Szczegóły publikacji
Opis bibliograficzny
The motion planning problem and exponential stabilisation of a heavy chain, Pt. 1 / Piotr GRABOWSKI // International Journal of Control ; ISSN 0020-7179. — 2009 — vol. 82 no. 8 art. no. PII 912532143, s. 1539–1563. — Bibliogr. s. 1558–1559. — Publikacja dostępna online od: 2009-06-18
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 56985 |
|---|---|
| Data dodania do BaDAP | 2011-02-14 |
| Tekst źródłowy | URL |
| DOI | 10.1080/00207170802588188 |
| Rok publikacji | 2009 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | International Journal of Control |
Abstract
A model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations is interpreted as an abstract semigroup system on a Hilbert state space. Our aim is to solve the output motion planning problem of the same nature as in the case of an unloaded heavy chain (Grabowski, P. (2003), 'Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem', in Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics, 25-28 August, Midzyzdroje, Poland, pp. 77-86 (IS1-2-3.PDF)). In order to solve this problem we first analyse its well-posedness and some basic properties. Next, we solve the output motion planning problem using a substitute of the inverse of the input-output operator represented in terms of the Laplace transforms. A problem of exponential stabilisation is also formulated and solved using a stabiliser of the colocated type. The exponential stabilisation is proved using the method of Lyapunov functionals combined with some frequency-domain tools. The method of Lyapunov functionals can be replaced by the spectral or exact controllability approach as shown in the second part (Grabowski, P. (2008), 'The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II', Opuscula Mathematica, 28 (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota), 481-505) of the present article. A laboratory setup which allows verification of the results in practice is described in detail. Its dynamical model is used as an example to illustrate the theoretical results.
