# Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems
## 5 Experimental Results
### Results of Tank 1  
Considering the system dynamics, the best parameter values for the controllers were provided to the system, and the control performances of the FF-PI, CNPIR, and FO-APIDSMC controllers for Tank 1 were obtained, as shown in Figure 9. In the experiments, the best controller parameters determined for Tank 1 are presented in Table 2. To achieve these optimal sensitivity parameters, simulation studies were first conducted. During the simulation studies, suitable parameter ranges were defined using a trial-and-error method. In real-time experiments, small variations were made to these parameters to obtain the optimal controller gain values. The error of the Tank 1 level in the real-time process can be described as the discrepancy between the provided reference and the actual measured trajectory. In the provided Figure 10, the tracking error of Tank 1 under the control of FF-PI, CNPIR, and FO-APIDSMC controllers is visualized. As seen, the FO-APIDSMC controller produces the most stable and robust performance in terms of error tracking compared to the other controllers. Its error curve (black line) maintains close proximity to zero with minimal overshoot and faster convergence to steady-state. The reduced error values indicate the superior performance of FO-APIDSMC in terms of precision and stability, especially in handling rapid setpoint changes. This enhanced performance is due to the FO-APIDSMC's adaptive capabilities, which allow it to adjust to dynamic changes more effectively than the CNPIR and FF-PI controllers. The zoomed section (32-40 s) highlights that the FO-APIDSMC controller significantly outperforms the others in minimizing tracking error, reinforcing its advantage in providing a more accurate control response under transient conditions. This superiority of FO-APIDSMC is crucial for applications requiring high-precision control, such as liquid level regulation in industrial processes. In Figure 10, the square wave reference exhibits a minimal error percentage for the suggested FO-APIDSMC method, while the step reference \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**FF-PI Parameters**} \\ \hline \(\text{K}_{\text{p1}}=7.0152\) & \(\text{K}_{\text{i1}}=9.2061\) & \(\text{K}_{\text{f1}}=2.354\) \\ \hline \multicolumn{3}{c}{**CNPIR Control Parameters**} \\ \hline
**Square Wave** & G = 0.422 & h = 0.0025 & \(\text{K}_{\text{p}}=0.84\) & \(\text{K}_{\text{i}}=25\) & \(\text{K}_{\text{ir}}=0.014\) \\ \hline \multicolumn{3}{c}{**FO-APIDSMC Control Parameters**} \\ \hline \multicolumn{3}{c}{\(k_{p1}=4.11\), \(k_{\text{i1}}=2.28\), \(k_{\text{d1}}=0.35\), \(\rho_{1}=12.1\), \(\gamma_{1}=11.6\), \(\delta=0.01\), \(\alpha_{1}=0.34\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Controller parameters for Tank 1. Figure 9: Control performances of the FF-PI, CNPIR, and FO-APIDSMC controllers for Tank 1.  
shows a maximum error percentage of around 1.39% for the CNPIR method. In FO-APIDSMC, the maximum exceedance error value is negligible. To demonstrate the effectiveness of the proposed FO-PIDSMC controller compared to the FF-PI and CNPIR controller, the integral square error (ISE) values, as formulated in Equation (62), were calculated. In this article, the control capability of the system was compared based on the integral square error, considering the changes in the h delay parameter, the application of the disturbance, and the duration of the disturbance. \[ISE=\int_{0}^{t}e(t)^{2}dt \tag{62}\]  
The ISE error values of the graph obtained in Figure 10, comparing the control controllers without applying any disturbance to the system, are provided in Table 3. As seen, a lower ISE error value was achieved with the proposed FO-APIDSMC controller technique. The ISE error values obtained for the designed system with the FO-APIDSMC controller, according to the changes in the h delay parameter, are provided in Table 4. The results show that the ISE error value increases significantly when the h delay parameter exceeds 200 milliseconds.