear process model for feedback control is shown to essentially eliminate the bias of the oscillations and to result in an average pH close to the setpoint, whereas standard linear feedback control does not.The main reason for the need of adaptation is changing buffering (titration curve).Advantages of adaptive control over nonadaptive control are illustrated with respect to robustness and performance, and convergence properties of nonlinear adaptive control compared to linear-model adaptive control are experimentally illustrated.Practical issues in the implementation of linear and nonlinear self-tuning control of pH are discussed.