Enhancing the Z-width of Haptic Rendering with a Compensator

Abstract

Discretization of signals can generate additional energy in the haptic systems, and make them unstable. The discretization effect becomes worse as stiffness of the virtual environment and sampling time increase. This paper presents a compensator to increase the Z-width, commonly used as a performance index of the haptic rendering. Zero-order hold (ZOH) and sampler are approximated using Padé approximation, and digital compensators are designed using a firstorder hold. Z-width of the system using the developed compensator is analyzed based on the uncoupled stability condition. The compensator improves the gain margin of the haptic system during rendering of stiff environment. Experiment results show that the maximum renderable stiffness using the compensator is improved by 22.8 times when the environment damping is zero.