Frequency-modulation input shaping for multimode systems

This paper presents an input shaping strategy for vibration control of multimode systems. The strategy combines the use of single-mode input shaping techniques with a model-based frequency-modulation system. The strategy utilizes the fact that a single-mode input shaper can eliminate vibrations in a multimode system provided that, there exists a common frequency for which all frequencies of the system are odd multiples of that common frequency. Model-based feedback is used to modulate the frequencies of the system to the point where the odd multiple frequencies condition is satisfied. The primary mode frequency of the model-based feedback system is designed to be the common frequency that satisfies the aforementioned condition. Several single-mode input shapers are implemented with design frequencies equal to the primary mode frequency of the modulated system, thus eliminating vibrations in all modes of the system simultaneously. Simulations and experiments on multiple pendulum models are used to demonstrate the effectiveness of the performance of the frequency-modulation input shaping strategy.