Optimal fractional controller design methodology for electric drive train

In this study, a nonlinear Archimedes wave swing (AWS) energy conversion system was employed to enable the use of irregular sea waves to provide useful electricity. Instead of the conventional PI controllers used in prior research, this study employed fractional-order PID (FOPID) controllers to control the back-to-back configuration of AWS. The aim was to maximize the energy yield from waves and maintain the grid voltage and the capacitor DC link voltage at predetermined values. In this study, six FOPID controllers were used to accomplish the control goals, leading to an array of thirty parameters required to be fine-tuned. In this regard, a hybrid jellyfish search optimizer and particle swarm optimization (HJSPSO) algorithm was adopted to select the optimal control gains. Verification of the performance of the proposed FOPID control system was achieved by comparing the system results to two conventional PID controllers and one FOPID controller. The conventional PID controllers were tuned using a recently presented metaheuristic algorithm called the Coot optimization algorithm (COOT) and the classical particle swarm optimization algorithm (PSO). Moreover, the FOPID was also tuned using the well-known genetic algorithm (GA). The system investigated in this study was subjected to various unsymmetrical and symmetrical fault disturbances. When compared with the standard COOT-PID, PSO-PID, and GA-FOPID controllers, the HJSPSO-FOPID results show a significant improvement in terms of performance and preserving control goals during system instability

This study provides an efficient torque and speed control method for brushless DC (BLDC) motor utilizing a fractional order proportional integral derivative (FOPID) controller based on the multiverse optimization algorithm and salp swarm optimization (SSO). When combined with a solar photovoltaic (PV) system and a voltage boosting architecture, standard PID controllers regulated the BLDC drive parameters due to their simplicity and improved steady-state performances. A solar PV system with a specific power range is chosen for the best output solution on the output side. The MPPT method employed is the incremental conductance approach for tracking maximum power from the source. However, it has a problem with unpredictability owing to load changes. The PID controller tuning also relates to the structure’s parametric uncertainties. Therefore, precise control methods may be offered with the aid of the FOPID controller to address the aforementioned issues. Simulation results of the proposed MVO and SSO-based FOPID controller for BLDC speeds run in the Matlab Simulink platform. To confirm the adaptability of the suggested control scheme for BLDC motor, the outcomes are interrelated using genetic algorithm, gray wolf, and PSO-based FOPID controllers.

This paper concerns design and implementation of PID and fractional-order PID (FOPID) controllers to control position of an electromagnetically suspended ferromagnetic ball in a magnetic levitation (Maglev) system in real time. The Maglev system, manufactured by Feedback Instruments (Model No 33-210) is used as a platform to test the performance of proposed controllers. Parameters of PID and FOPID controllers are tuned by firefly algorithm (FA). FA is a metaheuristic algorithm based on movement of fireflies toward more attractive and brighter ones. PID and FOPID controllers are implemented in MATLAB and SIMULINK environment inside PC using fractional-order modeling and control toolbox. Controller in the SIMULINK environment inside PC is connected to the Maglev system through Advantech card. Effectiveness of proposed controllers is tested by checking the ability of the suspended ball to track a reference signal. Step change, sine wave, and square wave are used as reference signals. Real-time results have revealed satisfactory transient and steady-state responses over the contemporary existing controllers. FOPID controller showed better results compared to PID.

A GBMO-based PI λ D μ controller for vibration mitigation of seismic-excited structures

A fractional-order proportional integral derivative (FOPID)controller has replaced the classical PID controller used in industries for process control application. FOPID is less sensitive to the change of control parameters than PID Controller, due to which better results are obtained. The FOPID provides a robust and stable system for a higher-order system as of iso- damping property. This study aims to find a stable and controlled structure by tuning the FOPID controller with the Particle Swarm Optimization (PSO) algorithm, fuzzy-based logic approach, and Adaptive Neuro-fuzzy inference system (ANFIS). The tuning of FOPID is done to overcome deficits of PID controller using the different types of optimization method to overcome large overshoot and large settling time. This paper presented useful techniques based on PSO, fuzzy logic, and ANFIS to optimize FOPID controlled high-performance drilling machines. On the analysis and comparisons of simulation findings, it is observed that the FOPID-PSO approach provides better performance over the Ziegler-Nichols (ZN)-FOPID and the above-mentioned intelligent techniques in terms of less settling time (ts=0.823sec.) & optimized peak overshoot (Mp=2.44%) for the mentioned target.

