Robust low-frequency oscillations damping in hybrid renewable energy systems using advanced controller and optimization

In this paper, a novel approach for the design of a fractional order proportional integral derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains a fast system response and significantly reduces the voltage spike at the controller output. The time-varying FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm (GA) to find the optimum constants and time-varying parameters. The improved control performance is validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created for comparison with all three PID gain constants replaced by the optimized time functions. The simulation results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage spike at the controller output but also is also able to keep approximately the same characteristics of the system response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation block between the controller output and the plant still performs best according to system overshoot, rise time, and settling time.

A nano-grid is an independent hybrid sustainable framework that utilizes non-renewable and renewable power resources for supplying continuous electrical energy to the load. Considering this scenario, in this research work, photovoltaic (PV) array, wind turbine, and fuel cell are taken as the three generation resources that have been used in the nano-grid. The active and reactive power of the all three generation resources is controlled using various controllers, i.e. integral, proportional-integral, proportional derivative, proportional integral derivative, fractional-order proportional-integral, fractional order proportional integral derivative (FOPID) and sliding mode controller (SMC). An advanced optimization technique based on a genetic algorithm (GA) and particle swarm optimization (PSO) algorithm has been utilized to optimize all of these controllers. The integral square error is taken as the objective function for both optimization algorithms. Finally, a graphical and tabular comparative analysis of all optimized controllers along with their control parameters and performance indexes is evaluated to find the best optimal solution. The performance of SMC has surpassed the performance of all other optimized controllers for power stability. In less than 0.267 seconds, the actual power yielded by using SMC is within 1% of the desired power. PSO algorithm has performed better than GA algorithm with all controllers. The worst performance is by FOPID controller with a steady state error of 6071.3W using GA algorithm and have a high magnitude of overshoot and undershoot. Moreover, a smart switching algorithm has been introduced for switching between the generation resources in accordance with the load demand and cost of the system in order to operate the nano-grid more economically. Finally, a case study has been performed in which the smart switching algorithm is utilized to switch to the best available generation resource in case of any fault at the generation side to provide uninterrupted power to the attached loads.

DC motor speed can be achieved by changing the armature voltage fed through converter that generally employed with conventional PID. However, conventional PID controller has some disadvantages such as the high starting overshoot and sensitivity to controller gains. On the other hand, fractional order PID has potential to accomplish what conventional PID cannot. In this study, fractional order PID controller was applied to control speed of DC motor. By calculated error that occurred by reference speed and actual speed, fractional order PID brought motor run at desired speed. The parameters of fractional order PID controller (proportional constant, integral constant, derivative constant, derivative order and integral order) are optimally tuned by using Genetic Algorithm, and the optimization performance target is based on Integral Time Absolute Error (ITAE) criterion. Oustaloup’s approximation method is used to approximate the fractional order differentiator and integrator. This controller performances are tested in simulation mode using MATLAB/Simulink. Speed response of motor DC are compared between fractional order PID and conventional PID controller. The result of fractional order PID controller could reduce overshoot, settling time and steady state error. With this result, show that fractional order PID controller perform better than conventional PID controller.

Chapter 21 - A BSA Tuned Fractional-Order PID Controller for Enhanced MPPT in a Photovoltaic System

ABSTRACTIn this paper, the design and analysis of Fractional Order PID (FOPID) controller for the application of the solar photovoltaic system is proposed. At the outset, a solar PV system is considered to investigate the better performance of the FOPID controller compared to PID controller. Fractional order PID (FOPID) controller is used to improve the dynamic response of the system and the optimal gain values are tuned by using FOTF toolbox. A Fractional order controller that has been conceptualized to improve the system performance, particularly to improve the rejection of possible disturbances, which may occur in the input voltage. The performance analysis and comparison of PID controller and FOPID controller is done using MATLAB. The working method of the proposed technique is demonstrated with the help of Boost converter. It is designed in order to tap the solar energy and convert it into an electrical energy.

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.

This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing the produced heat to follow a desired reference despite the unevenly varying solar irradiance. In addition to the unpredictable variations of the energy source, the parabolic solar collectors are subject to inhomogeneous distributed efficiency parameters affecting the heat production. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness with respect to disturbances. Thus, we propose a control strategy based on FOPID to achieve the control objectives. First, the FOPID controller is designed based on a linear approximate model describing the system dynamics under nominal working conditions. Then, the FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. Numerical simulations are carried out to evaluate the performance of the proposed FOPID controller. A comparison to the robust integer order PID is also provided. Robustness tests are performed for the nominal model to show the effectiveness of the FOPID. Furthermore, the proposed FOPID is numerically tested to control the distributed solar collector under real working conditions.

