A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer
The properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contribu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/18/6988 |
| _version_ | 1797482494243635200 |
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| author | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra |
| author_facet | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra |
| author_sort | Alejandro Rincón |
| collection | DOAJ |
| description | The properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contributions over closely related studies of the stability of state observers are: (i) the width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance terms of the observer error dynamics; (ii) it was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. In addition, the main advantages of the proposed algorithm over closely related algorithms are: (i) the definition of observer parameters is significantly simpler, as the fulfillment of Riccati equation conditions, solution of LMI constraints, and fulfillment of eigenvalue conditions are not required; (ii) unknown bounded terms are considered in the dynamics of the observer error for the known state. Finally, the algorithm is applied to a model of microalgae culture in a photobioreactor for the estimation of biomass growth rate and substrate uptake rate based on known concentrations of biomass and substrate. |
| first_indexed | 2024-03-09T22:34:07Z |
| format | Article |
| id | doaj.art-bac632d829af4383895e337421c25451 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T22:34:07Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-bac632d829af4383895e337421c254512023-11-23T18:52:33ZengMDPI AGSensors1424-82202022-09-012218698810.3390/s22186988A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust ObserverAlejandro Rincón0Fredy E. Hoyos1John E. Candelo-Becerra2Grupo de Investigación en Desarrollos Tecnológicos y Ambientales—GIDTA, Facultad de Ingeniería y Arquitectura, Universidad Católica de Manizales, Carrera 23 No. 60-63, Manizales 170002, ColombiaDepartamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, ColombiaDepartamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, ColombiaThe properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contributions over closely related studies of the stability of state observers are: (i) the width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance terms of the observer error dynamics; (ii) it was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. In addition, the main advantages of the proposed algorithm over closely related algorithms are: (i) the definition of observer parameters is significantly simpler, as the fulfillment of Riccati equation conditions, solution of LMI constraints, and fulfillment of eigenvalue conditions are not required; (ii) unknown bounded terms are considered in the dynamics of the observer error for the known state. Finally, the algorithm is applied to a model of microalgae culture in a photobioreactor for the estimation of biomass growth rate and substrate uptake rate based on known concentrations of biomass and substrate.https://www.mdpi.com/1424-8220/22/18/6988state estimationrobust observerbioprocess monitoringnonlinear systems |
| spellingShingle | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer Sensors state estimation robust observer bioprocess monitoring nonlinear systems |
| title | A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer |
| title_full | A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer |
| title_fullStr | A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer |
| title_full_unstemmed | A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer |
| title_short | A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer |
| title_sort | simplified algorithm for setting the observer parameters for second order systems with persistent disturbances using a robust observer |
| topic | state estimation robust observer bioprocess monitoring nonlinear systems |
| url | https://www.mdpi.com/1424-8220/22/18/6988 |
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