## 5 Results and Discussion  
This paper presented a CPA method with non-Gaussian statistical factors. First, we extracted four parameters \(\alpha\), \(\beta\), \(\gamma\), \(\delta\) with \(\alpha\) stable distribution and calculated the multifractal spectrum width \(\Delta(\alpha)\).  
It is well known that the PID tuning of the MIMO system is a time consuming and arduous work. Two sets of real data Var1, Var2, Var3 and Var1', Var2', Var3' with different PID parameters are compared in the end of article, in which the former settings are conservative and latter ones are more aggressive. In Table 1, the proposed FOSP method has been conducted according to the previous sections. The aggressive tuning with small \(\alpha\) depicts the broadness and fat tails of the distribution of the underlying process. Moreover, the absolute values of \(\beta\), \(\gamma\), \(\delta\) indicate the worse behavior with the latter tuning.  
In addition, the multi-scale Hurst spline fit with crossovers are located, compared with single Hurst estimation. Using multiple Hurst exponent fitting at different scales representing the dynamic behavior of the system with noise in Table 2.  
Review of the persistence properties of the data reveals visible effects of tuning and we observe changes in \(H_{1}\). For the first loop it moved from more sluggish value of 0.682 towards neutral tuning, while the second loop Var2 is slightly more sluggish. Loop Var3 is unchanged. However, the effect of tuning (whatever the set is) is evident in comparison with original MIMO system presented in R/S plots (Figures 6-8). Var1, Var2 require disturbance decoupling compared with aggressive tuning while Var3 requires possible redesign of the control philosophy and fine tuning.  
As it is well known there is no single universal measure that handles and detects all possible features that may be encountered in the industrial control. Each method well suites to the specific loop properties. Classical methods, such as integral, statisitical or minimum variance methods cover wide are of the applications. However, they may have difficulties in case of nonlinear and complex processes. FOSP approach enables to address controller performance, which depends on the controller tuning and control philosophy suitability. It allows to incorporate into the research the stable properties of the control error histogram. As distribution fitting may be inefficient, the multifractal spectrum can disclose further information about control properties. Complex cascaded properties of the overall  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variables** & \(\alpha\) & \(\beta\) & \(\gamma\) & \(\delta\) & \(h_{q}(-5)\) & \(h_{q}(5)\) & \(\Delta(\alpha)\) \\ \hline Var1 & 1.241 & 0.074 & 0.411 & 0.101 & 1.07 & 0.21 & 0.881 \\ Var2 & 1.634 & 0.056 & 0.025 & \(-\)0.030 & 0.82 & 0.06 & 0.757 \\ Var3 & 2.000 & \(-\)1.000 & 0.456 & \(-\)0.235 & 0.58 & 0.46 & 0.127 \\ \hline Var1’ & 1.171 & \(-\)0.156 & 0.456 & \(-\)0.235 & 1.04 & 0.25 & 0.798 \\ Var2’ & 1.695 & 0.287 & 0.123 & \(-\)0.246 & 0.71 & 0.41 & 0.307 \\ Var3’ & 2.000 & 1.000 & 1.567 & \(-\)0.208 & 0.57 & 0.53 & 0.069 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Indexes for variables with different PID tunings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & \(H_{1}\) & \(H_{1},H_{2}\) & \(H_{1},H_{2},H_{3}\) \\ \hline Var1 & 0.682 & 0.913, 0.450 & 0.991, 0.671, 0.392 \\ Var2 & 0.714 & 0.926, 0.500 & 0.964, 0.728, 0.436 \\ Var3 & 1.010 & 1.044, 0.974 & 1.041, 1.035, 0.930 \\ \hline Var1’ & 0.622 & 0.827, 0.416 & 0.905, 0.560, 0.415 \\ Var2’ & 0.824 & 1.099, 0.546 & 1.062, 0.951, 0.350 \\ Var3’ & 0.968 & 1.057, 0.878 & 1.006, 1.066, 0.751 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Hurst exponents at different memory scales.  
system, human impact or superposition of various impacts and oscillations (non-concave spectra) may be additionally assessed.