Fractional Order PI Controller Research Articles

A new predictive control strategy for improving operating performance of a permanent magnet synchronous generator-based wind energy and superconducting magnetic energy storage hybrid system integrated with grid

This research work proposes an unscented Kalman filter (UKF) as an observer for predictive current control (PCC) of a permanent magnetic synchronous generator (PMSG)-based wind energy conversion system (WECS) connected with a superconducting magnetic energy storage (SMES) system and the main power grid. The proposed UKF observer estimates the rotor angle, rotor angular speed, stator currents, and electromagnetic torque of PMSG connected in the proposed hybrid WECS-SMES configuration. The PCCs designed for both the rotor- and grid- side converters of the proposed hybrid configuration use estimated parameters instead of the measured quantities. Furthermore, due to the intermittent nature of wind energy, control of an energy storage device (which is SMES in this research) is necessary to mitigate the fluctuations in the DC-link voltage and output power being sent to the main power grid. Therefore, a novel control configuration based on fractional order-PI (FOPI) controllers has also been proposed for the SMES system to control the output power and the DC-link voltage. An artificial bee colony optimization algorithm has been used to tune the gains and integration operators of two FOPI controllers. For UKF estimation performance comparison, three popular observers i.e., Luenberger, sliding mode, and extended Kalman filter, have also been designed and implemented in MATLAB. Mean absolute percentage error and root mean squared error performance metrics are used to measure the estimation performance. The simulated results have demonstrated the superior performance of proposed the UKF observer for PCC and FOPI controllers for SMES under different realistic wind speed conditions and noisy measurements. The proposed UKF observer has improved estimation by up to 99.9 %. Lyapunov stability criteria are used to prove the stability of the proposed UKF based PCC control of hybrid WECS-SMES configuration.

PV/WT Integrated System Using the Gray Wolf Optimization Technique for Power Quality Improvement

This paper presents the integration of renewable energy sources such as photovoltaics, wind, and batteries to the grid. The hybrid shunt active power filter (HSHAPF) is optimized with the Gray wolf optimization (GWO) and fractional order proportional integral controller (FOPI) for harmonic reduction under nonlinear and unbalanced load conditions. With the use of GWO, the parameters of FOPI are tuned, which effectively minimizes the harmonics. The proposed model has effectively compensated the total harmonic distortions when compared with without the filter and with the passive filter, the active power filter with a PI controller, and the GWO-FOPI-based controller. The performance of the proposed controller is tested under nonlinear and unbalanced conditions. The parameters of the FOPI controller are better tuned with the GWO technique. The comparative results reflect the best results of GWO-FOPI-based HSHAPF. The suggested controller is built in the MATLAB/Simulink Platform.

A Robust Non-Integer Controller Design for Load Frequency Control in Modern Marine Power Grids

In this study, a new robust non-integer order controller is presented for the secondary load frequency control (LFC) of the shipboard microgrid (MG). During the design phase of the controller, the time delays between the controller and the sensor as well as the actuator are also taken into account, and a robust controller design against these time delays has been realized accordingly. The system frequency is regulated by a single input interval type-2 fuzzy fractional-order PI (SIT2-FFOPI) controller. The basic FOPI parameters of the SIT2 controller are determined offline with the help of the stability boundary locus (SBL) method depending on the time delay and integral order. For the determination of basic FOPI parameters, the characteristic equation of the shipboard MG LFC model is obtained, and the necessary arrangements are made. The geometric centroid is calculated to obtain the basic parameter values in the SBL curve obtained. The performance of the proposed controller design is assessed using real-world marine wave and solar irradiation data in the shipboard MG. Also, the process of verification of the applicability of the proposed method from a systemic perspective is done by real-time hardware-in-the-loop (HIL) simulation based on OPAL-RT.

