Hybrid input shaping to suppress residual vibration of flexible systems

This paper presents a hybrid input shaping method to eliminate residual vibration of multi-mode flexible systems. This method, initially designed for one degree of systems, is modified to apply on linear and nonlinear multi-mode systems. In this method, firstly the flexible system is uncoupled using modal analysis method, and then the parameters of the decoupled system are used to shape the command template signal. A ramp plus ramped cycloid plus ramped versine is proposed as the command template signal to be preshaped. The template function is preshaped to yield zero residual vibration for point to point motion and then the resulting trajectory is convolved with a sequence of two impulses to obtain a twice shaped input. The proposed method is applied to eliminate residual vibration of a linear multimass and flexible joint manipulator types of systems. Simulation results show that the oscillations are considerably decreased with a high degree of robustness in the presence of system parameters uncertainty.