Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments

This paper addresses the observability analysis and observer design for a nonlinear interacting three-tank system. The plant configuration is first described using the process and instrumentation diagram (P&ID) and a state–space realization is derived; some insights about the behavior of the nonlinear system, considering equilibrium points and the phase portrait are provided. Then, observability in the Hermann–Krener sense is analyzed. A high-gain observer (HGO) is then designed, using the equivalence of the original state–space realization with its observability canonical form, in order to guarantee convergence of the state estimation. The performance was validated through simulation and experiments in a multipurpose plant equipped with real sensors; the HGO response was compared to a Luenberger observer (for a linear approximation of the plant) and the Extended Kalman Filter (for which convergence is not guaranteed), considering nonlinearities, interaction, disturbances and noise. Theoretical and experimental results show that the HGO can provide robust estimation and disturbance rejection, despite the sensitivity of HGOs to noisy variables in processes such as level of liquids.