Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output
In this work, a controller is developed for a continuous bioreactor with an unknown reaction rate term, subject to input saturation. The substrate concentration and the dilution rate are chosen as output and input, respectively. The controller formulation and the stability analysis are performed by...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/6/1232 |
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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 | In this work, a controller is developed for a continuous bioreactor with an unknown reaction rate term, subject to input saturation. The substrate concentration and the dilution rate are chosen as output and input, respectively. The controller formulation and the stability analysis are performed by the theory of dead zone Lyapunov functions, Lyapunov stability, and model reference adaptive control. As the main results, the dynamics of the Lyapunov function is determined separately for saturation and non-saturation events, and then a unified expression is deduced. In addition, the asymptotic convergence of the tracking error and boundedness of updated parameters are determined for the whole closed loop regime encompassing saturation and non-saturation events, and also for input saturation events, as a function of the terms and parameters of the reference and system models. The main contributions over closely related control designs, are (i) the effect of input constraint limits and desired output on the convergence of the tracking error during input saturation events are determined, considering settling behavior of the desired output with a steep section; (ii) the upper limit of the input constraint that guarantees output convergence during input saturation events is determined as function of the model terms, but independently of the time derivative of the desired output and its limit; (iii) a new dead zone Lyapunov function is proposed which allows proving asymptotic convergence of the tracking error during input saturation events in the presence of a fast variation in the desired output. Finally, the effectiveness and advantages of the developed controller are illustrated by simulation. |
| first_indexed | 2024-03-09T22:21:54Z |
| format | Article |
| id | doaj.art-2944fa1f9b7a4c8f85e95988a53d693a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:21:54Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2944fa1f9b7a4c8f85e95988a53d693a2023-11-23T19:13:00ZengMDPI AGSymmetry2073-89942022-06-01146123210.3390/sym14061232Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired OutputAlejandro 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, ColombiaIn this work, a controller is developed for a continuous bioreactor with an unknown reaction rate term, subject to input saturation. The substrate concentration and the dilution rate are chosen as output and input, respectively. The controller formulation and the stability analysis are performed by the theory of dead zone Lyapunov functions, Lyapunov stability, and model reference adaptive control. As the main results, the dynamics of the Lyapunov function is determined separately for saturation and non-saturation events, and then a unified expression is deduced. In addition, the asymptotic convergence of the tracking error and boundedness of updated parameters are determined for the whole closed loop regime encompassing saturation and non-saturation events, and also for input saturation events, as a function of the terms and parameters of the reference and system models. The main contributions over closely related control designs, are (i) the effect of input constraint limits and desired output on the convergence of the tracking error during input saturation events are determined, considering settling behavior of the desired output with a steep section; (ii) the upper limit of the input constraint that guarantees output convergence during input saturation events is determined as function of the model terms, but independently of the time derivative of the desired output and its limit; (iii) a new dead zone Lyapunov function is proposed which allows proving asymptotic convergence of the tracking error during input saturation events in the presence of a fast variation in the desired output. Finally, the effectiveness and advantages of the developed controller are illustrated by simulation.https://www.mdpi.com/2073-8994/14/6/1232input saturationrobust controladaptive controlwindupdead zone Lyapunov functionconstrained control |
| spellingShingle | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output Symmetry input saturation robust control adaptive control windup dead zone Lyapunov function constrained control |
| title | Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output |
| title_full | Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output |
| title_fullStr | Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output |
| title_full_unstemmed | Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output |
| title_short | Conditioned Adaptive Control for an Uncertain Bioreactor with Input Saturation and Steep Settling Desired Output |
| title_sort | conditioned adaptive control for an uncertain bioreactor with input saturation and steep settling desired output |
| topic | input saturation robust control adaptive control windup dead zone Lyapunov function constrained control |
| url | https://www.mdpi.com/2073-8994/14/6/1232 |
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