A PDE approach to the derivation of the Brayton-Moser form for power-shaping control
(2012) 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) — Location: Orlando, Florida, USA (12.December.2011)
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- Abstract
- (en) Power-shaping control is an extension of energy-balancing passivity-based control based on a particular form of the dynamics, the Brayton-Moser form. One of the main difficulties in this approach is to write the dynamics in the suitable form since it requires the solution of a partial differential equation (PDE) system with an additional sign constraint. Here a general methodology is described for solving this partial differential equation system. The set of all solutions to the PDE system is given as the solution of a linear equation system. A necessary condition is given so that a solution of the linear system which meets the sign condition exists. This methodology is illustrated on a chemical reactor example, where the physical knowledge of the system is used to find a suitable solution.
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Citations
Favache, A., Dochain, D., & Winkin, J. (2012). A PDE approach to the derivation of the Brayton-Moser form for power-shaping control. 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, Florida, USA. https://doi.org/10.1109/CDC.2011.6160968