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 non...
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| Format: | Article |
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MDPI AG
2020-11-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/23/6738 |
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| author | Santiago Rúa Rafael E. Vásquez Naveen Crasta Carlos A. Zuluaga |
| author_facet | Santiago Rúa Rafael E. Vásquez Naveen Crasta Carlos A. Zuluaga |
| author_sort | Santiago Rúa |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:34:45Z |
| format | Article |
| id | doaj.art-3859e9f15a5e43fd873d2c8a1330d262 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T14:34:45Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-3859e9f15a5e43fd873d2c8a1330d2622023-11-20T22:16:45ZengMDPI AGSensors1424-82202020-11-012023673810.3390/s20236738Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and ExperimentsSantiago Rúa0Rafael E. Vásquez1Naveen Crasta2Carlos A. Zuluaga3School of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, ColombiaSchool of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, ColombiaInstitute for Systems and Robotics, Instituto Superior Técnico, 1049-001 Lisbon, PortugalSchool of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, ColombiaThis 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.https://www.mdpi.com/1424-8220/20/23/6738observability analysishigh-gain observerstate estimationadvanced process controlsoft sensorthree-tank system |
| spellingShingle | Santiago Rúa Rafael E. Vásquez Naveen Crasta Carlos A. Zuluaga Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments Sensors observability analysis high-gain observer state estimation advanced process control soft sensor three-tank system |
| title | Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments |
| title_full | Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments |
| title_fullStr | Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments |
| title_full_unstemmed | Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments |
| title_short | Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments |
| title_sort | observability analysis and observer design for a nonlinear three tank system theory and experiments |
| topic | observability analysis high-gain observer state estimation advanced process control soft sensor three-tank system |
| url | https://www.mdpi.com/1424-8220/20/23/6738 |
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