Conformable Fractional Order Controller Design and Implementation for Per-Phase Voltage Regulation of Three-Phase SEIG Under Unbalanced Load

Self-excited induction generators (SEIGs) usage is an effective way to generate electrical power in off-grid locations. This study aims to performance improvement for voltage regulation of the SEIG in wind turbine systems. To achieve this, a fixed-capacitor with thyristor controlled-reactor based per-phase voltage controller is designed with a conformable fractional order proportional integral (CFOPI) method. The SEIG system is modeled based on small signal analysis by using the input-output data, experimentally. To do this, system identification toolbox of Matlab is used. The proposed controller is established on conformable fractional integral approach proposed by Khalil et al. in 2014. Proposed CFOPI controller parameters Kp , Ki and γ are optimized using particle swarm optimization (PSO) according to minimization of integral time absolute error (ITAE). To validate the success of proposed scheme, CFOPI, traditional fractional order PI (TFOPI) and integer order PI (IOPI) controllers are tested under same experimental setup and results are compared. Three experiments, after voltage build-up process, under balanced and unbalanced load are done for each controller. Experimental results demonstrate that proposed voltage regulator improves the performance of SEIG systems. Moreover, robust voltage regulation is ensured thanks to independent control loops created for each phase.

Grid-Connected Inverter Based on a Resonance-Free Fractional-Order LCL Filter

The integer-order LCL (IOLCL) filter has excellent high-frequency harmonic attenuation capability but suffers from resonance, which causes system instability in grid-connected inverter applications. This paper studied a class of resonance-free fractional-order LCL (FOLCL) filters and control problems of single-phase FOLCL-type grid-connected inverters (FOGCI). The Caputo fractional calculus operator was used to describe the fractional-order inductor and capacitor. Compared with the conventional IOLCL filter, by reasonably selecting the orders of the inductor and capacitor, the resonance peak of the FOLCL filter could be effectively avoided. In this way, the FOGCI could operate stably without passive or active dampers, which simplified the design of control system. Furthermore, compared with a single-phase integer-order grid-connected inverter (IOGCI) controlled by an integer-order PI (IOPI) controller, the FOGCI, combined with a fractional-order PI (FOPI) controller, could achieve greater gain and phase margins, which improved the system performance. The correctness of the theoretical analyses was validated through both simulation and hardware-in-the-loop experiments.

Frequency regulation of hybrid multi-area power system using wild horse optimizer based new combined Fuzzy Fractional-Order PI and TID controllers

The increasing penetration of renewable energy sources (RES) into modern power systems may reflect the problem of frequency stabilization. Therefore, this paper proposes a new combined Fuzzy Fractional-Order Proportional-Integral (FOPI) and Tilt-Integral-Derivative (TID) controller to improve the frequency response of a hybrid power system. The proposed controller combines the advantages of intelligent Fuzzy FOPI and conventional TID controllers, resulting in more effective and robust load frequency control. In this study, the parameters of the proposed Fuzzy FOPI + TID combination are optimized using a novel metaheuristic algorithm, namely Wild Horse Optimizer (WHO). The case study system is a two-area conventional power system integrated with different RES including photovoltaic (PV) and wind generation as well as distributed electric vehicles (EVs) between the two areas. The effectiveness of the proposed controller is tested under various scenarios such as step load perturbation, random load variation, wind speed fluctuation, solar irradiance change and sensitivity analysis. In addition, the disturbance of wave energy oscillation is applied in Area 2 to evaluate the robustness of the proposed controller. For each scenario, the proposed Fuzzy FOPI + TID controller is compared with the conventional PID, single TID, and individual Fuzzy FOPI controllers using the proposed WHO algorithm and other optimization algorithms presented in the previous literature. The results show that the proposed FOPI + TID controller is superior to other controllers in terms of integral square error, peak overshoot, maximum undershoot and settling time for all scenarios. Furthermore, the presence of EVs helps in improving the frequency and tie-line power deviations. Finally, the time domain simulations are implemented using Matlab/Simulink.

