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Open AccessArticle

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

1
School of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, Colombia
2
Grupo de Investigación en Desarrollo Tecnológico GIDESTEC, Universidad Nacional Abierta y a Distancia, Carrera 45 # 55-19, Medellín 050012, Colombia
3
Institute for Systems and Robotics, Instituto Superior Técnico, 1049-001 Lisbon, Portugal
*
Author to whom correspondence should be addressed.
Sensors 2020, 20(23), 6738; https://doi.org/10.3390/s20236738
Received: 9 September 2020 / Revised: 18 October 2020 / Accepted: 19 October 2020 / Published: 25 November 2020
(This article belongs to the Section Intelligent Sensors)
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. View Full-Text
Keywords: observability analysis; high-gain observer; state estimation; advanced process control; soft sensor; three-tank system observability analysis; high-gain observer; state estimation; advanced process control; soft sensor; three-tank system
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MDPI and ACS Style

Rúa, S.; Vásquez, R.E.; Crasta, N.; Zuluaga, C.A. Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments. Sensors 2020, 20, 6738. https://doi.org/10.3390/s20236738

AMA Style

Rúa S, Vásquez RE, Crasta N, Zuluaga CA. Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments. Sensors. 2020; 20(23):6738. https://doi.org/10.3390/s20236738

Chicago/Turabian Style

Rúa, Santiago; Vásquez, Rafael E.; Crasta, Naveen; Zuluaga, Carlos A. 2020. "Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments" Sensors 20, no. 23: 6738. https://doi.org/10.3390/s20236738

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