In this paper, a low-order approximation (LOA) of fractional order PID (FOPID) for an automatic voltage regulator (AVR) based on the modified artificial bee colony (ABC) is proposed. The improved artificial bee colony (IABC) high-order approximation (HOA)-based fractional order PID (IABC/HOA-FOPID) controller, which is distinguished by a significant order approximation and by an integer order transfer function, requires the use of a large number of parameters. To improve the AVR system’s performance in terms of transient and frequency response analysis, the memory capacity of the IABC/HOA-FOPID controller was lowered so that it could fit better in the corrective loop. The new robust controller is named the improved artificial bee colony (IABC) low-order approximation (LOA)-based fractional order PID (IABC/LOA-FOPID). The performance of the proposed IABC/LOA-FOPID controller was compared not only to the original ABC algorithm-tuned PID controller, but also to other controllers tuned by state-of-the-art meta-heuristic algorithms such as the improved whale optimization algorithm (IWOA), particle swarm optimization (PSO), cuckoo search (CS), many optimizing liaisons (MOL), genetic algorithm (GA), local unimodal sampling (LUS), and the tree seed algorithm (TSA). Step response, root locus, frequency response, robustness test, and disturbance rejection abilities are all compared. The simulation results and comparisons with the proposed IABC/LOA-FOPID controller and other existing controllers clearly show that the proposed IABC/LOA-FOPID controller outperforms the optimal PID controllers found by other algorithms in all the aforementioned performance tests.

Recently, automotive manufacturers have prioritized cruise control systems and controllers, recognizing them as essential components requiring precise and adaptable designs to keep up with technological advancements. The motion of vehicles is inherently complex and variable, leading to significant non-linearity within the cruise control system (CCS). Due to this non-linearity, conventional PID controllers often perform suboptimally under varying conditions. This research introduces a fractionalized-order PID (FrOPID) controller, which has an extra parameter that makes regular PID controllers work better. A comparative analysis is conducted between classical PID controllers and FrOPID controllers optimized using three metaheuristic algorithms: Harris Hawks Optimization (HHO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). The evaluation is carried out using a linearized model of the vehicle cruise control system (VCCS). The results demonstrate that fractionalized-order PID controllers significantly outperform conventional PID controllers, particularly regarding rise time and settling time. Among the designs that were considered, the one that combines HHO and FrOPID works the best at finding a balance between responsiveness and stability. It is also the most durable and flexible, able to adapt to changes in vehicle mass and environmental conditions. This highlights the effectiveness of fractionalized-order controllers in managing the dynamic behavior of vehicles.

Drilling operations can encounter considerable challenges posed by strong, coupled vibrations that exert a complex influence on rotary drilling system performance. These vibrations are classified into three distinct types based on their propagation direction: axial, lateral, and torsional. Previous research efforts have predominantly focused on examining each vibration type in isolation. However, the effectiveness and resilience of developed controllers are profoundly affected by the often overlooked coupling effects arising from other types of vibrations. In this study, we propose the implementation of a Proportional-Integral-Derivative (PID) controller for the coupled Axial-Torsional vibration system. The research presented herein is dedicated to investigate the performance of the controller under strongly coupled vibrations. To address the dynamic vibrations encountered during drilling, it is imperative to understand the intricate behavior of the drill bit in response to these vibrations before designing controllers to mitigate their impact. Numerous models have been proposed in the existing literature to elucidate the behavior of the drill string under axial-torsional vibrations. The objective of this research is to develop a comprehensive model of the drilling system and investigate the robustness of the PID controller to mitigate the adverse effects of coupled Axial-Torsional vibrations. By effectively analysing the obtained results, this study has contributed to the optimization and improvement of drilling operations under sever coupled vibrations.

Fractional calculus has been rediscovered by scientists and engineers in the last two decades, and applied in an increasing number of fields, namely control theory. The current research work presents the use of the fractional adaptive PID controller approach optimized by a genetic algorithm to improve the performances (rise time, setting time, overshoot, and mean absolute error) for aircraft by introducing a fractional order integrator and differentiator in the classical feedback adaptive PID controller. To validate the arguments, the effectiveness and performance analysis of the proposed fractional order adaptive PID controller optimized by a genetic algorithm have been studied in comparison to the classical adaptive PID controller. Numerical simulation and analysis are presented to verify the best controller. The fractional order adaptive PID gives the best results in terms of settling time, rise time, overshoot, and mean absolute error. This approach can also be generalized to other fractional and integer systems in order to improve their performances and noise rejection.