Fractional Order PID Controller Research Articles

Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.

On the Use of FOPID Controllers for Maintenance Phase of General Anesthesia

This paper investigates the performance achievable with a fractional-order PID regulator controlling the Depth of Hypnosis (measured via the Bispectral Index Scale) through the administration of propofol during the maintenance phase of total intravenous anesthesia. In particular, two different methodologies were applied to tune the controller: in the first case, genetic algorithms (GAs) were used to minimize the integrated absolute error, while in the second case, the isodamping approach—a method that targets phase margin invariance with respect to the process dc gain—was employed. In both cases, the performance was extensively analyzed and compared with that of a standard PID controller by simulating multiple patients through a Monte Carlo method. The results demonstrate that a fractional-order PID controller can be effectively used to control the Depth of Hypnosis, but the improvement with respect to a standard PID controller is marginal.

Trajectory Tracking Control of Quadrotor Based on Fractional-Order S-Plane Model

Quadrotors possess traits such as under-actuation, nonlinearity, and strong coupling. Quaternions are primarily used for attitude calculations in drones, with error quaternions seldom being employed directly in the control of specific quadcopter drones. This paper focuses on the low tracking accuracy and weak anti-interference ability of quadcopter drones in trajectory-tracking control. By establishing the quadcopter quaternion model, a controller based on quaternion error is designed through a combination of fractional-order PID control with S-plane control. Trajectory-tracking experiments demonstrate that, in comparison with fractional-order PID, this method exhibits strong wind disturbance resistance and high tracking accuracy.

An Optimized Fractional-Order PID Horizontal Vibration Control Approach for a High-Speed Elevator

Due to factors such as uneven guide rails and airflow disturbance in the hoistway, high-speed elevators may experience significant vibrations during operation. This paper proposes an optimized fractional-order PID (FOPID) method to suppress vibrations of high-speed elevators. First, an accurate horizontal vibration model is established for the elevator car, in which the car frame and body are separate. Then, taking the control cost and the system performance as objective functions, we obtained an optimized FOPID controller based on multi-objective genetic algorithm optimization. Finally, the effectiveness of the controller in reducing elevator vibration was verified through numerical simulation. The results indicate that the horizontal acceleration controlled by the FOPID controller is reduced by about 68% compared to the case without a controller and about 25% compared to the conventional PID controller.

Stability comparison of different controllers for hydraulic turbine fractional order interval parameter time-delay system

This paper studies the stability comparison of four controllers for a hydraulic turbine fractional order interval parameter time-delay system. Considering the terms of parameter uncertainty and time-lag, the hydraulic turbine fractional order interval parameter time-delay system is established by using fractional calculus and identification technology. Through the edge theorem and D-decomposition method, the calculation process of controller parameter stability region is derived in every detail. Subsequently, the four different controllers including the PID, PID plus second order derivative (PID2D), fractional order PID (FOPID) and fractional order PID plus second order derivative (FOPID2D) controllers, are applied in the hydraulic turbine fractional order interval parameter time-delay system. According to the experimental results, the effect of the controller parameters kd , kd 2, α and λ on the stability region of the parameters kp and ki is analysed and the variable law of stability regions of the hydraulic turbine governing system is presented. Finally, the stability region of these four controllers is compared and the results validate the superiority of the FOPID2D controller over the other controllers.

A Fractional Order Tilt Integral Controller Based Load Frequency Control with Dispersed Generation and Electric Vehicle

The elevated level of entrance of decentralized power sources with their Intermittent and volatility gives us a accost task to control load frequency, moreover this quandary is getting worsen up with the Involvement of electric vehicles in the rundown. This paper presents a censorious robust fractional order operative established tilt integral derivative controller (FOTID) for regulating the frequency. To emulate distributed power sources a linearized model of a wind power plant is considered and a small signal model of EV is developed. With the consideration dynamic nature of EV & wind power plants, the dynamic pursuance of the envisaged FOTID controller is investigated by comparing them with integral order PID controller, Fractional order PID controller, sliding mode controller under various conditions. The transfer function model of proposed controllers is derived and the robustness of the proposed FOTID controller is examined by conducting detailed simulation studies.

