Abstract
This paper treats the question of feedback linearizing control oftwo-dimensional incompressible, unsteady wake flow. For definiteness,flow past a circular cylinder is considered, but the design approachpresented here is applicable to other flow control problems. Twofinite-dimensional lower-order models based on Proper OrthogonalDecomposition (POD) of dimension N with N actuators are considered.Models I and II are obtained using control function and penalty functionmethods, respectively. Control action can be achieved by a combinationof suction, injection, and synthetic jets. For the design ofcontrollers, it is assumed that the system matrices of the POD modelsare unknown. Nonlinear adaptive control systems for the two models arederived. For model I, nontrivial zero-error dynamics exists, which playa key role in the stability of the closed-loop system. But for model II,global adaptive trajectory control is achieved. In the closed-loopsystem, the mode amplitudes asymptotically follow the referencetrajectories. Simulation results for a 4-mode POD model obtained usingthe penalty function method are presented. These results show that inthe closed-loop system, unsteadiness in the mode amplitudes can besuppressed in spite of large uncertainties in the flow model.
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Singh, S.N., Myatt, J.H., Addington, G.A. et al. Adaptive Feedback Linearizing Control of Proper Orthogonal Decomposition Nonlinear Flow Models. Nonlinear Dynamics 28, 71–81 (2002). https://doi.org/10.1023/A:1014936903942
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DOI: https://doi.org/10.1023/A:1014936903942