Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems
- 9 November 2010
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 56 (3), 637-643
- https://doi.org/10.1109/tac.2010.2091187
Abstract
Compensation of infinite-dimensional input or sensor dynamics in SISO, LTI systems is achieved using the backstepping method. For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and observers that compensate the infinite-dimensional actuator or sensor dynamics. The explicit construction of the compensators are based on novel transformations, which can be considered of “backstepping-forwarding” type, of the finite-dimensional state of the plant and of the infinite-dimensional actuator or sensor states. Based on these transformations we construct explicit Lyapunov functionals which prove exponential stability of the closed-loop system, or convergence of the estimation error in the case of observer design. Finally, we illustrate the effectiveness of our controller with a numerical example.Keywords
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