Experimental Validation of Fractional PID Controllers Applied to a Two-Tank System

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.

A review of integer order PID and fractional order PID controllers using optimization techniques for speed control of brushless DC motor drive

A review of integer order PID and fractional order PID controllers using optimization techniques for speed control of brushless DC motor drive

Optimal tuning fractional order PID based on marine predator algorithm for DC motor

DC motors are a popular topic because they are widely applied in various electronic equipment. So, this requires a control that is fast and reliable. The development of optimized control methods is growing rapidly with the discovery of several new methods. Marine predator algorithm (MPA) is an optimization method based on marine life between living things. This article discusses the application of the MPA method for optimizing fractional order PID (FOPID) control on DC motors. The implementation of the FOPID controller is also difficult because the fractional calculus operators of the FOPID controller cannot be directly implemented in numerical calculations. The method proposed in this article is the FOPID-MPA method. To get a performance test of the proposed method, this study uses several comparison methods, namely the seagull optimization algorithm (ASO), chimp optimization algorithm (ChOA), and sine tree seed algorithm (STSA). This study also uses a variation of the reference speed to get the performance of the proposed method. From the experiment it is known that the FOPID-MPA method gives the best performance. The FOPID-MPA method has an overshoot value of 4.34% compared to the PID-MPA method in case study 1 and has an integrated of time-weighted-squared-error (ITSE) value of 7.44% better than the PID-MPA method in case study 2.

Least Mean Mixed Norm Square/Fourth Adaptive Algorithm With Optimized FOPID Gains for Voltage Power Quality Mitigation

The conventional adaptive Least Mean Square (LMS) algorithm employs Mean Square Error (MSE) as a cost function based on second-order power error. This limits the extraction of fundamental signals from the noise and suffers from performance degradation in certain dynamic scenarios. The proposed approach addresses this problem with a mixed norm-based step size adaptive algorithm which is devised from the second and fourth-order error optimization. The proposed Mixed-Norm Constraint-based Improved Proportionate Normalized Least Mean Square Fourth (MNC-IPNLMS/F) control strategy extracts the fundamental weight quantity from the polluted grid voltage and generates the reference load voltage. This method exploits the enhancement of Dynamic Voltage Restorer (DVR) performance in terms of convergence and stability. The DC and AC-link voltage is regulated by Fractional Order Proportional Integral Derivative (FOPID) controller. The coefficients of FOPID are self-tuned by several optimizations namely, JAYA algorithm, Accelerated Particle Swarm Optimization (APSO), and Biogeography Based Optimization (BBO). This reduces manual tuning and computational complexity. The major improvements of the proposed approach are less overshoot (6.6%), undershoot (3.3%), and fast settling time (0.14s). The comparative study reveals that the FOPID control based on JAYA Optimization (JO) outperforms the others. The efficacy of the MNC-IPNLMS/F is investigated through the performance results.

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.

Metaheuristic-Assisted Advanced Control Approach for Time Delayed Unstable Automatic Voltage Regulator

This work proposes a two-degree-of-freedom factional order proportional-integral-derivative (2-DOF FOPID) controller for automatic voltage regulator (AVR) to mitigate the impact of voltage transients and set-point variations in any power system network. An inherent communication time delay is considered in the investigated AVR plant. This inherent time delay occurs due to the presence of amplifier, exciter, generator, and sensor, making the system unstable. Such an unstable AVR system is still unexplored and difficult to control. The suggested control structure of the 2-DOF FOPID is flexible enough from the perspective of tuning and provides enhanced performance of an AVR system at the cost of a large number of controller design parameters. Therefore, the proposed controller is optimized by an advanced meta-heuristic technique; squirrel search algorithm (SSA) which leads to SSA tuned 2-DOF fractional order PID (S2DFPID) controller. Moreover, selecting an appropriate meta-heuristic approach is a very tedious task for such unstable systems and advanced control architecture. Hence, a systematic statistical approach is also employed to select an optimization technique for the specified purpose, and a rigorous comparative assessment of seven state-of-the-art optimization techniques is also presented in this work. Investigation reveals the superior performance of S2DFPID controller compared to SSA-tuned fractional order PID (SFPID), and SSA-tuned traditional PID (SPID) controllers in the presence of set-point variations, external load disturbances and parametric uncertainties.

