Some remarks on discretisation of spatially invariant systems

0432834 - ÚTIA 2015 RIV PL eng C - Conference Paper (international conference)
Augusta, Petr
Some remarks on discretisation of spatially invariant systems.
Proceedings of the 19th International Conference on Methods and Models in Automation and Robotics. Miedzyzdroje: IEEE, 2014, s. 474-479. ISBN 978-1-4799-5082-9.
[The 19th International Conference on Methods and Models in Automation and Robotics. Miedzyzdroje (PL), 02.09.2014-05.09.2014]
R&D Projects: GA ČR GPP103/12/P494
Institutional support: RVO:67985556
Keywords : discretisation * invariant systems * discretisation schemes
Subject RIV: BC - Control Systems Theory

The paper deals with discretisation of 2-D spatially invariant systems. Three different discretisation schemes are used — Tustin’s approximation, backward difference scheme and Crank-Nicolson discretisation. Their properties and importance are discussed in the paper. As an example a heat conduction in a rod is considered. Its model discrete in both time and space is obtained using all the above mentioned difference schemes. To determine whether the discrete model converges to the solution, von Neumann analysis of stability is applied to each scheme. The system is stabilised with use of each of obtained discrete models. Numerical simulations are included. Experiments with changing the parameters of discretisation are also given.
Permanent Link: http://hdl.handle.net/11104/0237208