Conference proceeding
Capture into resonance: A novel method of efficient control
2003 European Control Conference (ECC), pp 3022-3027
01 Sep 2003
Abstract
In the present paper we propose a method to use capture into resonance to control the behavior of a certain class of dynamical systems. In many dynamical systems the coupling between the unperturbed system and weak periodic perturbations (wave) can be reduced to a purely resonant interaction occurring in the vicinity of a certain surface in the phase space. While resonance interaction can change invariants of the unperturbed system (e.g. energy), it is random in nature, and, consequently, is rather inefficient as a mechanism of regular transport. We propose a method to structure the resonance interaction with little additional cost. When the nominal dynamics brings the system close to a resonance surface we apply a short control pulse to force the capture of a phase point into the resonance with the wave. A captured point is transported by the wave across the energy levels. We apply the second pulse to release a phase point from the resonance when the desired energy level is achieved. As a model problem we consider dynamics of a charged particle in an electromagnetic field. We compare the cost of the proposed control with other methods and discuss possible applications of this technique.
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Details
- Title
- Capture into resonance: A novel method of efficient control
- Creators
- Dmitri Vainchtein - University of California, Santa BarbaraIgor Mezic - University of California, Santa Barbara
- Publication Details
- 2003 European Control Conference (ECC), pp 3022-3027
- Publisher
- IEEE
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- C. and J. Nyheim Plasma Institute
- Scopus ID
- 2-s2.0-84949104469
- Other Identifier
- 991021862313204721