Estimation and filtering of nonlinear systems: Application to a wastewater treatment process

A fundamental task in design and control of biotechnological processes is system modelling. This task is made difficult by the scarceness of online direct sensors for some key variables and by the fact that identifiability of models, including the Michaelis-Menten type of nonlinearities, is not straightforward. The use of adaptive estimation approaches constitutes an interesting alternative To circumvent these kinds of problems. This paper discusses an identification technique derived to solve the problem of estimating simultaneoulsy inaccessible state variables and time-varying parameters of a nonlinear wastewater treatment process. An extended linearization technique using Kronecker's calculation provides the error model of the joint observer-estimator procedure, whose convergence is proven via Lyapunov's method. Sufficient conditions for stability of this joint identification scheme are given and discussed according to the persistency excitation conditions of the signals. A simulation study with measurement noises and abrupt jumps of the process parameters shows the feasability and significant robustness of the proposed adaptive estimation methodology.