Tilt Integral Derivative Controller Optimized by Battle Royale Optimization for Wind Generator Connected to Grid

Globally the countries are focusing on reducing the carbon footprint leading to a greater effort for electrical energy generation by renewable energy sources, particularly wind. The wind turbines are invariably using doubly fed asynchronous generator. In this paper a controller has been designed for a doubly fed induction motor. The proposed Tilt Integral Derivate controller for was compared with commonly used PI, PID controllers. Several optimization algorithms were used for tuning of controllers and the best one was selected for each type of controller. The controller has been optimized using battlefield optimization. It had been compared with proportional integral controller, fractional order proportional integral derivative controller. Other controllers were optimized using meta heuristic algorithms. The controller enhanced the system response in terms of settling time, rise time and other parameters. The Tilt controller gave the overall superior performance in terms of parameters like rise time, settling time, settling minimum, peak, and peak time. The results were obtained using MATLAB. This paper discusses operation of doubly fed induction motor operation and optimization methods.

A novel virtual inertia emulation technique for the single phase electric vehicle charging topology

The fast frequency stability limit is generally low in a short distribution system with a high penetration of renewables. The study proposes a single-phase virtual inertia emulation technique for residential slow charging systems to improve transient performance in islanded networks serving as an additional vehicle to the grid scheme. The proposed emulation technique is based on the novel notion of using a virtual two-phase space vector to ride over the frequency excursion propensity in a single-phase architecture. For the computation of the instantaneous active power reference to correctly alter network behavior through the control loop, the Self-Tuned Fractional Order Proportional Integral (ST-FOPI) controller has been proposed. The suggested ST-FOPI-based virtual inertia emulation technique's performance was tested on an ARM Cortex-A72 processor-driven hardware platform. The real-time performance gain is remarkable when compared to the typical emulation technique.

An enhanced control method for torque ripple minimization of switched reluctance motor using hybrid technique

In this manuscript, a hybrid technique is proposed for Torque Ripple (TR) minimization of Switched Reluctance Motor (SRM). The proposed technique is the consolidation of Wingsuit flying search (WFS) optimization and Gradient Boosting Decision Tree (GBDT) algorithm, hence it is known as WFS-GBDT technique. The control mechanisms consists of fractional order proportional integral derivative (FOPID) speed controller on external loop as well as current controller on internal loop with controlling turn activate and deactivate angles for SRM. The complexity of acquiring the ideal evaluation of proportional, integral and derivative gains for speed and current controller including turn activate and deactivate angles are deemed as a multi-objective optimization issue. Here, the WFS optimize the gain parameters of external speed loop along internal current loop with commutation angles for turn activate and deactivate switches. The WFS optimization processing is used to productive machine learning dataset under the types of SRM parameter. By using the satisfied dataset, the GBDT is predicted and mandatory forecasting is implemented in the entire machine operating stage. The optimized gain parameters based, the fractional order proportional integral derivative controller is tuned exactly. The proposed WFS-GBDT control technique lessens the torque ripple and quick settling time with this proper control, because of its systematic random search capabilities, thereby enhancing the dynamic execution of SRM drive. Finally, the proposed technique is activated in MATLAB/Simulink site, its performance is analyzed with existing techniques, like Base, ALO and WFS. The best, worst, mean, standard deviation for ISEspeed using proposed technique attains 230.5364, 231.5934, 230.952 and 0.05314. The best, worst, mean and standard deviation for torque ripple using proposed technique attains 0.4571, 0.6548, 0.585 and 0.472. The best, worst, mean, standard deviation for ISEcurrent using proposed technique attains 3.1257, 3.9754, 3.5783 and 0.0472.

