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Inversion‐based trajectory planning for the heat equation with temperature‐dependent parameters and radiation boundary conditions
Author(s) -
Utz Tilman,
Meurer Thomas,
Wild Daniel,
Kugi Andreas
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700946
Subject(s) - discretization , feed forward , control theory (sociology) , heat equation , inversion (geology) , mathematics , boundary value problem , nonlinear system , convergence (economics) , mathematical analysis , boundary (topology) , flatness (cosmology) , physics , computer science , engineering , control (management) , control engineering , geology , paleontology , cosmology , structural basin , artificial intelligence , quantum mechanics , economic growth , economics
Abstract This contribution is concerned with the trajectory planning for the nonlinear heat equation with radiation boundary conditions (BCs). For this, the infinite‐dimensional model is spatially discretized using finite differences. The discretized finite‐dimensional model serves as a basis for a flatness‐based feedforward control design. In the case of constant physical parameters, it is shown that the thus obtained feedforward controller converges to the feedforward controller for the original infinite‐dimensional problem in the limit as the discretization step size tends to zero. In the case of temperature‐dependent parameters, simulation results illustrate the convergence behavior. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)