Effect of negative velocity feedback control on the vibration of a nonlinear dynamical system

In this paper, a system of nonlinear, second-order differential equations describing the oscillations of a cantilever beam has been considered and solved. A proportional derivative (PD) and negative derivative feedback (NDF) controllers are applied for reducing the vibrations. MSPT as one of the perturbation techniques is used to get solutions for the system of first approximation with applying NDF controller and second approximation with applying PD controller. The worst resonance case is the primary resonance case for PD controller and the simultaneous [primary and internal] resonance case for NDF controller. Frequency response curves are obtained and the stability of the steady-state solution is studied near the selected resonance case. Effect of the parameters on the response curves are examined. A comparison between the two proposed controllers are explained numerically.