Fast Switching Transition Model Describing Parasitic Dynamics Intrinsically Induced by Discontinuous Control

Abstract

Variable Structure Control, in particular, inducing a Sliding Mode condition, might be affected by high frequency oscillations that reduce its performance. This behavior has been explained as the result of unmodelled dynamics in imperfect switching without regarding the intrinsic dynamics excited by a finite time transition in discontinuous control. In this paper, in order to provide a better understanding of the dynamics involved in the switching control, the author presents a model of fast switching transitions introducing the neglected dynamics of a almost instantaneous change, and analyses its effects on the natural dynamics of the plant using, as generic case of study, a second order linear plant. The analysis first recalls some basics differential equations concerning their general solution as the addition of both, the forced solution induced by the control input, and the homogeneous one of the free dynamics of the plant; then, introduces a switching model of the fast dynamic changes of a almost instantaneous transition to determine the excited free dynamic response, considering a second order linear system as a plant. Finally, discusses about its effects into the general dynamics of the plant inducing the oscillatory behavior observed in the state variables.