Controllability and observability of linear delay systems : an algebraic approach
M. Fliess, H. Mounier (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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Displaying similar documents to “Tracking control of a vibrating string with an interior mass viewed as delay system”
Controllability and observability of linear delay systems : an algebraic approach
On a class of linear delay systems often arising in practice
Michel Fliess, Hugues Mounier (2001)
Kybernetika
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We study the tracking control of linear delay systems. It is based on an algebraic property named -freeness, which extends Kalman’s finite dimensional linear controllability and bears some similarity with finite dimensional nonlinear flat systems. Several examples illustrate the practical relevance of the notion.
Tracking control of a vibrating string with an interior mass viewed as delay system
H. Mounier, J. Rudolph, M. Fliess, P. Rouchon (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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A vibrating string, modelled by the wave equation, with an interior mass is considered. It is viewed as a linear delay system. A trajectory tracking problem is solved using a new type of controllability.
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
Jean-Michel Coron (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
Exact boundary controllability of a hybrid system of elasticity by the HUM method
Bopeng Rao (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.