Abstract
Nonlinear time delay saturation controller (NTDSC) is used to minimize the vibrations of a vertical cantilever beam simulated as an airplane tail within harmonic excitation force. In the case of primary and 1:2 internal resonance as a simultaneous resonance case, an analytic solution is obtained by employing the multiple time scale perturbation technique to solve the nonlinear differential equations and modeling the system with NTDSC. Time histories and Poincare portraits were created to demonstrate the system without and with controller. The time-history response, as well as the impacts of the parameters on the system and controller, were simulated numerically using the MATLAB program. A good match is found when the approximate solutions are compared to the numerical simulations via the Runge-Kutta method fourth-order (RK4). The stability investigation of the steady state solution in the studied simultaneous resonance case is reviewed and analyzed via the Routh-Huriwitz approach. The impact of controller parameters and time delays on system response curves are examined. Also, the operation's safe zone is established from the outcomes of the effect via various values of time delays on the system after adding the control scheme. The numerical and analytical solutions at time-history were compared using the MATLAB program to confirm their comparability. The outcomes of this study were used to develop a theoretical foundation for the system's design and construction. A comparison is made with recently released papers to appear the difference between this study and the others.