Fractional order PID control of a motion platform

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

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.

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.

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.

In the paper the Fractional Order PID (FOPID) control for inverted pendulum system is addressed. The fractional order parts of the both controllers are approximated using ORA approximation, the FOPID-s were tuned using simulations. As the cost function the integral from sum of square control and position was considered. Results of simulations show that the use of FOPID controllers allows to obtain the better control performance in the sense of considered cost function than use of classic PID controllers, however the control performance in the FOPID control system is determined also by parameters of ORA approximation used to describe fractional parts of controllers.

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.

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.

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.

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

The main objective of this paper is to implement the Fractional Order Proportional Integral Derivative (FOPID) controller for output voltage control of DC - DC Zeta converter. Implementing a distinct control technique for DC-DC converters has also been introduced with the commercial availability of integrated circuits (ICs) to carry out this task. The simulation of Classical Proportional Integral Derivative (PID) and Fractional Order PID (FOPID) control techniques for the control of Zeta converter and its characteristics of a dc-dc converter, where aspects such as the output voltage, required peak overshoot and rise time specifications are investigated using MATLAB/ Simulink model. Through simulation it is confirmed that the propounded FOPID controller gives better the transient response of the feedback system by using a significantly smaller control effort (i.e., less on-off switches), the Internal Absolute Error (IAE) of the variations of the output voltage is minimized and improves the strength of the DC - DC ZETA converter to variations in the input voltage. Artificial Bee Colony (ABC) algorithm offers fine tuning the factors of the FOPID controller.

Maintaining the cathode pressure stable and avoiding oxygen starvation are crucial for the air supply of proton exchange membrane fuel cell (PEMFC). In most applications, the cathode pressure and oxygen excess ratio (OER) are unmeasurable parameters, which makes it difficult to precisely control the air supply system. This article proposes a fractional order PID (FOPID) controller based on an unknown input nonlinear observer for the fuel cell air supply system. The proposed nonlinear observer is able to estimate internal states including the cathode pressure of the PEMFC system. Then, the OER is obtained based on the observed system states. A fractional-order PID controller with a parameter optimization algorithm is developed to regulate as fast the OER and the cathode pressure to their desired values. Both the steady and transient performances of the proposed control method are simulated and experimentally validated compared with supertwisting sliding mode controller and traditional PID controller.

This paper presents the details of FPGA (field programmable gate array) implementation of a QFT based controller for a buck type DC-DC power converter. The performance of QFT controller is compared with PID and fractional order PID controllers. Computer simulations of the QFT based approach as well as integral order and fractional order PID controllers have been carried out. Nominal averaged and linearized model of the converter is used for all the simulations. It is observed that the QFT based controller exhibits better transient performance and higher stability against line voltage and load variations compared to the PID controllers. The QFT controller is implemented using a SPARTAN-3 FPGA board consisting of 400 K gates. All the analytical, simulation and hardware results are included and discussed.

Practical implementation of the fractional order PID (FOPID) controller for FLHex robot leg position control system with comparison of selected performance indexes for different controller's coefficients. In the case of systems such as the FLHex mobile robot, where multiple PID controllers are used, more advanced control algorithms such as FOPID controller can improve quality of control and energy consumption, which is extremely important in the case of mobile robots. Presented comparison of FOPID controllers with varied coefficients in case of leg underwater movement for step sequence setpoint shown differences in parameters of averaged step response, integrals of the squared error (ISE) and integrals of energy consumption (IEC).