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

Kai Liu, YangQuan Chen, Paweł Domański, Xi Zhang
2018 Algorithms  
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
more » ... tifractal 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). Algorithms 2018, 11, 90 2 of 15 usually encompassing different hierarchical levels, therefore it is inconceivable for plant personals to maintain them on regular basis. For example, control loops are often multivariable and exhibit nonlinear dynamics stemming either from the plant, the transducers, the actuators, or even in some cases the controllers themselves in industrial applications. To address the above issues, the fractional order signal processing (FOSP) techniques have been proposed to better characterize the control process in the recent years with the notion of fractional calculus [2] . FOSP techniques include fractional order linear systems, autoregressive fractional integrated moving average (ARFIMA), Hurst parameter estimation, fractional order Fourier transformation (FrFT), fractals, Multifractal detrended fluctuation analysis (MFDFA), etc [3] . In addition, fractional order thinking is inevitable to gain more insights to characterize complex objects [4] . CPA is an important asset-management technology to maintain highly efficient operation performance of automation systems in production plants [5] . There are many classic performance assessment approaches, such as mean squared error (MSE), integral absolute error (IAE), statistical indexes, fractal indexes, etc. In addition, they can be various depending on systems under the different conditions, for example, with control action constraints, with deterministic disturbances, with setpoint changes. How to evaluate the quality of the control system performance is an essential issue for process engineers. In recent years, multifractal analysis has become the focus among the control engineering after some researchers gave applied it with CPA. The on-line control loop performance monitoring with non-Gaussian statistical and fractal measure has been proposed in [6] . Domański presents results of the research on alternative CPA measures applied to control quality assessment for SISO loop with generalized predictive control (GPC) controller in [7, 8] . However, as mentioned in [8], the above CPA analyses and observations are accomplished with a simple linear SISO case, which cannot capture the monofractal and multifractal properties, since the process complexity, cross-dependencies with varying delays, LRD and human factors are not reflected in simulations. Many intriguing questions are left behind in the above articles, such as multiple input multiple output (MIMO) and systems with significant delays. Moreover, the origins and meaning of multifractal properties with crossover phenomena are still needed to be analyzed. Therefore, it is worth investigating more complex scenarios, such as nonlinear, MIMO and systems with significant delay cases to verify method applicability and effectiveness. The aim of this paper is to cast more light on the new directions for process engineers and provide some novel techniques to assess the process performance. More specifically, the purposes of this paper are to:
doi:10.3390/a11070090 fatcat:d737xtancvbq3asiw6xc224orm