An enhanced controller is proposed to investigate grid-connected photovoltaic systems employing cascaded two-level inverters. The primary focus is on optimizing power output, achieved through the development, modeling, and testing of photovoltaic systems using the suggested upgraded controller. This advanced controller, specifically a Fractional Order PID (FOPID) controller, incorporates the Ant-Lion Optimizer (ALO) algorithm for enhanced performance compared to conventional controllers. The FOPID controller’s reliability is emphasized, and further improvements are pursued by optimizing gain parameters through the prescribed method. Power supply under both schemes is examined, and the controller’s performance in extracting maximum power under specified operating conditions is deemed satisfactory. To validate the proposed approach, practical implementation is conducted using the MATLAB/Simulink platform. The effectiveness of proposed and conventional methodologies for analyzing the id and iq currents is assessed. A comparison is drawn between the suggested approach and current methods such as the base controller, GSA, and ABC methodologies. In comparison to the existing methods, the suggested FOPID controller demonstrates superior performance in maintaining the DC link voltage, achieving an efficiency of 94%, while the GSA method reaches 91.5%, the ABC method achieves 91%, and the base controller achieves 90%.

This paper presents the design and implementation of a dual inverter-based grid-connected photovoltaic (PV) system incorporating PI (Proportional-Integral) and FOPID (Fractional-Order Proportional-Integral-Derivative) controllers, along with a Quadratic Boost Converter (QBC) for enhanced energy conversion and grid integration. In order to guarantee optimal DC-AC conversion from the photovoltaic array and smooth grid integration, the dual inverter system features cascaded voltage source two level inverters (DI). Enhancing power quality, improving the system's dynamic response, and making sure the injected current satisfies the necessary requirements while lowering harmonic content are the main goals. While the FOPID controller is used to enhance the system's transient response and provide better dynamic performance under changing irradiance and grid disturbances, the PI controller is employed for steady-state control. The Quadratic Boost Converter is a great option for PV applications since it also has a high efficiency, a high step-up voltage conversion, and lower switching losses. The FOPID controller reduces settling time by 43% and overshoot for grid current by 38% when compared to the PI controller, according to a comparative study of the two controllers. Furthermore, the grid current's Total Harmonic Distortion (THD) is decreased from 4.41% (PI) to 4% (FOPID). These outcomes demonstrate how well the twin inverter-based PV system with the QBC works and how the FOPID controller provides better dynamic performance for grid-tied applications.

This paper deals with performance improvement of Pendulum Cart System (PCS) using fractional controller. A simpler control structure for stabilization of PCS is proposed. This control structure consists of two Fractional Order Proportional Integral Derivative (FOPID) controllers which are designed on the basis of Fractional Order Calculus (FOC). One controls cart's position while the other one controls pendulum's angle. FOC can provide higher performance extension for FOPID controllers. However, designing of FOPID controllers is hard as these controllers have two more parameters i.e., derivative and integral order to design in comparison with traditional Proportional Integral Derivative (PID) controllers. For designing of both FOPID controllers we have used a new toolbox of MATLAB i.e., Fractional Order Modeling and Control (FOMCON) which provides a set of tools for fractional-order control. Proper parameter tuning of FOPID controllers has been done by trial and error approach. Performance of the PCS with successfully designed FOPID controllers is analyzed by means of transients. It is also compared with performance of the conventional PID controller for PCS. Comparison ensures the improvement with FOPID controller.

A comprehensive analysis of the optimal GWO based FOPID MPPT controller for grid-tied photovoltaics system under atmospheric uncertainty

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.

Maglev (Magnetic Levitation) systems are an interesting class of systems since they work without any physical contact and are hence frictionless. Due to this attractive property, such systems have the potential for wide range of applications such as maglev trains. Maglev is non-linear due to magnetic field and unstable that suggest the need of stabilizing controller. An appropriate controller is required to levitate the object at desired position. FOPID (Fractional Order Proportional Integral Derivative) controller and ILC (Iterative learning Control) based FOPID controller are designed in this paper for the levitation of metallic ball with desired reference at minimum transient errors. Since maglev is unstable and ILC is used only for stable systems, FOPID controller is used to stabilize the plant. Non-linear interior point optimization method is used to obtain the parameters of FOPID controller. An ILC is used as a feedforward controller in order to improve the response iteratively. P, PD and PID-ILC control laws are used to update the new control input in ILC based FOPID controller. The overall control scheme is therefore a hybrid combination of ILC and FOPID. The effectiveness of proposed technique is analyzed based on performance indices via simulation. ISE (Integral Square Error) and IAE (Integral Absolute Error) is lesser in case of hybrid PID-ILC as compared to simple FOPID controller.

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.

In this paper, fractional-order PID controller (FOPID) for ball and beam is being considered. Ball and beam system is one of the control engineering prototypes used to illustrate balancing mechanism of dynamical systems. The challenge in this system is to make the ball to stay on a beam at a desired position while it is naturally unstable during open-loop. This paper demonstrates the results obtained for this application using fractional-order PID (FOPID). FOPID is an improvement of PID controller with more degree of freedom. This paper also presents the effect of different fractional-orders on the closed-loop response. For comparison, FOPID controller that was tuned using FOMCON toolbox integrated in MATLAB software was also presented. The results also demonstrated the comparison between FOPID and PID controller to see the improvement gains from FOPID controller. In overall, FOPID can reduce overshoot in the output response significantly and improved the response speed if the gains are optimally tuned. This research also presented the optimal FOPID gain that was obtained through minimum ISE of output response which is better compared to the one tuned using FOMCON.