Nonlinear vibration control of a piezoelectric beam with a fuzzy logic controller

Nonlinear vibration of a beam is active controlled with a fuzzy logic controller designed. The Von Karman's large deflection equation for a generally elastic beam partially covered by a macro fiber composite actuator (MFC) is established. Galerkin method is employed to convert the nonlinear partial differential equation derived into the nonlinear ordinary differential equation of motion, which is of Duffing's type. The method of multiple scales is adopted to figure out the relationship between the vibration amplitude and the nonlinear frequency. The nonlinear characteristics of the system are discussed when proportional and derivative feedback scheme is used. To depress the nonlinear vibration, a fuzzy logic controller is designed and the vibration of the beam is suppressed effectively.