Journal
EUROPEAN JOURNAL OF CONTROL
Volume 16, Issue 5, Pages 545-563Publisher
ELSEVIER
DOI: 10.3166/EJC.16.545-563
Keywords
Nonlinear systems; Shallow water equations; Passivity based control; Port-Hamiltonian distributed parameters models; Geometric reduction methods
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In this article a control algorithm for the reduced port Controlled Hamiltonian model (PCH) of the shallow water equations partial differential equations (PDEs) is developed This control is developed using the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method on the reduced PCH model without the natural dissipation It allows to assign desired structure and energy function to the closed-loop system The same control law is then derived using an energy shaping method based on Casimir s invariants, associated with a particular conservative interconnection between the boundary variables This gives a physical interpretation for the designed controller Finally, a stability analysis of the dissipative system in closed loop with the designed control is done using LaSalle s invariance principle Simulation results and an experimental validation of the control algorithm on an a micro-canal platform are presented showing the effectiveness of the control law
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