## 3 Results and Discussions
### Experimental Study
#### 3.2.2 Pressure Process Model  
The schematic diagram and piping and instrument diagram of the real-time pressure process plant illustrated in Refs. [40; 41; 42], provide a comprehensive overview of the system's operational dynamics. The pressure system is centred around the VL 202 buffer tank, specially designed to withstand the high pressure of up to 10 bar supplied by the centralized air compression system. The HV 202 manual valve enables precise control over the pressure. In contrast, the PCV 202 process control valve ensures that the pressure is constantly maintained at the desired level, allowing for a smooth and efficient operation. The PT 202 pressure transmitter facilitates accurate pressure monitoring by converting pressure values into digital voltage signals ranging from 0 to 5 V.  
The PIC 202 pressure indicator controller relays this voltage signal to the host PC via dedicated I/O interface cards, enabling real-time pressure process monitoring and control. This showcases a complex and comprehensive system architecture. The PT 202 pressure transmitter and PIC 202 pressure indicator controller suit various industries where precise pressure measurements are critical to operations. This technology ensures accurate and reliable pressure monitoring, ensuring smooth and efficient operations. Using the  
Figure 14: Flow process model’s disturbance response with compared controllers. open-loop response of the pressure process followed by its numerical analysis in Table 6, the transfer function of the process is given as  
\[G(s)=\frac{0.866}{1.365s+1}e^{-s}. \tag{12}\]  
Figures 15-17 show the step, set-point tracking, and disturbance-rejection responses of all the controllers in the pressure process plant. Controllers are employed to operate the plant to assess the system's stability, which is consistent with past methods and includes the addition of fractional and complex order controllers for comparison purposes. The resulting table and figure showcase the parameters, step response, and transient response characteristics, thoroughly assessing the control system's performance. The simulation study results revealed that the PID controller demonstrated a significant overshoot of 6.5841% with a settling time of 163.0095 s and a rise time of 18.5776 s. Conversely, the PI-PD controller exhibited a considerably lower overshoot of 0.3905%, albeit with a slightly longer settling time of 175.9587 s and a longer rise time of 38.7020 s. This comparison demonstrates that the PID controller trades off higher overshoot and faster settling and rise times. In contrast, the PI-PD controller has slightly longer settling and rise times but minimal overshoot. The optimal choice of these controllers depends on the specific application requirements, where it is essential to balance the overshoot and response time to optimize the system performance. In the fractional controllers, to evaluate the performance of FOPID and FOPI-FOPD controllers, the FOPID controller demonstrates a significant overshoot of 4.0610%, accompanied by a settling time of 162.1264 s and a rise time of 25.0510 s. In contrast, the FOPI-FOPD controller presents a considerably reduced overshoot, amounting to 0.2565%, albeit with a slightly longer settling time of 178.9595 s and a higher rise time of 40.4344 s. The comparison between the two controllers sheds light on the trade-off between the FOPID controller's faster settling time and shorter rise time, yet higher overshoot, and the FOPI-FOPD controller's minimized overshoot, prioritizing stability at the expense of marginally longer settling and rise times. The selection of the fractional controller depends on the specific application's needs, which requires careful consideration of the trade-off between the overshoot and response time for effective control system design.