A synchronization-based state observer for impact oscillators using only collision time information

• Published in: International journal of robust and nonlinear control Vol. 26; no. 12; pp. 2542 - 2563
• Main Authors: Baumann, Michael, Leine, Remco I.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.08.2016; Wiley Subscription Services, Inc; Wiley
• Subjects: Automatic; Coupling; Design engineering; Engineering Sciences; impact theory; Inequalities; Initial conditions; master-slave synchronization; measure differential inclusion; non-smooth dynamics; Oscillators; State observers; Synchronism; Synchronization; unilateral constraint; measure differential inclusion; unilateral constraint; impact theory; non-smooth dynamics; master–slave synchronization
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3460

Summary We present the design of a state observer for Lagrangian systems subjected to frictionless geometric unilateral constraints. A master–slave synchronization setup is used in which the unidirectional coupling only consists of the information of the impact time instants. After a brief synchronization phase, the obtained observer replicates the full state of the observed system, independently of the initial conditions and even in the presence of accumulation points (Zeno behavior). The key idea is that the (virtual) observer system is subjected to switched kinematic unilateral constraints such that it may enjoy the property of incremental stability when the impact law is maximal monotone. The main inequality impact laws for hard unilateral constraints, that is, the generalized Poisson's and Newton's impact law, are under mild assumptions maximal monotone, which is a stronger condition than dissipativity. The results are applied to two different examples of mechanical impact oscillators. Copyright © 2015 John Wiley & Sons, Ltd.