Minimizing residual vibrations for non-zero initial states: Application to an emergency stop of a crane

This paper presents an approach to design command inputs for the reduction of residual vibrations in mechanical systems for nonzero initial states. The technique starts with the development of a standard input shaper in a second order oscillator, and adds the initial states of the system to the formulation. However, it is proven that the obtained input shaper does not guarantee a null residual vibration when it is convolved with any unshaped command. To obtain an analytically proven zero-vibration response, it is required to include the parameters that characterize the response of the system to a selected normalized unshaped command in the formulation. By introducing an appropriate processing time delay and by measuring the initial states using a feedback sensor, the proposed method has been applied in a real time scenario where an emergency stop of a crane is required, assuming that initially the payload is swaying. The analyzed systems are those that can be modeled as discrete linear ones and can be described with constant parameter motion equations. Experimental results show the efficacy of the developed method with its application to a scaled crane test platform.