We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of nonlinearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.

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In the frame of a technological research and innovation network in water and environment technologies (RITEAU, Réseau de Recherche et d'Innovation Technologique Eau et Environnement), our research group, in collaboration with industrial partners and other research institutions, has been in charge of the development of a suitable flowmeter: an ultrasonic device measuring simultaneously the water flow and the concentration of size classes of suspended particles. Working on the pulsed ultrasound principle, our multi-frequency device (1 to 14 MHz) allows flow velocity and water height measurement and estimation of suspended solids concentration. Velocity measurements rely on the coherent Doppler principle. A self developed frequency estimator, so called Spectral Identification method, was used and compared to the classical Pulse-Pair method. Several measurements campaigns on one wastewater collector of the French city of Strasbourg gave very satisfactory results and showed smaller standard deviation values for the Doppler frequency extracted by the Spectral Identification method. A specific algorithm was also developed for the water height measurements. It relies on the water surface acoustic impedance rupture and its peak localisation and behaviour in the collected backscattering data. This algorithm was positively tested on long time measurements on the same wastewater collector. A large part of the article is devoted to the measurements of the suspended solids concentrations. Our data analysis consists in the adaptation of the well described acoustic behaviour of sand to the behaviour of wastewater particles. Both acoustic attenuation and acoustic backscattering data over multiple frequencies are analyzed for the extrapolation of size classes and respective concentrations. Under dry weather conditions, the massic backscattering coefficient and the overall size distribution showed similar evolution whatever the measurement site was and were suggesting a global wastewater particles behaviour. By comparison to sampling data, our data analysis lead to the characterization of two particle groups: the ones occurring during rain events and the ones typical of wastewater under dry weather conditions. Even with already encouraging results on the several weeks of data recorded on several wastewater collectors, the validation of our data inversion method is still under progress.