Dynamical Analysis and Control of Parametric Surface Waves in a Nonlinear and Non-ideally Excited Tank

Abstract

In this work, we revisited and investigated the nonlinear parametric resonance of free surface oscillations of fluid inside a tank excited by a non-ideal power source with limited power supply. Numerical analysis of nonlinear dynamics is presented as phase portrait diagrams, power spectrum and maximum Lyapunov exponents to determine the regions in which the resonant sloshing vibrations have a chaotic or periodic behavior. We also present a State Dependent Riccatti Equation (SDRE) control design that can reduce the chaotic movement to a stable condition. The SDRE technique is based on the Linear Quadratic Regulator (LQR) and it has the characteristic of separating nonlinearity from the system and applying feedback control.