Robust three‐parameter fractional‐order proportional integral derivative controller synthesis for permanent magnet synchronous motor speed servo system

AbstractThis paper proposes a three‐parameter fractional‐order PID (TPFOPID) controller synthesis for the PMSM speed servo system. This TPFOPID contains complete proportional/integral/differential elements but with only three parameters to tune. A systematic design scheme of this TPFOPID to satisfy a flat phase constraint and two specifications, that is, gain crossover frequency ( ) and phase margin ( ), is presented for the PMSM speed servo system. Furthermore, the entire achievable region of and can be collected following the scheme. With this region, one can choose feasible combination specifications of and before the controller design. To show the effectiveness of the TPFOPID controller, the achievable region of specifications is compared with the fractional‐order PI (FOPI) also with three parameters. Simulation illustration and experimental verifications using the TPFOPID for the PMSM speed servo system are presented and compared with those using FOPI controller, IOPI controller, and IOPID controller to demonstrate the advantages of the designed TPFOPID controller, and also compared with FOPID based on differential evolution (DE) algorithm to present comparable control performance.

Fractional order-based hierarchical controller design and evaluation with Bürger-Diehl settler model in a total nitrogen removal wastewater treatment process.

The primary objective of this study was to establish two-level structured control techniques based on the globally known benchmark simulation model no. 1 (BSM1) and the Bürger-Diehl settler model in order to improve effluent quality. The latter was based on the activated sludge model no. 1 (ASM1), while the classic Takacs model was superseded by the more recent Bürger-Diehl settler model with enhanced predictive potential. A two-level hierarchical control structure was considered to maintain the dissolved oxygen concentration basing on the ammonia levels and also a nitrate controller was considered to improve nitrogen removal efficiency. Fractional order PI controllers were considered at the secondary level and advanced control techniques, namely, MPC and fuzzy, were implemented at the primary level. Two advance control schemes, being, FPI-MPC and FPI-fuzzy were designed in the present work. The controllers were designed based on the plant model which was identified using prediction-error minimization method. It was observed that the implemented control strategies in consideration with the plant modifications showed a profound impact in improving the plant performance in terms of the effluent quality. FPI-fuzzy resulted in noticeable 60% and 53% reduction in total nitrogen violations for dry and storm climatic conditions, respectively.

Arithmetic optimization approach for parameters identification of different PV diode models with FOPI-MPPT

The Maximum Power Point Tracker (MPPT) provides the most efficient use of a Photo-voltaic system independent of irradiance or temperature fluctuations. This paper introduces the modeling and control of a photo-voltaic system operating at MPPT using the arithmetic optimization algorithm (AOA). The single and double Photo-voltaic models are investigated. Their optimal unknown parameters are extracted using AOA based on commercial Photo-voltaic datasheets. A comparison is performed between these optimal parameters extracted by AOA and other optimization techniques presented in the literature. These parameters generate the P - V and I - V curves for the studied models considering the temperature factor. A good match is achieved relative to the manufacturer data. A DC-DC boost converter is used as a link between the PV modules and the load. The converter duty cycle is adjusted, varying the climatic conditions using three cases: without a controller, using PI controller, and using the fractional-order PI controller (FOPI). The AOA is employed to set the optimum controllers parameters to maintain the impedance matching between the PV modules and the load. The FOPI shows a significant improvement in controlling the system performance.

Novel chaos game optimization tuned-fractional-order PID fractional-order PI controller for load\u2013frequency control of interconnected power systems

In this work, chaos game optimization (CGO), a robust optimization approach, is employed for efficient design of a novel cascade controller for four test systems with interconnected power systems (IPSs) to tackle load–frequency control (LFC) difficulties. The CGO method is based on chaos theory principles, in which the structure of fractals is seen via the chaotic game principle and the fractals’ self-similarity characteristics are considered. CGO is applied in LFC studies as a novel application, which reveals further research gaps to be filled. For practical implementation, it is also highly desirable to keep the controller structure simple. Accordingly, in this paper, a CGO-based controller of fractional-order (FO) proportional–integral–derivative–FO proportional–integral (FOPID–FOPI) controller is proposed, and the integral time multiplied absolute error performance function is used. Initially, the proposed CGO-based FOPID–FOPI controller is tested with and without the nonlinearity of the governor dead band for a two-area two-source model of a non-reheat unit. This is a common test system in the literature. A two-area multi-unit system with reheater–hydro–gas in both areas is implemented. To further generalize the advantages of the proposed scheme, a model of a three-area hydrothermal IPS including generation rate constraint nonlinearity is employed. For each test system, comparisons with relevant existing studies are performed. These demonstrate the superiority of the proposed scheme in reducing settling time, and frequency and tie-line power deviations.

