Investigating the Existence of Time Delay in Rotating Beams

Abstract

A mathematical model of a revolving beam at different speeds is examined. The approximation solution of the system behaviour in the resonance situation is studied through the application of the multiple time scales method to the nonlinear system of differential equations. We looked at the system when a proportional-derivative (PD) controller was used to apply delayed control to displacement and velocity. Using the Routh-Huriwitz method, the consistency of the steady state solution in the near-resonance scenario is evaluated and examined. We identify and examine the factors affecting the steady state solution of the different parameters. The MATLAB software package is used to obtain simulation effects. To demonstrate and contrast controller effects at different system settings, different response curves are used.