Stability of haptic systems with fractional order controllers

Fractional order calculus is a generalization of the familiar integer order calculus in that, it allows for differentiation/integration with orders of any real number. The use of fractional order calculus in systems and control applications provides the user an extra design variable, the order of differointegration, which can be tuned to improve the desired behavior of the overall system. We propose utilization of fractional order models/controllers in haptic systems and study the effect of fractional differentiation order on the stability robustness of the overall sampled-data system. Our results demonstrate that fractional calculus generalization has a significant impact on both the shape and area of stability region of a haptic system and inclusion of fractional order impedances may improve the stability robustness of haptic rendering. Our results also include experimental verification of the stability regions predicted by the theoretical analysis.