# Design of PIDD(r) Controller for Robust Performance of Process Plants
## 1 Introduction
### Control System Applications  
Due to their high productivity and accuracy standards, there is a growing interest in using intelligent control methods for robotic applications. Recent years have seen numerous advancements in this area, including an open-closed-loop control design using a PIDD\({}^{2}\)/PID controller to control a robot arm, as the authors in [26] proposed. The control parameters have been improved using iterative learning control, and the design has been tested in both simulation and real-time. However, more information is needed to evaluate its performance measures and viability compared to other controller designs. Unmanned aerial vehicles, such as quadcopters, are typically flown remotely from the ground or by onboard computers. However, quadcopters have significant power efficiency limitations due to their flying stability and their four motors' constant, quick acceleration. To address this issue, a hybrid FLC-PID-PIDD\({}^{2}\) controller is proposed with controller parameters tuned using complementary error minimisation algorithms [27]. The simulations showed that this design outperforms other controllers, such as FLC-PID and PID controllers, regarding response time and control accuracy, making it an effective measure for enhancing stability during unmanned aerial vehicle flights. Using magnetic levitation involves lifting or suspending a magnetic item by interacting with a magnetic field. The system requires dynamic adjustments of its electromagnets to maintain the desired position of the item. As the maglev system is naturally unstable, electronic feedback control is necessary to stabilise the levitated magnetic item. In [28], the authors proposed the PIDD\({}^{2}\)-PID controller for a magnetic levitation system, which uses the slime mould algorithm to tune its control parameters. The simulation results of this design were compared with other controllers like ASO-FOPID, AEF-FOPID, ABC-FOPID, SCA-PID, WDO-PID, and ABC-PID controllers, and it outperformed them in termsof performance measures. Similarly, in [2], the author proposed a method for optimal higher-order controllers, where multiple controllers such as PI2 IDD2, PI2 ID, PIDD2, PID2, and PI2D are tuned with multi-objective GA algorithms. The proposed design performs better in the angular velocity's transient response and the controller's control gain. It has been observed through practical implementations that the higher-order controllers perform better than the lower-order controllers, with slight deviations in performance measures among each other. In [4], the authors suggest using a PIDD2D3 controller for a ship power plant, which uses a digital control system simulation model and tests the proposed design's performance. The results were compared with PID and PIDD2 controllers, and the proposed controller performed better. A marine internal combustion engine is an essential component of a ship's propulsion system that provides power. The efficiency of MICE is greatly affected by the temperature and pressure of the coolant, lubricating oil, and fuel in the engine's fuel line. The design constraints of these automated control systems come from the heat exchangers, making adjusting the temperature and pressure of lubricating oil and coolant challenging. In [29], the PIDD2 controller proposed by the authors for the fuel preparation system of a combustion engine outperforms the PID controller in terms of integral criterion, oscillation index, and control parameter deviation. Similarly, the controller design proposed in [30] for the hydraulic actuator, utilising a feedforward PIDD2, is proven superior in step response compared to the PID controller. The valve-controlled hydraulic motor speed servo system, known for its quick, accurate, and efficient response due to the high-frequency response of the servo valve, is typically used in low- and medium-power applications requiring excellent accuracy.