Analytical and experimental analyses of nonlinear vibrations in a rotary inverted pendulum

Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before design and application. The results such a study can significantly help prevent instability in closed-loop stabilized by avoiding the excitation system neighborhood its resonance. This paper investigates nonlinear oscillations rotary inverted pendulum (RIP) with full-state feedback controller. Lagrange’s equations are employed to derive accurate 2-DoF mathematical model, whose parameter values extracted both measurement 3D modeling real components. Although governing difficult solve, performing analytical solution great importance, mostly because, compared numerical solution, function as pattern. Additionally, generally more appealing engineers because computational costs less than those solution. In this study, perturbative method multiple scales used obtain coupled motion system. Moreover, parameters controller determined using findings reveal existence hardening- softening-type resonances at first second vibrational modes, respectively. leads wide frequency range moderately large-amplitude vibrations, avoided when adjusting time-varying set-point for vibration RIP verified experimental measurements, very good agreement observed between approaches.