Fractional Control Performance Assessment of the Nonlinear Mechanical Systems

There are many approaches to assess control quality, starting from the mean-square error or the variance, through model-based or model-free approaches, to fractal or entropy measures. These indicators can be used for a variety of control systems. Nonlinear industrial applications pose new challenges. The indicator must be robust, reliable, and informative. It must cope with disturbances and uncertainties. Process complexity and its nonlinearities, mutual correlations, variable delays, and outlying anomalies or human influence should not limit it. Fractional calculus can meet these demands. The fractional order of the ARFIMA filter represents persistence of time series and it is a potential control quality index. The research shows that the Geweke-Porter-Hudak (GPH) fractional order estimator can assess control system quality. The research is validated using laboratory nonlinear mechanical servomechanism.