Fractional PI Research Articles

Multi-objective network resource allocation method based on fractional PID control

In this paper, a fractional proportional–integral–derivative (PID) distributed optimization algorithm is proposed to solve the network resource allocation problem. The algorithm combines fractional calculus and the concept of PID control, which improves the convergence rate and increases the freedom, flexibility and potential with multiple parameters compared with the existing algorithms. Meanwhile, the results of simulation study verified the efficiency and superiority of the algorithm.

Revolutionizing PV grid integration: Metaheuristic optimization of fractional PI controllers in T-type neutral point piloted inverters for enhanced performance

This study investigates the efficacy of FOPI regulators as a substitute for conventional proportional integral (PI) controllers in grid-connected PV inverters. The research's objective is to improve the dynamic efficiency of these systems by integrating intelligent optimization techniques that utilize both PI and FOPI controllers and employing different metaheuristic optimization procedures. The study introduces four new optimization algorithms: the Tyrannosaurus Optimization Algorithm (TROA), the Nutcracker Optimization Algorithm (NOA), the Golden Eagle Optimizer (GEO), and the Jellyfish Search Optimizer (JSO). These are made to meet the needs of multi-objective optimization. The proposal suggests using two PI/FOPI regulators to regulate both voltage and amperage provided by the multilayer inverter. The proposal employs a T-type three-level inverter, known for its superior conversion efficiency over conventional inverters. Matlab-Simulink simulations demonstrate that the Nutcracker optimization algorithm (NOA) outperforms other metaheuristic techniques for optimizing dynamic behavior, such as overshoot, settling time, execution, and rising time. Comparisons with existing methods, such as the Manta Rays Foraging Optimization (MRFO) and Grey Wolf Optimizer (GWO), show that all four new algorithms consistently outperform these existing algorithms. The data suggest that using NOA improves stability, efficiency, and power factor while reducing the inverter's THD.

Integer PI, fractional PI and fractional PI data trained ANFIS speed controllers for indirect field oriented control of induction motor

Induction motor drives with variable speed applications that employ vector control are quite popular nowadays because they provide strong dynamic performance and flexible speed control. By decoupling the torque-producing current components of stator current from the rotor flux, Indirect Field Oriented Control is recognized for generating excellent performance in induction motor drives. This investigation is being done to show the effectiveness of the novel FPI input-output data-trained ANFIS controller and compare the three controllers' performance in terms of load variation capabilities, motor parameter variation, and speed tracking. Consequently, a comparison of the three controllers is important to select which controller performs high in induction motor drive. Indirect Field Oriented Control of induction motor with Fractional Proportional Integral (FPI), Integer Proportional Integral (IPI), and Adaptive Neuro-Fuzzy Inference System (ANFIS) controllers are all discussed in this work along with their designs and comparative analysis. The square of error was used as a fitness function to genetically optimize the FPI and IPI controller parameters. The suggested Adaptive Neuro-Fuzzy Inference System (ANFIS) controller uses a hybrid learning approach. It is trained by the FPI controller's input-output data. Using the results of MATLAB simulations under various operating situations, the performance of the ANFIS controller was compared with FPI and IPI controllers. Because of FPI controller includes an extra parameter for adjustment, namely integration order, it performed better than IPI controller for speed control of the induction motor. According to the simulation findings, the percentage peak overshoots while employing ANFIS, FPI, and IPI controllers were 0.495 %, 12.062 %, and 14.699 % respectively. As a result, ANFIS exhibits a drastic reduction in overshoot. Additionally, with the ANFIS controlled induction motor drive, the speed achieves the required set value at 0.14 s. For no load, constant, and changing loads, the induction motor drive's performance has been examined.

Optimal fractional PI controller-based VSC-HVDC system with LCL filter design

For decades, high voltage direct current (HVDC) has been an essential means in designing smart microgrids. Though, a control approach for Voltage Source Converter (VSC)-based HVDC, like dampening oscillations, must be established for improved operational execution, as these oscillations can cause stability issues. Considering its versatility, the Fractional order Proportional Integral (FPI) controller is used in this study's control approach instead of the PI controller. With frequency domain analysis, comprehensive modelling and design of LCL filters for harmonic reduction to improve power quality are presented. The dynamic characteristics of VSC-HVDC are comprehensively presented based on dq axis synchronous frame of reference. The VSC-HVDC improved control outcome is validated by the result analysis using PI and FPI controller using ITLBO. It is found in both frequency and time-domain simulations and analysis that the AFPI-VSC-HVDC system is capable of effectively dampening oscillations to enhance the small-signal stability.

