Compensation of a Class of Infinite-Dimensional Actuator Dynamics without Distributed Feedback

Abstract

This paper deals with output-based stabilization of a class of systems whose actuator dynamics can be described in terms of partial differential equations (PDEs). The main novelty of the proposed controllers lies in the fact that they avoid integral terms. This work is motivated by the recent efforts reported in the literature pursuing that goal for input-delay systems (which are equivalent to a cascade connection between an ordinary differential equation and a first-order hyperbolic PDE). The structure of the proposed control law is as simple as that of an observer-based feedback controller. The methodology is also developed for systems whose actuator dynamics are governed by diffusion, i.e., modeled by a parabolic PDE. In both cases, the exponential stability of the closed-loop is proved using Lyapunov-Krasovskii functionals. The feasibility of this approach is illustrated in simulations with a second-order unstable system.