A novel passivity based controller for a piezoelectric beam

Abstract

This paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. We present two new control methodologies by exploiting the integrability property of the port-variables. The derived controllers have a Proportional-Integral (PI) like structure. Finally, we present the simulation results and an in-depth analysis on the tuning gains explaining their transient and the steady-state behaviours.

On control of voltage-actuated piezoelectric beam: A Krasovskii passivity-based approach

“…C " C 11 `γ2 β) than for the models with a static electric field assumption. The systems (40) are known to be observable and exponentially stabilizable, see for instance [17]- [19], making these models interesting for controller design, as is shown in [36], [37]. This concludes the comparison of piezoelectric beams.…”

Exponential Stabilization of Port-Hamiltonian Boundary Control Systems via Energy Shaping

“…Under the conditions of Proposition 3.1, when u = 0, energy is not increasing along the trajectories of (7) since…”

“…On the other hand, convergence to the equilibrium can be obtained by damping injection, provided that a dual output to u is defined. With ( 4)- (7) in mind, the "natural" choice is…”

“…Boundary control systems (BCS) [1], [2] are dynamical systems modelled by partial differential equations (PDEs) with input and output defined at the boundary of the spatial domain. The study of the existence of solution and stabilisation of undamped or weakly damped linear BCS via static or dynamic controllers has raised a major attention in the last decade [3]- [7] due to an increase use of boundary controlled flexible / wave-like structures in engineering applications (smart grids, traffic-flows, compliant structures, etc.). For the class of linear BCS in port-Hamiltonian form introduced in [8], powerful techniques that exploit the geometric structure of the system to study the well-posedness or to design in a constructive manner stabilising control laws have been presented in the last years, see e.g.…”