On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems

Abstract

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Robust Regulation of Infinite-Dimensional Port-Hamiltonian Systems

“…Robust output regulation of port-Hamiltonian systems has been considered by the authors in [10,11] where first-and even-order port-Hamiltonian systems were considered, respectively. Outside robust regulation, stability, stabilization and dynamic boundary control of port-Hamiltonian systems have been considered, e.g., in [2,13,18,21]. This paper generalizes the results of [10,11] for port-Hamiltonian systems of arbitrary order N .…”

A novel passivity based controller for a piezoelectric beam

“…Moreover, if a step-response is applied to the closed-loop system proposed in [13], the dynamical controller (20) and the one proposed in [13] coincide. The storage function proposed in this paper takes on a differential passivity approach, while the storage function used in [13] to stabilize the system, takes on an incremental passivity approach.…”

“…Remark 3: In this note, the output of the open-loop system is the velocity at the tip, i.e. e p (1, t) =ẇ(1, t), The controller proposed in [13] is described as a PD-controller with respect to the longitudinal displacement at the tip, i.e. w (1, t).…”

“…It is well known that boundary control of these systems are constrained by the dissipation obstacle like the problems in [12]. A work around for this problem is recently presented in [13] using shifted passivity properties [14]. On the other hand, we propose an alternative methodology, which has the following key contributions:…”

“…Next, we start with showing the first condition (13) in Theorem 1. Firstly, it is straight forward to show that δ x S d (x * ) = 0.…”