# Design of PIDD(r) Controller for Robust Performance of Process Plants
## 4 Experimental Study
### Real-Time Flow Process Plant  
The schematics of the real-time flow process plant are displayed in Figure 26. The process tank, VE 420, can hold up to 100 L of liquid from the product tank, VE 410, thanks to the assistance of a centrifugal pump P412. The tank's level can be adjusted using the hand valve, HV 420, while the process control valve, FCV 413, maintains a constant flow rate at the desired level. The pressure transmitter FT 413 measures the flow rate, converted into digital voltage values ranging from 0 to 5 volts. These values are then sent to the FIC 413 via a pressure-indicating controller, which sends the control signal to the host PC through I/O interface boards. Figure 27 illustrates the real-time flow process P&ID. The facility operates similarly to the previous pressure process plant, running in \"Remote Desktop Connection\" mode with PCI cards connecting the field instruments and the remote workstation. Figure 26: Schematic of real-time flow process plant. The transfer function of the pressure process plant can be derived from the open-loop response of the plant in Figure 28.  
Thus, the computed transfer function is given as  
\[G(s)=\frac{0.072}{0.126s+1}e^{-3s} \tag{15}\]  
Four controllers control the plant, and these controllers have similar parameters, transient response characteristics, and step response as previous systems. The controller parameters and transient response characteristics for the real-time flow process plant are given in Table 7. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Controller** & \(K_{P}\) & \(K_{i}\) & \(K_{H}\) & \(K_{H2}\) & \(\mu\) & \(\beta\) & \(\alpha\) & \(M_{P}\) (\%) & \(t_{r}\) (\(s\)) & \(t_{s}\) (\(s\)) \\ \hline PID & 1 & 1 & 0.1 & - & - & - & - & 0 & 25.8559 & 46.788 \\ PIDD\({}^{2}\) & 1 & 1 & 0.1 & \(-\)0.01 & - & - & - & 0 & 25.8284 & 46.2981 \\ FOPID & 1 & 1 & 0.1 & - & 0.99 & 0.1 & - & 0 & 27.2797 & 50.6053 \\ PIDD\({}^{*}\) & 1 & 1 & 0.1 & \(-\)0.01 & - & - & 2.05 & 0 & 25.7819 & 46.0495 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Controller parameters and transient response characteristics for real-time flow process plant. Figure 28: Open-loop response of flow process plant before and after Pade approximation. Figure 27: P&ID of the flow process plant. In Figure 29, the simulation results for set-point tracking performance indicate that all controllers have achieved 0% overshoot. However, regarding rise time, the proposed PIDD\({}^{\alpha}\) controller outperforms the PID and PIDD2 controllers with a time of 25.7819 s compared to 25.8559 s and 25.8284 s, respectively. The FOPID controller has the worst rise time at 27.2797 s. The same trend can be seen in settling time, where the PIDD\({}^{\alpha}\) controller performs better than its competitors with a time of 46.0495 s compared to the PID, PIDD2, and FOPID controllers with times of 46.788 s, 46.2981 s, and 50.6053 s, respectively. The process of variable set-point tracking involves changes to 2, 3, and 1.5 at 100 s, 200 s, and 300 s, respectively, from the initial value of 1 at zero seconds. These changes cover both positive and negative changes in the controller. The intervals between these changes ensure that the step responses reach their respective steady-state values, as noted in Table 7. Figure 30 shows that each controller structure can control the output to reach every set-point change following the step response. A disturbance magnitude of \(-1.2\) is introduced to the controller structure at 100 s for disturbance rejection to simulate real-world plant behaviour when external disturbances  
Figure 30: Variable set-point tracking of controller structure for flow process plant. Figure 29: Step response of controller structure for flow process plant. affect the overall process plant. Figure 31 demonstrates that each controller structure can control the output to achieve the set-point and reject the disturbance, as shown in the step response.