Membrane humidity control of proton exchange membrane fuel cell system using fractional-order PID strategy

Dynamic humidity control is a crucial factor affecting the working performance of proton exchange membrane fuel cell (PEMFC) system. Proper membrane humidity can guarantee power generation performance, improve energy utilization efficiency, prevent irreversible degradation of the proton exchange membrane (PEM). In this paper, a dynamic control model for PEMFC humidity management is proposed, and a fractional-order PID (PIλDμ) control strategy is introduced to balance the membrane humidity of PEMFC. The results show that comparing with traditional PID control methods, the PIλDμ control shows shorter response time, lower overshoot in membrane humidity control, and higher power generation efficiency in PEMFC system. In addition, the performance of the PEMFC using PIλDμ control method at different pressure and temperature conditions is discussed. The power generation efficiency of the PEMFC under PIλDμ control is improved, which is 2.1 %, 3.9 % higher than that of fuzzy PID and conventional PID control method.

Fractional-order PID control of tipping in network congestion

Tracing the rapid progress of communication network, the control of dynamic evolution of network has become a central issue. There are a lot of tipping phenomena in network congestion systems. Therefore, tipping control principally centres on traditional control policies, and some advanced control approaches need to be supplemented. In this paper, a fractional-order proportional-integral-derivative (PID) controller is introduced to a network congestion model to ponder corresponding bifurcation-induced tipping regulation. First, a fractional-order congestion model with fractional-order PID controller is constructed. Then the onset of the tipping induced by Hopf bifurcation of the uncontrolled model is studied. By contrast, the tipping point can be delayed under the controller for the controlled model. Some conditions under which Hopf bifurcation occurs are given. The stable and unstable ranges of control parameters for the controlled model are also deduced. At last, some simulated examples are given to verify the theoretical results and demonstrate the superiority of the controller in tipping regulation. Moreover, the bidirectional effects of the controller are displayed by manipulating the control parameters.

Fractional Order Internal Model PID Control for Pulp Batch Cooking Process

Pulp batch cooking is performed in a sealed high-temperature and high-pressure digester and is a complex black-box process. Based on the analysis of the mechanism of batch cooking, a model with nonlinear characteristics was established. To optimize the nonlinear part of the model, function fitting and numerical approximation were used for the simple cooking process. A novel fractional-order model is proposed to solve the problems of model inaccuracy and uncertain system parameters during batch cooking. For fractional-order systems, a two-degree-of-freedom fractional-order PID (FO-PID) controller based on internal model control is designed. The internal model control simplifies the number of parameter settings of the fractional-order controller and allows accurate adjustment of the adjustable parameters of the FO-PID controller based on the maximum sensitivity and stability margin. The simulation results show that the fractional-order internal model control in the batch cooking process is superior to the integer-order control in terms of overshoot, response speed, and robustness. Compared to internal model control, it provides better setpoint tracking dynamics and better robustness to system parameter disturbances. The practical application results in paper mills are given to illustrate the effectiveness of the method.

Bifurcation and stability analysis of a hybrid energy harvester with fractional-order proportional–integral–derivative controller and Gaussian white noise excitations

Hybrid energy harvester (HEH) has received much attention in the field of energy harvesting. The HEH inevitably suffers from external stochastic disturbances in the working environment such as winds, waves, and ocean currents. Only few works deal with the stochastic dynamics of a hybrid energy harvester with fractional-order proportional–integral–derivative (PID) controller. This paper aims to investigate bifurcation control and stability analysis of a HEH with fractional-order PID controller subjected to Gaussian white noise excitations. An approximately equivalent dimensionally reduced system is formulated via the variables transformation method, and its approximate stationary solutions are derived through the stochastic averaging method. One example is worked out in detail to verify the effectiveness of the proposed procedure. It is shown that the analytical results provide a good approximation to the numerical simulation results. The influences of system parameters on the stochastic bifurcation and the asymptotic Lyapunov stability are also discussed.

RETRACTED: Identification and control of Maglev system using fractional and integer order PID controller

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219433.

