### Abstract

For replacing Lyapunov's ingenious but complicated 2nd method in designing adaptive controllers for nonlinear systems the use of Robust Fixed Point Transformations (RFPT) was extensively studied in the past few years mainly for Classical Mechanical Systems (CMS). In spite of the strongly nonlinear coupling that is typical in the Euler-Lagrange equations of motion CMS are simple in the sense that their state variables (i.e. the generalized coordinates and their time-derivatives), driving force or torque components, as well as the tracking error signals are physically well interpreted both in the positive and the negative domains. Furthermore, the time-derivatives of the control forces do not occur in the equations of motion. Therefore simple PIDtype controllers with great feedback gains as well as RFPT-based adaptive ones of smaller feedback gains but of the aptitude for introducing strong nonlinear transient fluctuations after their switching on can successfully deal with such systems. In contrast to CMS Chemical Systems (CS), besides their multiplication and power-type terms in the reaction equations also have further strong nonlinearities due to phenomenological restrictions. Neither negative concentrations, nor negative ingress rates of pure reagents can occur in the case of Continuous Stirring Tank Reactors (CSTR). Such effects were recently investigated by assuming the ingress of very concentrated reagents in the control that do not considerably dilute the other reagents in the CTRS. In this paper the far reaching consequences of this mutual diluting effect are studied. It is shown that the RFPT-based adaptive controller still can be useful but the control strategy has to take far more complicated form.

Original language | English |
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Title of host publication | LINDI 2012 - 4th IEEE International Symposium on Logistics and Industrial Informatics, Proceedings |

Pages | 157-162 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2012 |

Event | 4th IEEE International Symposium on Logistics and Industrial Informatics, LINDI 2012 - Smolenice, Slovakia Duration: Sep 5 2012 → Sep 7 2012 |

### Other

Other | 4th IEEE International Symposium on Logistics and Industrial Informatics, LINDI 2012 |
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Country | Slovakia |

City | Smolenice |

Period | 9/5/12 → 9/7/12 |

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### ASJC Scopus subject areas

- Information Systems

### Cite this

*LINDI 2012 - 4th IEEE International Symposium on Logistics and Industrial Informatics, Proceedings*(pp. 157-162). [6319479] https://doi.org/10.1109/LINDI.2012.6319479

**Adaptive controllability of the brusselator model with input coupling.** / Tar, J.; Rudas, I.; Nadai, Laszlo; Kosi, Krisztian.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*LINDI 2012 - 4th IEEE International Symposium on Logistics and Industrial Informatics, Proceedings.*, 6319479, pp. 157-162, 4th IEEE International Symposium on Logistics and Industrial Informatics, LINDI 2012, Smolenice, Slovakia, 9/5/12. https://doi.org/10.1109/LINDI.2012.6319479

}

TY - GEN

T1 - Adaptive controllability of the brusselator model with input coupling

AU - Tar, J.

AU - Rudas, I.

AU - Nadai, Laszlo

AU - Kosi, Krisztian

PY - 2012

Y1 - 2012

N2 - For replacing Lyapunov's ingenious but complicated 2nd method in designing adaptive controllers for nonlinear systems the use of Robust Fixed Point Transformations (RFPT) was extensively studied in the past few years mainly for Classical Mechanical Systems (CMS). In spite of the strongly nonlinear coupling that is typical in the Euler-Lagrange equations of motion CMS are simple in the sense that their state variables (i.e. the generalized coordinates and their time-derivatives), driving force or torque components, as well as the tracking error signals are physically well interpreted both in the positive and the negative domains. Furthermore, the time-derivatives of the control forces do not occur in the equations of motion. Therefore simple PIDtype controllers with great feedback gains as well as RFPT-based adaptive ones of smaller feedback gains but of the aptitude for introducing strong nonlinear transient fluctuations after their switching on can successfully deal with such systems. In contrast to CMS Chemical Systems (CS), besides their multiplication and power-type terms in the reaction equations also have further strong nonlinearities due to phenomenological restrictions. Neither negative concentrations, nor negative ingress rates of pure reagents can occur in the case of Continuous Stirring Tank Reactors (CSTR). Such effects were recently investigated by assuming the ingress of very concentrated reagents in the control that do not considerably dilute the other reagents in the CTRS. In this paper the far reaching consequences of this mutual diluting effect are studied. It is shown that the RFPT-based adaptive controller still can be useful but the control strategy has to take far more complicated form.

AB - For replacing Lyapunov's ingenious but complicated 2nd method in designing adaptive controllers for nonlinear systems the use of Robust Fixed Point Transformations (RFPT) was extensively studied in the past few years mainly for Classical Mechanical Systems (CMS). In spite of the strongly nonlinear coupling that is typical in the Euler-Lagrange equations of motion CMS are simple in the sense that their state variables (i.e. the generalized coordinates and their time-derivatives), driving force or torque components, as well as the tracking error signals are physically well interpreted both in the positive and the negative domains. Furthermore, the time-derivatives of the control forces do not occur in the equations of motion. Therefore simple PIDtype controllers with great feedback gains as well as RFPT-based adaptive ones of smaller feedback gains but of the aptitude for introducing strong nonlinear transient fluctuations after their switching on can successfully deal with such systems. In contrast to CMS Chemical Systems (CS), besides their multiplication and power-type terms in the reaction equations also have further strong nonlinearities due to phenomenological restrictions. Neither negative concentrations, nor negative ingress rates of pure reagents can occur in the case of Continuous Stirring Tank Reactors (CSTR). Such effects were recently investigated by assuming the ingress of very concentrated reagents in the control that do not considerably dilute the other reagents in the CTRS. In this paper the far reaching consequences of this mutual diluting effect are studied. It is shown that the RFPT-based adaptive controller still can be useful but the control strategy has to take far more complicated form.

UR - http://www.scopus.com/inward/record.url?scp=84868246613&partnerID=8YFLogxK

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U2 - 10.1109/LINDI.2012.6319479

DO - 10.1109/LINDI.2012.6319479

M3 - Conference contribution

SN - 9781467345194

SP - 157

EP - 162

BT - LINDI 2012 - 4th IEEE International Symposium on Logistics and Industrial Informatics, Proceedings

ER -