Control strategies for grid-connected hybrid renewable energy systems: Integrating modified direct torque control based doubly fed induction generator and ANFIS based maximum power point tracking for solar PV generation

This research article introduces advanced control strategies for grid-connected hybrid renewable energy systems, focusing on a doubly fed induction machine (DFIM) based wind power plant and a photovoltaic based solar power plant. The proposed approach integrates Direct Torque Control (DTC) with modified filters and a fractional Proportional-Integral (PI) controller for the DFIM wind power plant. The modified DTC utilizes estimated torque and flux, employing a modified filter to minimize deviations, and a fractional PI controller for improved vector selection. This results in an enhanced duty cycle for the rotor side converter, optimizing power output to the grid. Additionally, an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based Maximum Power Point Tracking (MPPT) algorithm is implemented for the solar power plant, dynamically adjusting the duty cycle for increased power output compared to conventional MPPT methods. Simulation results in MATLAB and experimental verification demonstrates the stability and feasibility of the proposed controllers, showcasing superior performance compared to conventional counterparts under various operating conditions.

Effluent quality improvement in sequencing batch reactor-based wastewater treatment processes using advanced control strategies.

The treatment of wastewater is highly challenging due to large fluctuations in flowrates, pollutants, and variable influent water compositions. A sequencing batch reactor (SBR) and modified SBR cycle-step-feed process (SSBR) configuration are studied in this work to effectively treat municipal wastewater while simultaneously removing nitrogen and phosphorus. To control the amount of dissolved oxygen in an SBR, three axiomatic control strategies (proportional integral (PI), fractional proportional integral (FPI), and fuzzy logic controllers) are presented. Relevant control algorithms have been designed using plant data with the models of SBR and SSBR based on ASM2d framework. On comparison, FPI showed a significant reduction in nutrient levels and added an improvement in effluent quality. The overall effluent quality is improved by 0.86% in FPI in comparison with PI controller. The SSBR, which was improved by precisely optimizing nutrient supply and aeration, establishes a delicate equilibrium. This refined method reduces oxygen requirements while reliably sustaining important biological functions. Focusing solely on the FPI controller's performance in terms of total air volume consumption, the step-feed SBR mechanism achieves an excellent 11.04% reduction in consumption.

Design and Implementation DC/DC Luo Converter Controlled by Adaptive Fractional PI and P&O MPPT

Design and Implementation DC/DC Luo Converter Controlled by Adaptive Fractional PI and P&O MPPT

A novel fractional-order dead-time compensating controller for the wireless networks

Wireless technology is becoming increasingly critical in industrial environments in recent years, and the popular wireless standards are WirelessHART, ZigBee, WLAN and ISA100.11a, commonly used in closed-loop systems. However, wireless networks in closed-loop control experience packet loss or drops, system delay and data threats, leading to process instability and catastrophic system failure. To prevent such issues, it is necessary to implement dead-time compensation control. Traditional techniques like model predictive and predictive PI controllers are frequently employed. However, these methods’ performance is sluggish in wireless networks, with processes having long dead times and set-point variations, potentially affecting network and process performance. Therefore, this paper proposes a fractional calculus-based predictive PI compensator for wired and wireless networks in the process control industries. The proposed technique has been simulated and evaluated on industrial process models, including pressure, flow, and temperature, where measurement and control are carried out wirelessly. The wireless network’s performance has been evaluated based on packet loss, reduced throughput, and increased system latency. The proposed compensator outperformed traditional methods, demonstrating superior set-point tracking, disturbance rejection, and delay compensation characteristics in the performance evaluations of the first, second, and third-order systems. Overall, the findings indicate that the proposed compensator enhances wireless networks’ performance in the process control industry and improves system stability and reliability by reducing almost half of the overshoot and settling an average of 8.3927% faster than the conventional techniques in most of the systems.