Lion swarm optimisation‐based tuning method for generalised predictive fractional‐order PI to control the speed of brushless direct current motor

In order to enhance the speed tracking performance of brushless direct current motor (BLDCM), a new generalised predictive fractional-order PI (GPFOPI) control algorithm ground on lion swarm optimisation (LSO-GPFOPI) is proposed in this paper. First, GPFOPI combines robust generalised predictive control with scalable fractional-order PI, whose optimal control law is obtained through the model parameters and the predicted speed reference values. Next, the lion swarm algorithm is utilised to optimally tune the three parameters K P , K I , λ of GPFOPI, so as to make them be optimised. Finally, the optimal control signal is input into the system of BLDCM to control its speed. To verify the effectiveness of LSO-GPFOPI, its performance is compared with other algorithms. The results show that LSO-GPFOPI has better response speed, speed tracking ability, anti-interference ability, robustness, and self-adaptability than other algorithms. Moreover, an experimental platform of the BLDCM drive system is built to verify the feasibility of the LSO-GPOPI algorithm, and the test results prove that LSO-GPOPI can guarantee the smooth and accurate operation of BLDCM.

Application of Fractional-Order PI Controllers and Neuro-Fuzzy PWM Technique to Multi-Rotor Wind Turbine Systems

In recent years, the methods of controlling electrical machines have been witnessing increasing development to reduce torque and electric current fluctuations in electrical power generation systems from renewable sources such as wind energy. The generation of electric power from wind plants imposes the need for an efficient and more robust method in order to obtain fewer ripples in active and reactive power. In this work, a new fractional-order proportional-integral (FOPI) controller and intelligent PWM (IPWM) technique are proposed to control an existing asynchronous generator (AG) in variable-speed multi-rotor wind turbines (VSMRWTs). This proposed method depends on combining or using two methods, namely nonlinear area and fractional calculus, to obtain a more robust method and to reduce current and torque ripples. In the framework of this study, the electric power generation system consists of a 1.5 MW AG and VSMRWTs. The AG is controlled using a simpler and easily accomplished method called direct vector control, based on FOPI controllers and the IPWM technique (DVC-FOPI-IPWM). The maximum power point tracking (MPPT) method is used to generate the maximum energy from the VSMRWTs. The proposed DVC-FOPI-IPWM technique is modeled in the Matlab/Simulink platform to obtain good quality current and active power. Simulation results show that the proposed strategy reduces the ripples of torque, current, and active power compared to the classical technique. Moreover, the reduction ratio is about 85%, 99%, and 93.33% for the current, active power, and torque, respectively.

Fractional-Order PI Controller Design Based on Reference–to–Disturbance Ratio

The presence of disturbances in practical control engineering applications is unavoidable. At the same time, they drive the closed-loop system’s response away from the desired behavior. For this reason, the attenuation of disturbance effects is a primary goal of the control loop. Fractional-order controllers have now been researched intensively in terms of improving the closed-loop results and robustness of the control system, compared to the standard integer-order controllers. In this study, a novel tuning method for fractional-order controllers is developed. The tuning is based on improving the disturbance attenuation of periodic disturbances with an estimated frequency. For this, the reference–to–disturbance ratio is used as a quantitative measure of the control system’s ability to reject disturbances. Numerical examples are included to justify the approach, quantify the advantages and demonstrate the robustness. The simulation results provide for a validation of the proposed tuning method.

