A Neumann subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constant-free upper and lower bounds for non-linear outputs of the Helmholtz equation in two-dimensional exterior domains is presented. The bound procedure is firstly formulated, with p
A three-dimensional finite element model for the control of certain non-linear bioreactors
โ Scribed by J. Tervo; M. Vauhkonen; P. J. Vauhkonen; J. P. Kaipio
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 182 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0170-4214
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โฆ Synopsis
This paper deals with the dynamics of non-linear distributed parameter "xed-bed bioreactors. The model consists of a pair of non-linear partial di!erential (evolution) equations. The true spatially three-dimensional situation is considered instead of the usual one-dimensional approximation. This enables one to take into account the e!ects of #ow pro"les and the true location of the measurement transducer. The (output) evolution of the corresponding open-loop control system is simulated. Furthermore, the associated closed-loop system with respect to the relevant output function is considered. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on the state feedback linearization.
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