Euler-Bernoulli beam flatness based control with constraints

Maria Bekcheva (1) , Luca Greco (1) , Hugues Mounier (1) , Alban Quadrat (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments

The control of infinite dimensional systems with constraints is a notoriously difficult task. We consider a general class of linear systems governed by partial differential equations with boundary control. This problem is here treated in a quite natural manner through the freeness property, the analogue of differential flatness for linear systems. Any variable is then expressed as infinite order differential operators applied to the basis components, the analogue of the flat output components. The specialisation of the basis components are functions which are both of Gevrey regularity (in order for the infinite order differential operators to be convergent) and pertaining the flexibility of polynomial splines. An illustration is made through an Euler Bernoulli beam example.

Keywords: Flexible structures; infinite dimensional systems; rings; modules; controllability; Euler–Bernoulli partial differen-tial equation; Gevrey–Roumieu functions; input constraints

Domains: Engineering Sciences [physics]; Automatic

Maria Bekcheva, Luca Greco, Hugues Mounier, Alban Quadrat. Euler-Bernoulli beam flatness based control with constraints. IEEE 9th International Workshop on Multidimensional (nD) Systems, Sep 2015, Vila Real, Portugal. pp.1-6, ⟨10.1109/NDS.2015.7332635⟩. ⟨hal-01264912⟩