State and unknown input estimation for nonlinear singular systems: application to the reduced model of the activated sludge process

Abstract

An estimation of the state and the unknown inputs of the reduced nonlinear model of an activated sludge process using the Extended Kalman Filter (EKF) is proposed. First, we present the reduced nonlinear model. This model contained five state variables and four unknown inputs. For satisfying the rank condition for the construction of an EKF, one unknown input has been approximated and the daily mean value of another unknown input has been used. Then, to estimate conjointly the state and the unknown inputs, the reduced nonlinear system is transformed to a nonlinear singular system. High performances of the proposed observer will be shown through the simulation results.

Unknown Inputs Nonlinear Observer for an Activated Sludge Process

“…Each observer would provide the estimation of just an UI-vector component, with the exception of the last one which would really give an adjustment of full state variables. Given its utility, UIO has received big attention and has been applied to ASP, as in [30] where the authors suggested estimated states and the UIs as regards a minimized ASP nonlinear model through the use of the Extended Kalman Filter (EKF). Reference [31] treated the problems of Waste Water Treatment Plants (WWTP) sensor fault detection with the basic UIO (HGO).…”

A nonlinear observer design for an activated sludge wastewater treatment process

“…To solve this problem, various methods are proposed. We can quote, for example [32], [23], [14], [11], [34] and lately [6] and references therein. Reference [11] gives an excellent overview of available results on the state and parameter estimation approaches for chemical and biochemical processes.…”