A pressurized heavy water reactor (PHWR) is a nuclear power reactor,that commonly uses unenriched natural uranium as its fuel and heavy water as its coolant and moderator. The PHWR has become an important component of the present day power generation industry. Working of a PHWR may often require reduction of nuclear power within a small finite time interval in accordance to the varying load conditions. This phenomenon is referred to as step back condition. Therefore, for the efficient working of the PHWR it is very important to have a control algorithm that has the capability to handle the step back condition very precisely. The fractional order control strategy has emerged as one of the very versatile and accurate control strategies in the recent times. The fractional order PID (FOPID) controllers are known to give very robust performance both in nominal as well as varying operating conditions. However, most of the design techniques available for the FOPID controllers are mathematically very lengthy and complex. Therefore, in this paper an FOPID controller design technique has been suggested using the concept of internal model control (IMCFOPID) for the PHWR under step back conditions. Further, the performance of the proposed controller has been compared with the conventional FOPID controller using the various integral error criterions. The proposed IMC-FOPID controller is found to give an improved performance as compared to the conventional FOPID controller.

In this paper, fractional order PID (FOPID) controller is implemented to stabilize x-z inverted pendulum (vertical inverted pendulum). Three FOPID controllers are used to control the angle and position (horizontal and vertical) of inverted pendulum. Mathematical model of the pendulum is used for designing the Simulink model and various parameters of the FOPID are obtained using the Whale optimization algorithm (WOA) technique. Simulation results obtained from FOPID is compared with PID controller. From the simulation results it is noticed that overall performance of the proposed controller is satisfactory with and without disturbances.

This article presents a fuzzy fractional-order PID (FFOPID) controller scheme for a pneumatic pressure regulating system. The industrial pneumatic pressure systems are having strong dynamic and nonlinearity characteristics; further, these systems come across frequent load variations and external disturbances. Hence, for the smooth and trouble-free operation of the industrial pressure system, an effective control mechanism could be adopted. The objective of this work is to design an intelligent fuzzy-based fractional-order PID control scheme to ensure a robust performance with respect to load variation and external disturbances. A novel model of a pilot pressure regulating system is developed to validate the effectiveness of the proposed control scheme. Simulation studies are carried out in a delayed nonlinear pressure regulating system under different operating conditions using fractional-order PID (FOPID) controller with fuzzy online gain tuning mechanism. The results demonstrate the usefulness of the proposed strategy and confirm the performance improvement for the pneumatic pressure system. To highlight the advantages of the proposed scheme a comparative study with conventional PID and FOPID control schemes is made.

<span>This paper proposes the fractional-order proportional integral derivative (FOPID) controller, as a speed controller for permanent magnet direct current (PMDC) motor, instead of the traditional integer-order PID controller. The FOPID controller is the general form of the integer-order PID controllers, which found wide applications in all engineering fields. In this work a hybrid M-file and SIMULINK program is developed to simulate the overall system, the FOPID controller has five associated parameters. The optimum values of those parameters are found out by using particle swarm optimization technique. Simulation results show excellent command speeds tracking and superior dynamic response in conjunction with that of the integer-order PID controller. The proposed controller shows a high ability to overcome any external disturbance the system may be exposed; also, it performs a high degree of robustness to control the system in motoring and regenerative operating modes.</span>

Direct Current (DC) motors are extensively used in various applications due to their versatile and precise control capabilities. However, they face operational challenges such as speed instability and sensitivity to load variations and external disturbances. This study compares the performance of several advanced control methods—Proportional Integral Derivative (PID), Fractional Order PID (FOPID), Integral State Feedback (ISF), Sliding Mode Control (SMC), and Fuzzy Logic Controller (FLC) for DC motor control. Particle Swarm Optimization (PSO) is employed to optimize the tuning parameters of PID, FOPID, ISF, and SMC controllers, while FLC is implemented without optimization. The simulation results indicate that the PSO-FOPID controller exhibits the best overall performance, characterized by the fastest rise and settling times and the lowest ITSE, despite a minor overshoot. The PSO-PID controller also performs well, with fast response times, although it is less efficient in terms of settling time and ITSE compared to PSO-FOPID. The OBL/HGSO-PID controller, while stable and overshoot-free, has a slower response. The PSO-ISF controller shows the highest stability with the lowest SSE values, making it suitable for applications requiring high stability. The PSO-SMC controller demonstrates good stability but is slightly slower than PSO-ISF. The FLC controller, however, performs the worst, with significant overshoot and long recovery times, making it unsuitable for fast and precise control applications. The robustness analysis under varying motor parameters further confirms the superiority of the PSO-FOPID controller, which outperforms OBL/HGSO and OBL-MRFO-SA optimizations across both PID and FOPID controllers, making it the most effective solution for applications requiring high precision and rapid response.

