Control Design of Hybrid Systems via Dehybridization

摘要: Abstract Hybrid dynamical systems are those with interaction b etween continuous and discrete dynamics. For the analysis control of such concepts theories from either or domain typically readapted. In this thesis ideas p erturbation theory readapted for approximating a hybrid system using one. To purp ose, that ossess two-time scale prop erty, i.e. states evolving in fast time-scale slow time-scale, considered. Then, as singular averaging methods, is approximated by time system. Since nature process removed averaging, procedure referred to dehybridization thesis. It seen transitions required corresp ond switching all but one (modes). Here, notion dominant mode defined maximum interval sp ent non-dominant modes considered ‘small’ parameter which determines quality approximation. shown finite interval, solutions model averaged stay ‘close’ error them goes zero zero. utilize oses, cascade design scheme osed, where inner-loop artificially creates ehavior, while outer-loop exp onentially stabilizes approximate if origin common equilibrium oint modes, then sufficiently small values parameter, onential stability can e guaranteed. However, it not an some tra jectories ultimately ounded, ound eing function parameter. The approach used here defines works along lines robust stability. key technical difference though norm small, its integral small. This was motivated stick-slip drive, friction-based micro-p ositioning setup, op erates two distinct ‘stick’ ‘slip’. consists masses stick together when interfacial force less than Coulomb frictional force, slips otherwise. osed methodology illustrated through simulation erimental results on drive. 1