(untitled) (European Journal of Pure and Applied Mathematics, 2023)
This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.