Precise and stable trajectory tracking in mobile robotics is challenging due to dynamic disturbances and uncertain conditions. Traditional controllers like P-D and PID often underperform in non-linear, unpredictable environments. They also lack the adaptability needed for real-time, vision-based control systems. To address these issues, this paper explores and compares the effectiveness of three control approaches: P-D, PID, and a Fractional Order PID (FOPID) controller optimized using the World Cup Optimization Algorithm (WCOA). The control system is driven by inputs from a computer vision setup, and the controllers are evaluated on their ability to maintain accurate setpoint tracking under simulated dynamic disturbances. The FOPID controller’s parameters are tuned using WCOA, enhancing its adaptability and precision. The robustness of WCOA is also validated using standard benchmark functions including Sphere, Rastrigin, Ackley, Rosenbrock, and Griewank. Simulation results show that the WCOA-tuned FOPID controller significantly outperforms both P-D and PID controllers in minimizing error, maintaining control stability, and ensuring accurate trajectory tracking. Its superiority is also demonstrated through real-time tests on a mobile robot. Furthermore, feasibility evaluations reveal high levels of usability, operability, and learnability. These results highlight the strong potential of WCOA as a robust optimization method for advanced control systems and provide a foundation for future research in dynamic environments, hybrid optimization techniques, and broader engineering applications.

In this paper, a high-performance optimal fractional emotional intelligent controller for an Automatic Voltage Regulator (AVR) in power system using Cuckoo optimization algorithm (COA) is proposed. AVR is the main controller within the excitation system that preserves the terminal voltage of a synchronous generator at a specified level. The proposed control strategy is based on brain emotional learning, which is a self-tuning controller so-called brain emotional learning based intelligent controller (BELBIC) and is based on sensory inputs and emotional cues. The major contribution of the paper is that to use the merits of fractional order PID (FOPID) controllers, a FOPID controller is employed to formulate stimulant input (SI) signal. This is a distinct advantage over published papers in the literature that a PID controller used to generate SI. Furthermore, another remarkable feature of the proposed approach is that it is a model-free controller. The proposed control strategy can be a promising controller in terms of simplicity of design, ease of implementation and less time-consuming. In addition, in order to enhance the performance of the proposed controller, its parameters are tuned by COA. In order to design BELBIC controller for AVR system a multi-objective optimization problem including overshoot, settling time, rise time and steady-state error is formulated. Simulation studies confirm that the proposed controller compared to classical PID and FOPID controllers introduced in the literature shows superior performance regarding model uncertainties. Having applied the proposed controller, the rise time and settling time are improved 47% and 57%, respectively.

A fractional order PID control strategy in active magnetic bearing systems

An experimental validation of fractional-order PID (FOPID) controllers, which were applied to a two coupled tanks system, is presented in this article. Two FOPID controllers, a continuous FOPID (cFOPID) and a discrete FOPID (dFOPID), were implemented in real-time. The gains tuning process was accomplished by applying genetic algorithms while considering the cost function with respect to the tracking error and control effort. The gains optimization process was performed directly to the two-tanks non-linear model. The real-time implementation used a National Instruments PCIe-6321 card as a data acquisition system; for the interface, we used a Simulink Matlab and Simulink Desktop Real-Time Toolbox. The performance of the fractional controllers was compared with the performance of classical PID controllers.

As a position servo system to isolate disturbance from its carrier, stabilized platform requires high-precision and high-adaptability control. However, conventional integer-order PID (IOPID) control fails to meet that requirement. In this paper, a new controller design scheme is proposed for stabilized platform based on fractional calculus. The designed controller is called fractional-order PID (FOPID) controller, which has two extra parameters compared to conventional PID controller. On one hand, it provides more degrees of freedom to design FOPID controller. On the other hand, its differential order and integral order provides more flexibility to tune the controller performance. Therefore, a design method of FOPID controller based on dynamic software modeling is presented. To obtain the ideal controller's parameters, the particle swarm optimization (PSO) bionic algorithm is used to optimize an objective function. In addition, software simulation platform and hardware experiment system are built to design and test the FOPID controller. Finally, the results of simulation and experiment are included to show the effectiveness of the new control method.