A novel optimized dynamic fractional-order MPPT controller using hunter pray optimizer for alleviating the tracking oscillation with changing environmental conditions

Introducing new control strategies in the photovoltaic (PV) system to continuously harvest the maximum power with the changes in environmental conditions is a crucial issue. Therefore, this paper proposes an efficient maximum power point tracker (MPPT) using the perspective of fractional calculus to provide an accurate dynamic response to the rapid changes in environmental conditions. The proposed control scheme is an integration between the fractional proportional–integral (FPI) controller and dynamic variable fractional-order perturb and observe (P&O) MPPT. To optimally identify the proposed MPPT controller parameters, a novel hunter-pray optimizer (HPO) is implemented as it is featured by its efficient balance between exploration and exploitation capacity. The proposed MPPT controller is examined with a series of experiments under dynamically changed environmental conditions. Furthermore, a detailed comparison is conducted versus a set of state-of-the-art including; incremental conductance (INC), basic P&O, MPPT-based particle swarm optimizer(PSO), MPPT-based Grey Wolf Optimizer(GWO), and MPPT-based cuckoo search algorithm (CSA). The results prove that the proposed MPPT is capable to track the global maximum generated power with a notable steady-state response and is almost free of oscillations which ensures an optimal adaptive dynamic performance in response to the rapid variation in the environmental conditions. Moreover, the proposed approach affirms its superiority compared to the set of state-of-the-art techniques in providing the highest maximum power levels in the shortest conversion time. The outcomes provide proof of the remarkable impacts of integrating fractional calculus in enhancing the dynamic response of the proposed MPPT because of the extra degree of freedom that enhance the flexibility of the MPPT.

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

The power circuit of AC voltage controller capable of operating at a leading, lagging, and unity power factor is studied by a lot of researchers in the literature. Circuits working with high switching frequency are known as power factor correctors (PFCs). The single-phase boost converter has become the most popular topology for power factor correction (PFC) in general purpose power supplies. Power factor correction circuit provides conventional benefits to electric power systems. The benefits are the reduction of power factor penalty and utility bill and power loss. Therefore, a boost converter power factor correction scheme is presented in this paper. A PI, fuzzy logic PI and fractional order PI (FOPI) controllers are used to fix an active shaping of input current of the circuit and to improve the power factor. The controller parameters (coefficients) are optimized using the Particle Swarm Optimization (PSO) algorithm. Average current mode control (ACMC) method is used in the circuit. The converter circuit consists of a single-phase bridge rectifier, boost converter, transformer and load. A mathematical model of the plant is required to design the PI controller. A model for power factor correction circuit is formed in MATLAB/Simulink toolbox and a filter is designed to reduce THD value. The proposed model is simulated using a combination of PI, fuzzy logic and FOPI controllers. The control scheme is applied to 600 Watt PFC boost converter to get 400 Volt DC output voltage and 0.99 power factor. The input voltage is 230 VRMS with 50 Hz. The combination of FOPI and PI controller has the best solution to control the power factor according to PI and fuzzy controllers.

Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control

In this work, a fractional integral sliding-mode control scheme based on the Caputo–Fabrizio derivative and the Atangana–Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler–Lagrange method and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are controlled by fractional PI controllers based on the Atangana–Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo–Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana–Baleanu integral, is introduced on the sliding surface further improving system performance with less power consumption. The conventional integral sliding mode control and an optimal super-twisting sliding mode control are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and trajectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo–Fabrizio and Atangana–Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them.

Multi-Drug Scheduling for Chemotherapy Using Fractional Order Internal Model Controller

Chemotherapy is a widely used cancer treatment method globally. However, cancer cells can develop resistance towards single-drug-based chemotherapy if it is infused for extended periods, resulting in treatment failure in many cases. To address this issue, oncologists have progressed towards using multi-drug chemotherapy (MDC). This method considers different drug concentrations for cancer treatment, but choosing incorrect drug concentrations can adversely affect the patient’s body. Therefore, it is crucial to recognize the trade-off between drug concentrations and their adverse effects. To address this issue, a closed-loop multi-drug scheduling based on Fractional Order Internal-Model-Control Proportional Integral (IMC-FOPI) Control is proposed. The proposed scheme combines the benefits of fractional PI and internal model controllers. Additionally, the parameters of IMC-FOPI are optimally tuned using a random walk-based Moth-flame optimization. The performance of the proposed controller is compared with PI and Two degrees of freedom PI (2PI) controllers for drug concentration control at the tumor site. The results reveal that the proposed control scheme improves the settling time by 43% and 21% for VX, 54% and 48 % for VY, and 48% and 40% for VZ, respectively, compared to PI and 2PI. Therefore, it can be concluded that the proposed control scheme is more efficient in scheduling multi-drug than conventional controllers.

