# Design of PIDD(r) Controller for Robust Performance of Process Plants
## 5 Conclusions  
This research proposes a new controller structure for PIDD\({}^{\alpha}\), which includes the second derivative term from PIDD\({}^{2}\) and utilizes fractional order parameters exclusively for the second derivative term. The controller has shown robust performance while tested in both simulation and experiment compared to PID, PIDD\({}^{2}\), and FOPID controllers regarding transient response characteristics. The controllers' robust performance is also tested for fixed and variable set points and in the presence of external disturbances. In all the cases, the controller gain's parameters were chosen based on literature reviews, while the fractional order parameters were determined through trial and error. The proposed controllers have been evaluated for various systems, and the results indicate their superior performance in overshoot and settling time. The proposed controllers show better performance for the first-order system, with an overshoot of 9.6332% and a settling time of 14.2615 s. Similarly, the proposed and FOPID controllers exhibit the least overshoot for the second-order system of 0.0864% and 0%, respectively. The magnetic levitation system performs better with the proposed controller, which has the least overshoot and rise time of 12.8299% and 0.0075 s, respectively. In the case of the automatic voltage regulator system, the proposed controller also outperforms the others with the least overshoot and rise time of 0.1923% and 0.0232 s, respectively. The proposed controller for the pressure process plant has the least overshoot, rise time, and settling time of 4.838%, 2.6272 s, and 8.9543 s, respectively. On the other hand, all controllers for the flow process plant have 0% overshoot, but the proposed controller has the least rise time and settling time of 25.7819 s and 46.0495 s, respectively. For all the six considered process plants, the proposed controller achieved better dynamic responses, shorter settling times, faster rise times, and reduced overshoot. This research also highlights that selecting fractional-order parameters using trial and error is inadequate. Thus, future recommendations include utilizing the tuning algorithms covered in the literature review to enhance the controller's performance and implementing the proposed controller for other control loop operations, such as feedforward and cascade control loops.  
Figure 31: Disturbance rejection of controller structure for flow process plant.  
**Author Contributions:** Conceptualization, K.B. and R.I.; methodology, M.A.F. and R.I.; software, M.A.F.; validation, M.A.F., K.B. and P.A.M.D.; formal analysis, M.A.F. and P.A.M.D.; investigation, M.A.F. and P.A.M.D.; resources, K.B. and B.R.P.; data curation, M.A.F. and P.A.M.D.; writing--original draft preparation, M.A.F. and P.A.M.D.; writing--review and editing, K.B. and B.R.P.; visualization, K.B. and B.R.P.; supervision, K.B. and R.I.; project administration, K.B.; funding acquisition, K.B. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Short-Term Internal Research Funding (STIRF) with grant number 015 LA0-048.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
**Conflicts of Interest:** The authors declare no conflict of interest.