Control Of Impacting Dynamical Systems

Impacting systems are encountered frequently in nature, and often in mechanical systems. Impacts can be undesirable in some applications, and desirable and deliberate in others. A subset of impacting systems are vibro&ndashimpact systems, wherein the impacts arise during vibrations or oscillatory behavior. Considering their potential prominence in a number of day&ndashto&ndashday applications, such vibro&ndashimpact systems have become the subject of extensive research in the past few decades. A significant number of these studies have been specifically aimed at controlling vibro&ndashimpact systems. To date, a wide variety of control algorithms have been proposed, a subset of which account for the effects of noise in an attempt to validate their utility in practical application. This work focuses on exploring the dynamics of a single&ndashdegree&ndashof&ndashfreedom (SDOF) vibro&ndashimpact system. The system has been modeled and subsequently controlled using an existing control algorithm which finds its origins in the Ott&ndashGrebogi&ndashYorke (OGY) method designed to control chaos. This particular control algorithm is discrete in that it indirectly affects the motion of the oscillating mass in a SDOF system, by bringing about discrete changes in the position of the impact obstacle. The discrete nature of control, which has been validated in simulation here, makes it more feasible and easier to implement in practice, as compared to an algorithm which relies on the continuous control of the oscillating mass. To validate the practicality of this algorithm, in the absence of experiments, a noise&ndashsampling technique was implemented to impose noise on system parameters in accordance with the severity of uncertainty they are likely to see in practice. Simulations have shown that the control algorithm is robust to parameter uncertainty. Thus, this control algorithm promises significant utility in practical applications