A fractional PI observer for incommensurate fractional order systems under parametric uncertainties

The problem of state observation in incommensurate fractional order systems has been poorly studied. Currently some observers that have been proposed are based on a copy of the system, which causes them to be highly dependent on the system parameters, additionally they are redundant (estimate variables that are available). So this paper proposes a novel fractional observer against parametric uncertainties for a certain type of incommensurate fractional order systems. The fractional observer design is based on a property concerning observability in incommensurate fractional order systems which allows us to construct the observer only considering the available output and its fractional derivatives. On the other hand, the convergence analysis of the observation error is carried out using a particular approach of fractional order systems related to the Global Mittag-Leffler boundedness. We prove that there is a compact set GMLA (Globally Mittag-Leffler Attractive, according to Definition 4) where the system that represents the observation error dynamics is attractive and we also prove that the observation error is uniformly bounded. Additionally, the fractional observer is model-free i.e., a system copy is not required, this gives robustness in spite of parametric uncertainties and it is also reduced order therefore one observer must be designed for each variable that we want to estimate consequently the observer is non-redundant (no estimation of variables that are already available). Moreover, our proposed fractional observer can be designed for commensurate fractional order systems and we also show that if we consider integer derivative order, the proposed fractional observer presents certain properties. Finally, in order to show the effectiveness of the proposed fractional observer, an incommensurate fractional order Rössler hyperchaotic system is considered as a numerical example and an incommensurate fractional model of the COVID-19 pandemic as a real-world application.

Research on Fractional Order Modeling and PIλ Control Strategy of V2G Two-Stage Bidirectional Converter

With regard to the insufficiency of independent modeling accuracy in V2G two-stage bi-directional converter in the two-stage system of integer order, it is impossible to accurately describe the actual situation of the poor dynamic performance of the classical PI control strategy as well as the lower power transmission efficiency. Based on the fractional calculus theory, the modeling methods based on the fractional, namely, the state space averaging method and the extended description function method are proposed. The integer inductance and capacitance in the system are extended to fractional inductance and capacitance, and the Fourier decomposition in the extended description function method is extended from integer order to fractional order. The joint mathematical model and small signal model of fractional order for V2G two-stage bidirectional converter are constructed, and the fractional order transfer function of the whole system is obtained. Therefore, a fractional PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> control strategy for V2G two-stage converter is designed. Finally, a 3kW prototype is built in the laboratory, which verifies the correctness and feasibility of fractional modeling and fractional PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> control strategy.

Robust Fractional PI Controller Design for Stand-Alone Microgrid under Load Variation: An Optimization-Based Approach

Robust Fractional PI Controller Design for Stand-Alone Microgrid under Load Variation: An Optimization-Based Approach

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

In this study, a reduced inverse integer-order controller design methodology for single fractional-order pole model is proposed. First, the higher integer-order equivalent of this model is found using the Oustaloup approximation to fractional operator. Then, the poles and zeros of the higher integer-order model are determined in terms of fractional-order system model parameters employing characteristic equation format and root-locus idea. The order of the higher integer-order model is reduced using dominant pole–zero couples. The proximity of the pole–zero couples to each other as well as their proximity to the origin is key dominance requirement for order reduction. The controller is obtained inverting the reduced order integer system model in terms of fractional-order system model parameters. The proposed controller is compared with integer and fractional proportional–integral–derivative (PID) controllers using the experiments carried out on two-tank liquid-level process. The real-time experiment outcomes demonstrate that the proposed controller has superior performance over integer and fractional proportional–integral–derivative controllers.

