Beam equation with saturating piezoelectric controls. Issue 16 (2019)

• Record Type: Journal Article
• Authors: Prieur, C.; Tarbouriech, S.
• Is Part Of: IFAC-PapersOnLine. Volume 52:Issue 16(2019)
• Page Start: 66
• Page End: 71
• Publication Date: 2019
• Subjects: infinite-dimensional systems -- saturation -- well-posedness -- semi-global asymptotic stability -- Lyapunov function; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2019.11.757
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper deals with a controlled beam equation for which the input is subject to magnitude saturation. A partial differential equation describes the dynamics of the deflection of the beam with respect to the rest position. The input is the voltage applied on an actuator located in a given interval of the space domain. Two kinds of control are considered: a static controller and a dynamical one. In both cases, the saturated control is indeed applied to the beam equation. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical beam equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a generalized sector condition to tackle the control nonlinearity, the semi-global asymptotic stabilization system is proven by Lyapunov-based arguments.