Sensor fault reconstruction and observability for unknown inputs,with an application to wastewater treatment plants

In this article, we propose a general methodology for identifying and reconstructing sensor faults on dynamical processes. This methodology is issued from the general identification theory developed in the previous papers (Busvelle, E., and Gauthier, J.-P. (2003), ‘On Determining Unknown Functions in Differential Systems, with an Application to Biological Reactor’, ESAIM: Control, Optimisation and Calculus of Variations, 9, 509–553; Busvelle, E., and Gauthier, J.-P. (2004), ‘New Results on Identifiability of Nonlinear Systems’, in 2nd Symposium on Systems, Structure and Control, Oaxaca, Mexico; Busvelle, E., and Gauthier, J.-P. (2005), ‘Observation and Identification Tools for Non Linear Systems. Application to a Fluid Catalytic Cracker’, International Journal of Control, 78, 208–234): in fact, this identification theory also provides a general framework for the problem of ‘observability with unknown inputs’. Indeed, many problems of fault detection can be formulated as such observability problems, the (eventually additive) faults being just considered as unknown inputs. Our application to ‘sensor fault detection’ for wastewater treatment plants (WWTP) constitutes an ideal academic context to apply the theory: first, in this 3-5 case (3 sensors, 5 states), the theory applies generically and, second, any system is naturally under the ‘observability canonical form’ required to apply the basic high-gain observer from Gauthier and Kupka (Gauthier, J.-P., and Kupka, I. (1994), ‘Observability and Observers for Nonlinear Systems’, SIAM Journal on Control, 32, 975–994). A simulation study on the Bleesbrük WWTP is proposed to show the effectiveness of this approach.