MSP designing with optimal fractional PI–PD controller for IPTD processes

Abstract An effective tuning methodology of modified Smith predictor (MSP) based fractional controller designing for purely integrating time delayed (IPTD) processes is reported here. IPTD processes with pole at the origin are truly difficult to control; exhibit large oscillations once get disturbed from their steady state. Proposed MSP design consists of fractional PI (proportional-integral) and fractional PD (proportional-derivative) controllers together with P (proportional) controller. Fractional controllers are competent to provide improved closed loop responses due to flexibility of additional tuning parameters. Fractional tuning parameters of PI and PD controllers are derived through optimization algorithms where integral absolute error (IAE) is considered as cost function. Efficacy of the proposed methodology is validated for IPTD processes having wide range of time delay. Stability and robustness issues are explored under process model uncertainties with small gain theorem. Performance of the proposed MSP-FO(PI–PD) controller is validated through simulation study relating five IPTD process models. Overall satisfactory closed loop responses are observed for each case during transient as well as steady state operational phases.

Online tuning of derivative order term of variable‐order fractional proportional–integral–derivative controllers for the first‐order time delay systems

SummaryIn this study, an online tuning strategy for the fractional derivative order term of the variable‐order fractional proportional–integral–derivative (PID) controller is proposed for processes with dead time. The classical step response is divided into regions, and meta‐rules are developed for each region in order to improve the control performance. To achieve the goals of the meta‐rules, a set of equations that are the functions of absolute error and model parameters are proposed to manipulate the fractional order derivative during the process. These equations can handle the changes in model parameters since the coefficients of these equations are functions of model parameters. On both simulation studies and experimental results on the active suspension system, we show that the proposed method improves the time domain performance criteria both in relation to reference tracking and load disturbance rejection. Moreover, the robustness of the proposed method has also been tested and analyzed for the dead time variation within the process.

Self-regulatory Fractional Fuzzy Control for Dynamic Systems: An Analytical Approach

This paper presents an analytical design of a fractional order fuzzy proportional integral plus derivative (FOFPI + D) controller. Artificial intelligence is incorporated into the controller with the help of a formula-based fuzzy logic system. The designed scheme combines fractional order fuzzy PI (FOFPI) and fractional order fuzzy D (FOFD) controller, derived from fundamental FOPID control law. The proposed scheme enjoys the linear structure of the FOPID controllers with non-linear gains that provide self-tuning control capability. The sufficient condition for stability of the closed-loop system is also established using the graphical approach. Performance of the proposed FOFPI + D, its integer order variant (FPI + D), and conventional controllers is examined for control of a highly non-linear and uncertain two-link robotic manipulator system. The optimum parameters of controllers are found by minimising aggregated control variation and error objective through non-dominated sorting genetic algorithm-II (NSGA-II). The comparison for trajectory tracking shows that FOFPI + D has the minimum integral absolute error (IAE) compared to other controllers. Further, rigorous performance investigations are performed to verify the robustness of designed controllers against parametric uncertainties, the varying boundary conditions of reference trajectory and disturbance rejection. It is concluded from the results that the proposed FOFPI + D controller exhibits superior performance.

A Robust Fractional-Order Control Technique for Stable Performance of Multilevel Converter-Based Grid-Tied DG Units

In this article, we propose a sliding fractional-order (FO) control strategy to provide robustness feature for integrating a multilevel converter into the power grid under the system parameter uncertainties, nonlinear load alterations, and grid voltage sag. All dynamics achieved from the input capacitors and output inductances of the multilevel converter are utilized to design the proposed sliding fractional surfaces (SFSs) such that a robust operation of the grid-tied converter-based system is achieved. Then, an SFS-based Lyapunov function is built to assess the proposed controller stability. A thorough analysis of the Lyapunov function is carried out for distinguishing suitable boundaries of the controller coefficients when the error components of the system state variables are changed, accordingly. Using the derivative of Lyapunov function and SFS, a comprehensive evaluation is executed to detail the regulation procedure for the robustness and fractional PI controller coefficients. Finally, a closed-loop system using the converter current dynamics aims to discern the differences between different values of FO. Experimental tests using dSPACE-1202 along with MATLAB/Simulink simulations are employed to verify the effectiveness of the proposed control technique for providing proper harmonic compensation, enhanced power quality, unity power factor, voltage sag tolerance, and very low total harmonic distortion grid current.