The impulse spectrum method for vibration suppression of a flexible multilink robot arm

Abstract

The impulse spectrum method is proposed systematically, extending the method of vibration control by model-based feedforward. The impulse spectrum of multilink suggests free feeding directly responsible for flexible precessions, capable of vibration suppression (VSP) while maintaining swift response. The invariance criterion over piecewise extents of multilink configuration is proposed, with the extent given by allowable insensitivity as the basis of outputs interference for VSP. On the invariance assumption, the spectral functions are extractable for the annihilator of vibration of multilink, with the oscillatory matrix for multimode oscillators derived as the key of the annihilator, showing the feasibility of simultaneous VSP of the oscillators of multilink. Robust VSP is ensured by designing the impulse spectrum with respect to the augmented oscillatory matrix of some order, and hybrid robustness against variation of concerned parameters that can reduce response delay. The properties of the impulse spectrum for VSP of flexible multilink are presented for the guidelines to design impulse spectra for diverse potential and purposes, including the metric array-based bandwide VSP of nonconcurrent multimode in favor of disturbance-rejection. Numerical simulations are conducted to validate the theoretical study, demonstrating the effectiveness of the method.