## 1 Introduction  
Control loops are the most significant elements in automation systems. Product quality, operation safety, material and energy consumption, and thus the financial performance, are directly or indirectly linked to the performance of control systems. Control Performance Assessment (CPA) provides a benchmark for detecting and diagnosing root-causes of poor performance, reviewing and evaluating current performance, as well as improving control performance or avoiding performance degradation [1]. However, the mainstream assumption of Gaussian character of process signals contributes to the basis for CPA analysis algorithms and methods. On the contrary, a typical industrial process, which includes thousands of control loops, has witnessed many non-Gaussian behaviors, such as long range dependency (LRD), self-similarity, power-law of autocorrelation, infinite variance, spiky signals. Non-Gaussian signals and noises tend to produce large-amplitude fluctuations from the average value more frequently than Gaussian ones do [2]. Process control systems are very complex,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]. [PERSON] 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:  
1.