@inproceedings{6197b4f293cd4112943d0dc5c93f0f9a,
title = "A Review on Self-oscillating Relay Feedback Systems and Its Application to Underactuated Systems with Degree of Underactuation One",
abstract = "A tool for the design of a periodic motion in underactuated systems via generating a self-excited oscillation of a desired amplitude and frequency driven by a variable structure control is reviewed. In this chapter, we overview the capabilities of the two-relay controller to induce oscillations in dynamical systems. In this chapter, we will focus on underactuated mechanical systems with degree of underactuation one, that is, n degrees-of-freedom and n-1 actuators only. Three methods to set the frequency and amplitude of oscillation and its application to one-degree of underactuation systems are reviewed: describing function method, Locus of the perturbed relay system design (LPRS), and Poincar{\'e} map based design. Theoretical and practical open problems are also discussed.",
author = "Aguilar, \{Luis T.\} and Igor Boiko and Leonid Fridman and Rafael Iriarte",
year = "2013",
doi = "10.1007/978-3-642-36986-5\_9",
language = "British English",
isbn = "9783642369858",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer Verlag",
pages = "187--205",
booktitle = "Advances in Sliding Mode Control",
address = "Germany",
note = "12th IEEE International Workshop on Variable Structure System, VSS 2012 ; Conference date: 12-01-2012 Through 14-01-2012",
}