Passivity‐based control of nonlinear active dynamic vibration absorber

Abstract

AbstractIn this article, a nonlinear active dynamic vibration absorber based on passivity‐based energy shaping control is proposed. Using the proposed method, the vibrations that are excited by force and velocity disturbances simultaneously can be controlled. The control law only uses the relative displacement and velocity of the vibration system, which can be easily measured by sensors. The numerical solutions to the partial differential equations are not required in our proposed method. The main idea of the controller's parameters design is to convert a plant system with a nonlinear dynamic vibration absorber into a desired system with multiple virtual skyhook dampers. We also derive the parameters' selection guidelines for the proposed controller. The global asymptotical stability is guaranteed through passivity‐based control theory, although the parameter design is based on linearization. We verify the effectiveness of the proposed controller by some simulations on a cart‐pendulum system.