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.

This study proposes an adaptive control synthesis for a class of second-degree fractional order systems with different eigenvalues in the state-space domain. The proposed fractional order adaptive controller is a generalization of the MRAC controller for the class of scalar fractional order systems. In order to control the fractional order plant, an adaptive state space feedback controller is applied based on the error between the system output and a chosen reference model using a fractional adaptation law to make the fractional order plant track the fractional order reference model. We show that the resulting adaptive regulator is able to stabilize the fractional order second degree system with a satisfying performance. A simulation example illustrating these performance properties is provided along with a comparison with a fractional order sliding mode control (FOSMC) to demonstrate the superiority of the proposed control scheme.

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.

In recent years, there has been a significant increase in the study of fractional systems and fractional-order control (FOC), which has proven effective in enhancing plant dynamics, particularly in terms of disturbance rejection and response time improvement. Traditionally, the Proportional-Integral-Derivative (PID) controller has been valued for its simplicity and ease of parameter adjustment. However, as the complexity of control systems escalates, several specialised PID controllers have been designed to address specific challenges. Despite its effectiveness, the conventional PID controller often faces limitations in complex systems requiring high precision and adaptive dynamics. Researchers have increasingly focused on the Fractional Proportional-Integral-Derivative (FPID) controller to address these deficiencies. The FPID controller incorporates fractional integrators and derivatives, facilitating improved tuning of system dynamics and offering increased control over response characteristics. This study introduces a fractional integrator in PID control to improve trajectory tracking and reduce delay time in Selective Compliance Articulated Robot Arm (SCARA) systems. Unlike traditional PID controllers, which may struggle with high-frequency noise and parameter variations, the fractional integrator offers enhanced noise suppression and adaptability. The fractional PID approach is relevant beyond robotics, including many systems like temperature control, electrical motor regulation, power electronics, and biomedical control systems, where accuracy and resilience to disturbances are essential. Unlike traditional PID, the proposed technique offers more adaptability in handling transient responses and greater disturbance suppression, making it a viable solution for modern, complex control environments.

This chapter presents a fractional adaptive interval type-2 fuzzy logic control strategy based on active fractional sliding mode controller (FAIT2FSMC) to synchronize tow chaotic fractional-order systems. The interval type-2 fuzzy logic systems (IT2FLS) are used to approximate the plant dynamics represented by unknown functions of the system, and the IT2F adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. One of the main contributions in this work is the use of an IT2F and an adaptive fractional order PIλ control law to eliminate the chattering action in the control signal. Based on fractional order Lyapunov stability criterion, stability analysis is performed for the proposed method for an acceptable synchronization error level. The performance of the proposed scheme is demonstrated through the synchronization of two different fractional order chaotic gyro systems. Simulations are implemented using a numerical method based on Grünwald-Letnikov approach to solve the fractional differential equations.