Parametric Control of Oscillations

Abstract

Any oscillating system is described by certain parameters, and very often these parameters can be dynamically changed in a certain way to reach control goals. We overview a number of designs in which periodic variation of parameters in linear time-variant and nonlinear systems is the main control paradigm. We use frequency analysis and one-frequency approximation as the mathematical instrument. The approach that is also known as stationarization uses equivalent transfer functions for each time-variant and nonlinear element and reduces the stability analysis to classical Nyquist plot. The study presents in a unified framework several problems that have been solved in the last decades and new ideas, such as parametric synchronizing of oscillation. As the approach uses si mple mathematics, it can be used by field engineers for inventive oscillation control design for cranes, ships, rotors and many other vibrating systems.