Modulating function-based fast convergent observer for the Coupled Tanks system

TL;DR

This paper applies a modulating function-based observer to estimate water levels in a coupled tanks system, achieving rapid and finite-time convergence with robustness validated through numerical simulations.

Contribution

It introduces a novel application of the $T_n$ modulating function transformation for fast, finite-time convergence in coupled tanks systems.

Findings

Achieves instantaneous convergence in water level estimation.

Demonstrates robustness of the method through numerical simulations.

Ensures bounded estimation error within finite time.

Abstract

In this research, we apply the observer approach introduced by Djennoune et al. \cite{djennoune2019modulating} to estimate water levels in a coupled tanks system. Central to this approach is the use of a remarkable modulating function-based transformation $T_n $, which employs a time/output-dependent coordinate transformation. This transformation converts the original system into a form where the effects of initial conditions are effectively nullified. The primary advantage of utilizing the $T_n $ transformation is its ability to achieve instantaneous convergence, ensuring both rapid and accurate state estimation. The observer's finite-time convergence is assured, with the estimation error remaining bounded within a finite period. Numerical simulations further validate the effectiveness of this method for the Coupled Tanks system, demonstrating the robustness of the $T_n $ transformation in practical applications.