Open AccessOn the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller
Author(s) -
Y. A. Amer,
Taher A. Bahnasy,
Ashraf M. El-Mhlawy
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i130268
Subject(s) - control theory (sociology) , controller (irrigation) , nonlinear system , matlab , consistency (knowledge bases) , displacement (psychology) , derivative (finance) , beam (structure) , time derivative , stability (learning theory) , resonance (particle physics) , steady state (chemistry) , mathematics , physics , mathematical analysis , computer science , control (management) , chemistry , optics , geometry , artificial intelligence , psychotherapist , financial economics , biology , operating system , psychology , quantum mechanics , machine learning , agronomy , economics , particle physics
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.