Abstract
This paper presents an efficient numerical method to realize discrete models of fractional order controllers for systems containing backlash nonlinearity. The presented method is to calculate fractional derivatives and integrals on inhomogeneous time intervals which are getting longer as the operation points go back toward the initial time. It leads to the effective quality which has low computational costs and enough accuracy. A practical controller design is applied for an inverted pendulum system containing gear-backlash. The simulation and experimental results show that the fractional control system has superior performance against backlash nonlinearity and thus the backlash vibration can be suppressed.
