Section: New Results

Pole placement techniques for time-delay systems

Participants : Islam Boussaada, Silviu-Iulian Niculescu, Sami Tliba [L2S, CentraleSupélec] , Fazia Bedouhene [University Mouloud Mammeri de Tizi Ouzou, Algeria] .

The interest in investigating multiple roots does not rely on the multiplicity itself, but rather on its connection with the dominance of this root, and the corresponding applications in stability analysis and control design. The work [31] extends the analytical characterization of the spectral abscissa for retarded time-delay system with real spectral values which are not necessarily multiple. The effect of the coexistence of such non oscillatory modes on the asymptotic stability of the trivial solution is explored. In particular, the coexistence of an appropriate number of real spectral values makes them rightmost-roots of the corresponding quasipolynomial. Furthermore, if they are negative, this guarantees the asymptotic stability of the trivial solution. As an application of the proposed rightmost-characteristic root assignment, the problem of the vibration damping for a thin flexible beam is considered in [33]. The considered beam is equipped with two piezoelectric patches: one of them works as a sensor and the other as an actuator. Each one of them is bonded on one side of the beam and both are collocated. The model of this system is obtained numerically thanks to a finite element modeling, leading to a linear state-space model. The design of a controller based on proportional and delayed-proportional actions on the input and output signals is proposed, where the properties of the proposed output feedback controller in terms of vibration damping and of robustness is discussed.