A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions
In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/9/8/82 |
| _version_ | 1797524261070438400 |
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| author | Alejandro Rincón Gloria M. Restrepo Fredy E. Hoyos |
| author_facet | Alejandro Rincón Gloria M. Restrepo Fredy E. Hoyos |
| author_sort | Alejandro Rincón |
| collection | DOAJ |
| description | In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor. |
| first_indexed | 2024-03-10T08:54:48Z |
| format | Article |
| id | doaj.art-b67547d52af2472a992de60a449dfba6 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T08:54:48Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-b67547d52af2472a992de60a449dfba62023-11-22T07:15:21ZengMDPI AGComputation2079-31972021-07-01988210.3390/computation9080082A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov FunctionsAlejandro Rincón0Gloria M. Restrepo1Fredy E. Hoyos2Grupo de Investigación en Desarrollos Tecnológicos y Ambientales—GIDTA, Facultad de Ingeniería y Arquitectura, Universidad Católica de Manizales, Carrera 23 N. 60–63, Manizales 170002, ColombiaGrupo de Investigación en Microbiología y Biotecnología Agroindustrial—GIMIBAG, Instituto de Investigación en Microbiología y Biotecnología Agroindustrial, Universidad Católica de Manizales, Carrera 23 N. 60–63, Manizales 170002, ColombiaFacultad de Ciencias, Escuela de Física, Universidad Nacional de Colombia, Sede Medellín, Carrera 65 No. 59A–110, Medellín 050034, ColombiaIn this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.https://www.mdpi.com/2079-3197/9/8/82state observerrobust controladaptive controlsecond-order systemlyapunov stability |
| spellingShingle | Alejandro Rincón Gloria M. Restrepo Fredy E. Hoyos A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions Computation state observer robust control adaptive control second-order system lyapunov stability |
| title | A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions |
| title_full | A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions |
| title_fullStr | A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions |
| title_full_unstemmed | A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions |
| title_short | A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions |
| title_sort | robust observer based adaptive control of second order systems with input saturation via dead zone lyapunov functions |
| topic | state observer robust control adaptive control second-order system lyapunov stability |
| url | https://www.mdpi.com/2079-3197/9/8/82 |
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