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

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.