Studies on the analysis of nonlinear processes via functional expansions—I. Solution of nonlinear ODEs

Batıgün, Ayşegül; Harris, Kenneth R.; Palazoğlu, Ahmet

doi:10.1016/s0009-2509(97)00117-6

Cited by 16 publications

(2 citation statements)

References 11 publications

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“…For many cases, the product generation rate ε is proportional to μ. Hence the first and third equations in eq 1 are mathematically identical, which is clearly seen after the Laplace−Borel transform 25 of both equations,…”

Section: ■ Unforced Process Modeling and Analysismentioning

confidence: 78%

“…For many cases, the product generation rate ε is proportional to μ. Hence the first and third equations in eq are mathematically identical, which is clearly seen after the Laplace–Borel transform of both equations, where x 0 is the transform variable and c is the constant satisfying ε = c μ. The integrating factor could eliminate P if eq is applied.…”

Section: Unforced Process Modeling and Analysismentioning

confidence: 87%

See 1 more Smart Citation

Strategies for the Analysis of Continuous Bioethanol Fermentation under Periodical Forcing

Zhai

Palazoğlu

Wang

et al. 2017

Ind. Eng. Chem. Res.

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The process of continuous bioethanol fermentation often exhibits strong nonlinear dynamics and tends to generate self-oscillatory-state trajectories. The aim of this work is to further investigate such oscillators by coupling with outside periodic forcing, so as to improve process performance. To that end, several strategies for analyzing periodically forced self-oscillatory processes are proposed. By periodically and deliberately forcing an operational parameter, the behavior of the forced fermentor is investigated using limit cycle bifurcation analysis. Specifically, periodic doubling and Neimark–Sacker bifurcations are investigated with limit cycle continuation diagrams. The limit cycle bifurcation analysis is compared with the simulation-based methods, such as stroboscopic and maximum bifurcation maps, and it is shown to be an efficient analysis tool for the periodically forced self-oscillatory system. Process performance enhancement by designing the fermentor to be self-oscillatory is also discussed, as well as the possibility of controlling the oscillatory behavior using external periodic forcing.

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Section: ■ Unforced Process Modeling and Analysismentioning

confidence: 78%

Section: Unforced Process Modeling and Analysismentioning

confidence: 87%