A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

The significant task for control performance assessment (CPA) is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties of Hurst exponent estimations and proposes a novel method for feature extraction of the nonlinear multi-input multi-output (MIMO) systems. At first, coupled data from real industry are analyzed by multifractal detrended fluctuation analysis (MFDFA) and the resultant multifractal spectrum is obtained. Secondly, the crossover points with spline fit in the scale-law curve are located and then employed to segment the entire scale-law curve into several different scaling regions, in which a single Hurst exponent can be estimated. Thirdly, to further ascertain the origin of the multifractality of control signals, the generalized Hurst exponents of the original series are compared with shuffled data. At last, non-Gaussian statistical properties, multifractal properties and Hurst exponents of the process control variables are derived and compared with different sets of tuning parameters. The results have shown that CPA of the MIMO system can be better employed with the help of fractional order signal processing (FOSP)