Wave transformation using unit delayed reflection

Wave variables have been used to overcome the transmission delay of a system from the viewpoint of passivity. During implementation of the wave transformation for the sampled-data system, a unit delay arises due to causality of the reflection wave. The property of the wave transformation using delayed reflection, which is different from the standard wave transformation, can be verified with the passivity condition of the scattering matrix. The unit delay on the reflection wave occasionally becomes a positive damping. From the passivity condition of the sampled-data system, the wave impedance can be designed such that the wave transformation using delayed reflection wave provides the effect of positive damping. As an example, the wave transformation using delayed reflection wave makes it possible that the stable haptic interface is achieved on the sampled-data system with appropriate wave impedance. The simulation and the experiment results show that the stable haptic interface can be accomplished by use of the wave transformation using delayed reflection.