Design and High-Order Precision Numerical Implementation of Fractional-Order PI Controller for PMSM Speed System Based on FPGA

In this paper, the design of a fractional-order proportional integral (FOPI) controller and integer-order (IOPI) controller are compared for the permanent magnet synchronous motor (PMSM) speed regulation system. A high-precision implementation method of a fractional-order proportional integral (FOPI) controller is proposed in this work. Three commonly used numerical implementation methods of fractional operators are investigated and compared for comprehensively evaluating the numerical implementation performance in this work. Furthermore, for the impulse response invariant implementation method, the effects of different discretization orders on the control performance of the system are compared. The high-order fractional-order controller can be implemented accurately in a control system with the field-programmable gate array (FPGA) with the capability of parallel calculation. The simulation and experimental results show that the high-precision numerical implementation method of the designed high-order FOPI controller has better performance than the ordinary precision fractional operation implementation method and traditional order integer order PI controller.

Linearized Fraction Order Control and Stability Analyses for Switched Reluctance Motor Drives

The nonlinearity and double salient pole of the switched reluctance motor make the control difficult and the torque fluctuation is large. To achieve good control performance, this study introduces a novel linearized fractional-order controller with the disturbance observer to regulate the speed and torque of a switched reluctance motor. Based on fractional differential calculus theory, the fractional-order proportional integral controller is designed. The disturbance observer is introduced to overcome the influence of nonlinearity on the switched reluctance motor and reduce the torque fluctuation. By using the extended state in the disturbance observer, the disturbances are estimated and compensated to achieve linearization and determinism. The parameter values of the proposed controller are obtained by employing the trial-and-error method. The frequency-domain analysis of the proposed controller shows that it has a good suppression performance for medium- and high-frequency disturbances. Through simulation, the performance of the system is analyzed. The results show good performance of the controller in speed change, current, and torque fluctuation reduction.

Atom Search Optimized FOPI Controller of the DC–DC SEPIC Model with Matignon’s Theorem Stability Analysis

In this work, the design and implementation of an optimized fractional-order proportional-integral (FOPI) controller for a DC–DC single-ended primary inductance converter (SEPIC) is considered to fulfill the application of power factor correction and voltage regulation along with improved robustness, efficiency, and performance characteristics of the converter. An Atom Search Optimization technique is proposed to optimize the parameters of the controller in the outer voltage and inner current control loop of the DC–DC SEPIC model. The model is developed using MATLAB –Simulink, and the simulation analysis is carried out at rated load, setpoint tracking, source voltage, and load variation. The effectiveness of the proposed atom search optimized FOPI controller is verified by comparing its performance with the particle swarm optimized FOPI controller. Furthermore, Matignon’s theorem-based closed-loop stability analysis is carried out for the tuned values of the FOPI controller with the SEPIC model. According to the simulation results, the proposed technique provides a more dominant dynamic response, an improved efficiency, and a power factor than the particle swarm-tuned controller of the SEPIC model. In addition, better voltage regulation is achieved in the case of source voltage and load variation. Furthermore, the closed-loop stability analysis reveals that the proposed Atom Search Optimization-tuned FOPI controller performance is more stable than the particle swarm optimization method. The hardware-in-the-loop implementation is carried out to validate the proposed controller in real-time.

Stabilisation of network-controlled aircraft pitch control system with time delay

This paper describes the stability assurance of network-controlled aircraft pitch control system with time delays. A frequency-domain method is used to determine the upper bound of time delay for aircraft pitch control system with gain and phase margin constraint. The effectiveness of proportional-integral (PI) and fractional-order PI controller on aircraft pitch control system stability and performance is investigated in presence of time delay. The parametric space of the PI and fractional-order PI controller are plotted in two-dimensional space to determine the stability region and controller is designed with concern to the time delay. The relation between controller parameters and time delay is estimated and these findings contribute significantly for the design of the controller for aircraft pitch control system. The accuracy of the proposed results is validated using simulation benchmark.