Design of Quasipolynomial-Based Controllers with Dynamical Parameters—Application to Active Vibration Damping

Sami Tliba (1) , Islam Boussaada (1, 2, 3) , Silviu-Iulian Niculescu (2, 1) , Ricardo Falcón-Prado (1)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 IPSA - Institut Polytechnique des Sciences Avancées

Recent works on delay systems have seen the emergence of a new control structure based on delayed actions, including an auto-regressive term carrying on the control variable, with the purpose of achieving a partial pole placement in closedloop for linear time-invariant systems of finite dimension. The ensuing controllers, called quasipolynomial-based controllers, correspond to some output feedback control laws with constant parameters. This specific feature has a limited number of degrees of freedom, limiting the potential performances in closed-loop. To overcome this issue, the original quasipolynomial-based controller is enhanced by using dynamical parameters, allowing to increase the number of degrees of freedom available for the controller's design. It turns out that the use of dynamical parameters corresponds to linear filtered terms in the control law of the original one. To emphasize the benefits brought by such a controller, the active vibration damping problem is addressed for a flexible mechanical structure equipped with a collocated pair of piezoelectric sensor and actuator.

Mots clés: Active vibration damping; Time-delay systems; Frequency domain; Control design; MID property

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]

Sami Tliba, Islam Boussaada, Silviu-Iulian Niculescu, Ricardo Falcón-Prado. Design of Quasipolynomial-Based Controllers with Dynamical Parameters—Application to Active Vibration Damping. Control Theory and Inverse Problems, Springer Nature Switzerland, pp.241-263, inPress, Trends in Mathematics, 978-3-031-68045-8. ⟨10.1007/978-3-031-68046-5_12⟩. ⟨hal-04844537⟩