A Novell Backstepping Nonlinear Controller Design for Nonlinear Vibration Systems

Introducing basic design methodology for developing backstepping nonlinear controller for vibration control system. With a simplified second-order system model of nonlinear vibration system (Duffing’s equation), where, the process has illustrated the backstepping design step-by-step. Backstepping is a novel nonlinear design tool, which is based on constructing the Lyapunov function for the closed-loop systems and guarantees the stability and tracking performance through energy dissipation. In general, this nonlinear control design approach generates aggressive control effort to reduce the tracking error presented in this control system and significantly improve the system bandwidth. The effectiveness of the design scheme is shown through the computer simulation.