On the control of complementary-slackness juggling mechanical systems

International audienceThis paper studies the feedback control of a class of complementary-slackness hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the "object") and a controlled one (the "robot"), linked by a unilateral constraint and an impact rule. A systematic and general control design method for this class of systems is proposed. The approach is a nontrivial extension of the one degree-of-freedom (DOF) juggler control design. In addition to the robot control, it is also useful to study some intermediate controllability properties of the object's impact Poincaré mapping, which generally takes the form of a non-linear discrete-time system. The force input mainly consists of a family of dead-beat feedback control laws, introduced via a recur-sive procedure, and exploiting the underlying discrete-time structure of the system. The main goal of this paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases

Study of charge-charge coupling effects on dipole emitter relaxation within a classical electron-ion plasma description

Studies of charge-charge (ion-ion, ion-electron, and electron-electron) coupling properties for ion impurities in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential without short-range Coulomb divergence. This work is motivated in part by questions arising from recent spectroscopic measurements revealing discrepancies with present theoretical descriptions. Many of the current radiative property models for plasmas include only single electron-emitter collisions and neglect some or all charge-charge interactions. A molecular dynamics simulation of dipole relaxation is proposed here to allow proper account of many electron-emitter interactions and all charge-charge couplings. As illustrations, molecular dynamics simulations are reported for the cases of a single ion imbedded in an electron plasma and for a two-component ion-electron plasma. Ion-ion, electron-ion, and electron-electron coupling effects are discussed for hydrogen-like Balmer alpha lines.Comment: 13 figures, submitted to Phys. Rev.