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Invariant Slow Manifold Approach for Exact Dynamic Inversion of Singularly Perturbed Linear Mechanical Systems with Admissible Output Constraints
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- Authors
- Joono Cheong, Youngsu Cho, Seung-Ik Lee
- Issue Date
- 2012-06
- Citation
- Journal of Sound and Vibration, v.331, no.16, pp.3710-3720
- ISSN
- 0022-460X
- Publisher
- Elsevier,
- Language
- English
- Type
- Journal Article
- Abstract
- We propose an approach for the exact dynamic inversion of singularly perturbed second-order linear systems through asymptotic expansion in a singular parameter. We show that the inversion solution, corresponding to the invariant slow manifold, can be expressed as a converging infinite series under desired output constraints composed of exponential support functions in the complex domain. We provide systematic mathematical procedures to obtain the closed-form invariant slow manifold, along with required admissible boundary conditions. Numerical examples are given to validate the proposed approach. © 2012 Elsevier Ltd. All rights reserved.
- KSP Keywords
- Asymptotic expansion, Boundary conditions, Complex domain, Infinite series, Linear systems, Numerical examples, Output Constraints, Slow manifold, Support functions, closed-form, dynamic inversion