Ant Colony Optimization of Fractional-Order PID Controller based on Virtual Inertia Control for an Isolated Microgrid

Background: Increasing the penetration of renewable energy sources has become necessary, especially in isolated microgrids. This increase leads to a decrease in the total inertia of the microgrids, which affects microgrid stability. Moreover, voltage and frequency control in lowinertia microgrids is more difficult and sensitive. Objective: Improve low inertia isolated microgrids' dynamic response and save the microgrid stability at different contingency and uncertainty conditions. Moreover, it allows for more penetration of renewable energy sources. Method: Proposing different control strategies based on virtual inertia control. The first is a proportional- integral-derivative (PID) controller, and then, to allow for more tuning flexibility, a fractional- order proportional-integral-derivative (FOPID) controller is used. MATLAB TM/Simulink is used to compare the response of the isolated microgrid without virtual inertia control, with conventional virtual inertia control, PID-based virtual inertia control, and FOPID-based virtual inertia control. The PID and FOPID controllers’ parameters are tuned using the ant colony optimization (ACO) technique. Results: The proposed control techniques save the isolated microgrids' stability at different penetration levels of renewable energy sources and operating conditions. At the same time, the isolated microgrid without virtual inertia control or conventional virtual inertia control can not save its stability in many operating conditions. Conclusion: The proposed fractional-order proportional-integral-derivative (FOPID)-based virtual inertia control has proven its effectiveness in saving the isolated microgrid stability and gives the best controller response. FOPID-based virtual inertia control minimizes the frequency deviation with different disturbances and operating conditions.

Load Frequency Control of One and Two Areas Power System Using Grasshopper Optimization Based Fractional Order PID Controller

In this paper, grasshopper optimization based fractional order PID controller for load frequency control of single and multi-area power system is presented. It is paramount to minimize large frequency deviation in power system control. Large frequency deviation occurs when the parameter values of the various generating units of the power system like generators, turbine and governors keeps changing due to numerous on/off witching in the load side. As such, for a more realistic study, nonlinearities and boiler dynamics has been introduced into the power system design and measures also put in place to mitigate large frequency deviation. This is because large frequency deviation can damage equipment at the generation level and the consumer devices at the distribution level. Anti-windup control will then be used to compensate the effects of the nonlinearities. The gain of the FOPID controller will be optimized using grasshopper optimization algorithm and objective function for minimization is the Integral Square Error (ISE). The Errors to be minimized are the summation of frequency deviation, tie-line power deviation and the area control errors. Simulations were carried out on the designed power system using MATLAB/Simulink and results obtained show a significant improvement in mitigating frequency deviation. However, the proposed method took a longer time to balance the generated power and load demand. This is because the proposed method considers boiler dynamics and nonlinearities in the power system designed and results were compared with other designed method for power system without nonlinearities.

Satellite Tracking Control System Using Optimal Variable Coefficients Controllers Based on Evolutionary Optimization Techniques

Satellite tracking control system is mechanism that redirects the parabolic antenna to the chosen satellite automatically. It perfectly tracks the satellite as it spins across the sky in its orbit. To maintain a continuous communication signal throughout multiple satellite tracking missions, the tracking process must be fast and smooth, with minimal deviations from the target position. Various controller models have been presented over time to address the problem of antenna positioning in satellite systems and to track moveable targets using servomechanism. The purpose of this study is to describe and debate a satellite tracking control system based on a DC servo motor. For optimal tuning of Proportional-Integral-Derivative (PID), Fractional Order PID (FOPID) and Variable Coefficient Fractional Order PID (V-FOPID) controllers that were used in satellite control system, Particle Swarm Optimization (PSO), Gravitational Search Algorithm with Particle Swarm Optimization (GSA-PSO) and Eagle Strategy with Particle Swarm Optimization (ES-PSO) techniques were proposed. Dynamic Performance Indices Based Objective Functions is used to compute the Performance Index. Furthermore, Self-Tuning Fuzzy FOPID (STF-FOPID) is proposed for satellite tracking control system. The system's response is analyzed, and the outcomes of various control strategies are measured and compared to others. The obtained results implies that Variable Coefficient Fractional Order PID controller tuned using Eagle Strategy with Particle Swarm Optimization can precisely trace the desired position with the fastest settling time and free overshoot when compared to other control strategies.