Proceedings ArticleDOI
Motion planning and nonlinear simulations for a tank containing a fluid
François Dubois,Nicolas Petit,Pierre Rouchon +2 more
- pp 3232-3237
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TLDR
An algorithm is provided, based on Godunov scheme, with a dedicated way of dealing with boundary conditions, to numerically simulate the evolution of the nonlinear system and provide a way of checking the accuracy of the motion planning based on the tangent linear system.Abstract:
We consider a tank containing a fluid. The tank is subjected to a one-dimensional horizontal move and the motion of the fluid is described by Saint-Venant's equations. We show how to parameterize the trajectories of the linearized system thanks to the horizontal coordinate of a particular point in the system — the “flat output”, see figure 2- and a periodic function. The motion planning problem of the linearized model is solved in the general case of joining two steady states. Next we provide an algorithm, based on Godunov scheme, with a dedicated way of dealing with boundary conditions, to numerically simulate the evolution of the nonlinear system. Nonlinear simulations provide a way of checking the accuracy of the motion planning based on the tangent linear system.read more
Citations
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Flat systems, equivalence and trajectory generation
TL;DR: In this paper, the authors define flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential-geometric framework, utilizing the infinite dimensional geometry developed by Vinogradov and coworkers.
Journal ArticleDOI
Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems
Alan F. Lynch,Joachim Rudolph +1 more
TL;DR: In this article, the flatness property of the system is considered and the system solution can be differentially parameterized in terms of a flat output which, in the case considered, is a boundary value.
Journal ArticleDOI
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
TL;DR: In this paper, the authors consider a 1-D tank containing an inviscid incompressible irrotational fluid and prove the local controllability of this nonlinear control system around any steady state.
Journal ArticleDOI
Dynamics and solutions to some control problems for water-tank systems
Nicolas Petit,Pierre Rouchon +1 more
TL;DR: For irrotational flows, a new variational formulation of Saint-Venant equations is proposed that provides a simple method to establish the equations when the tank is moving and provide a simple and flatness-based algorithm for computing the steering open-loop control.
Journal ArticleDOI
Factoring and decomposing a class of linear functional systems
Thomas Cluzeau,Alban Quadrat +1 more
TL;DR: In this paper, a constructive homological algebra approach is used to study the factorization and decomposition problems for a class of linear functional (determined, over-defined, under-determined) systems.
References
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Journal ArticleDOI
Flatness and defect of non-linear systems: introductory theory and examples
TL;DR: In this paper, the authors introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous feedback, which subsumes the physical properties of a linearizing output and provides another nonlinear extension of Kalman's controllability.
Journal ArticleDOI
Paradigms and puzzles in the theory of dynamical systems
TL;DR: In this article, a self-contained exposition is given of an approach to mathematical models, in particular to the theory of dynamical systems, which leads to a new view of the notions of controllability and observability, and of the interconnection of systems.
Book
Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws
James Glimm,Peter D. Lax +1 more
Journal ArticleDOI
Boundary conditions for nonlinear hyperbolic systems of conservation laws
TL;DR: In this paper, the boundary conditions for nonlinear hyperbolic systems of conservation laws were formulated based on the vanishing viscosity method and the Riemann problem, and the equivalence between these two conditions was studied.