| 1. |
- Aguilar, Luis T., et al.
(author)
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Generating oscillations in inertia wheel pendulum via two-relay controller
- 2012
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In: International Journal of Robust and Nonlinear Control. - Malden : Wiley-Blackwell. - 1049-8923 .- 1099-1239. ; 22:3, s. 318-330
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Journal article (peer-reviewed)abstract
- The problem of generating oscillations of the inertia wheel pendulum is considered. We combine exact feedback linearization with two-relay controller, tuned using frequency-domain tools, such as computing the locus of a perturbed relay system. Explicit expressions for the parameters of the controller in terms of the desired frequency and amplitude are derived. Sufficient conditions for orbital asymptotic stability of the closed-loop system are obtained with the help of the Poincare map. Performance is validated via experiments. The approach can be easily applied for a minimum phase system, provided the behavior of the states of the zero dynamics is of no concern. Copyright (C) 2011 John Wiley & Sons, Ltd.
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| 2. |
- Sætre, Christian Fredrik, et al.
(author)
-
Robust orbital stabilization : A Floquet theory-based approach
- 2021
-
In: International Journal of Robust and Nonlinear Control. - : John Wiley & Sons. - 1049-8923 .- 1099-1239. ; 31:16, s. 8075-8108
-
Journal article (peer-reviewed)abstract
- The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched- and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.
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