On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller
Y. A. Amer
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.
Taher A. Bahnasy
*
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
Ashraf M. Elmhlawy
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
*Author to whom correspondence should be addressed.
Abstract
A rotating beam at varying speed mathematical model is studied. Multiple time scales method is applied to the nonlinear system of differential equations and investigated the system behavior approximate solution in the instance of resonance case. We studied the system in case of applying the delayed control on the displacement and the velocity with Proportional–derivative (PD) controller. The consistency of the steady state solution in the near-resonance case is reviewed and analyzed using the Routh-Huriwitz approach. The factors on the steady state solution of the various parameters are recognized and discussed. Simulation effects are obtained using MATLAB software package. Different response curves are involved to show and compare controller effects at various system parameters.
Keywords: Non-linear dynamical system, multiple time scales method, active feedback controller, time delay