Time delay compensation using equivalent elastic force feedback

This paper proposes a novel time-delay compensation based on the feedback of an elastic force from a wave system. In the previous research, the authors derived wave representation of a time-delay system and showed that there is equivalence between a resonant system, which is expressed by the wave equation, and a time-delay system: both systems consist of a position-input system and a wave-transmission system. Considering the above equivalence, we can infer that the cause of vibrations in the time-delay system is the robustness of the position-input system against the wave-transmission system, as in the case of the resonant system. To reduce the robustness, the feedback of an equivalent elastic force, which is derived from the wave representation, is introduced according to the concept of a resonant ratio control, which is one of vibration control method on a two-mass resonant system. Because the feedback of the elastic force can reduce the equivalent mass of the position-input system, the vibrations due to the time delay are suppressed. The disturbance-suppression performance of the proposed method is superior to that of a Smith predictor and a communication disturbance observer because the proposed method can maintain the feedback characteristic. The validity of the proposed method is confirmed by simulation and experimental results.