Name
Abstract | ||
|---|---|---|
This paper is concerned with the energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1109/TAC.2016.2595263 | IEEE Trans. Automat. Contr. |
Keywords | Field | DocType |
Asymptotic stability,State feedback,Shape,Damping,Closed loop systems,Stability analysis | Control theory,Mathematical optimization,Control theory,Dissipation,State function,Dissipative system,Hamiltonian system,Root locus,Exponential stability,Casimir effect,Mathematics | Journal |
Volume | Issue | ISSN |
62 | 4 | 0018-9286 |
Citations | PageRank | References |
7 | 0.64 | 12 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alessandro Macchelli | 1 | 238 | 25.59 |
| Yann Le Gorrec | 2 | 43 | 11.22 |
| Ramirez, H. | 3 | 14 | 5.28 |
| Hans Zwart | 4 | 53 | 10.37 |