Vibration Control of Time-Varying Nonlinear Systems

A predesigned shaped input command is proposed to control the residual vibration of a nonlinear system with time-varying parameters. The designing process of the proposed shaped command accounts for the changes in the system parameters during the maneuver as well as satisfies any predefined input and system constraints. Knowing that the hoisting and lowering operations when conveying a payload in an overhead crane induce a time-dependent natural frequency and a positive-negative damping-like behavior, the proposed controlling technique was tested by suppressing the induced residual payload oscillation of the overhead crane with simultaneous traveling and hoisting/lowering maneuvers. The numerical results demonstrate the performance of the proposed shaped command in suppressing the residual vibration regardless of the hoisting and lowering profiles used during the maneuver.