Minimum variance control, estimation and simulation of nonlinear models of wastewater-treatment systems

A problem of increasing importance is that of efficient regulation of wastewater-treatment systems. In the paper a set of model equations for the activated-sludge process are derived and shown to be nonlinear. These are Itÿ stochastic differential equations for which analytic solutions are not tractable. A 1st-order simulation algorithm based on the properties of Itÿ calculus is used to validate the model equations and assess various control schemes. In particular, a minimum-variance-control law is investigated; the structure of the controller is selected a priori on the basis of ease of physical implementation and cost. The derived control is a state-feedback law. Implementation of the controls requires online knowledge of the system states and a new nonlinear discrete recursive state estimator based on the statistics of the systems equations is introduced. Although the paper highlights the control of wastewater systems, the techniques of simulation, minimum variance control and state estimation introduced are of a very general applicability.