Order Proportional Integral Derivative Controller Research Articles

Optimal nonlinear Fractional-Order Proportional-Integral-Derivative controller design using a novel hybrid atom search optimization for nonlinear Continuously stirred Tank reactor

Atom search optimization (ASO) algorithm derived from physics molecular dynamics. Lennard-Jones(L-J) and bond length potential of molecules are used to derive the model for optimization. In this paper, ASO is used for developing a nonlinear Fractional Order Proportional Integral Derivative controller (NL-FOPID) for Continuously Stirred Tank Reactor (CSTR). The convergence characteristics of ASO was improved by proposing a novel hybridization approach. The proposed hybridization approach called Hybrid ASO(HASO) guides the Atom search algorithm to optimally replace the atoms that goes out of the boundary of the search space. The designed algorithm is implemented to optimize various unimodal and multi model standard benchmark functions. From results obtained from this extensive simulation, it is indicated that proposed approach increased the convergence rate and also improved the optimization effort of conventional ASO. The proposed algorithm also tested with controller design for nonlinear CSTR. The NLPID and NL FOPID designed by HASO was better than conventional controllers found in the literature.

Innovative design for enhancing transient stability with an ATFOPID controller in hybrid power systems

In order to make multi-area power systems more efficient and stable, this study aims to create a new intelligent controller design based on adaptive property. The integrated power grid becomes more unstable as renewable energy sources become more prevalent, and system inertia decreases. Resultant, the penetration of renewable and load variance causes frequency changes to be more pronounced. Keeping frequency stable is essential for the electrical energy transmission system to work reliably and efficiently. This paper presents an adaptive design based on the tilt fractional order proportional integral derivative (TFOPID) controller by using an optimized property of bio inspired tunicate search algorithm (TSA). The gains of the TFOPID controller are continuously updated by utilizing the ancillary TPID controller, which is dependent on changes in area frequency. The suggested control system is implemented in the northern and southern regions, which consist of photovoltaic (PV), wind, redox flow battery (RFB), hydro, and thermal power plants. Therefore, this study contributes in the creation of more resilient and efficient power grids, which are critical for incorporating renewable energy sources and satisfying the increasing need for environmentally friendly power solutions.

Enhancing power quality in grid-connected hybrid renewable energy systems using UPQC and optimized O-FOPID

Hybrid Renewable Energy Systems (HRES) have recently been proposed as a way to improve dependability and reduce losses in grid-connected load systems. This research study suggests a novel hybrid optimization technique that regulates UPQC in order to address the Power Quality (PQ) problems in the HRES system. The load system serves as the primary link between the battery energy storage systems (BESS), wind turbine (WT), and solar photovoltaic (PV) components of the HRES system. The major objective of the study is to reduce PQ issues and make up for the load requirement inside the HRES system. The addition of an Optimized Fractional Order Proportional Integral Derivative (O-FOPID) controller improves the efficiency of the UPQC. The Crow-Tunicate Swarm Optimization Algorithm (CT-SOA), an enhanced variant of the traditional Tunicate Swarm Optimization (TSA) and Crow Search Optimization (CSO), is used to optimize the control parameters of the FOPID controller. Utilizing the MATLAB/Simulink platform, the proposed method is put into practice, and the system’s performance is assessed for sag, swell, and Total Harmonic Distortion (THD). The THD values for the PI, FOPID, and CSA techniques, respectively, are 5.9038%, 4.9592%, and 3.7027%, under the sag condition. This validates the superiority of the proposed approach over existing approaches.

Load frequency control in power systems with high renewable energy penetration: A strategy employing P[formula omitted](1+PDF) controller, hybrid energy storage, and IPFC-FACTS

The high penetration of Renewable Energy Sources (RESs) in the modern power system poses a challenge to power system stability. This stability is affected by the stochastic, fluctuating output of RESs, which is influenced by weather conditions, and a lack of inertia resulting from reduced rotating mass. To address this issue, a new controller, referred to as Proportional-Fractional Integrator Plus Proportional-Derivative with Filter, PIλ(1+PDF), is designed for Load Frequency Control (LFC) with the support of a Hybrid Energy Storage System (HESS) for power systems with high-RES penetration. The HESS comprises a Superconducting Magnetic Energy Storage System (SMES) and a Vanadium Redox Flow Battery (VRFB) coupled with an Interline Power Flow Controller Flexible AC Transmission Systems (IPFC-FACTs) controller. The HESS, working in conjunction with the proposed LFC, injects virtual inertia and maintains power flow to expedite the frequency stability process. These systems are also integrated with Alternating Current (AC) and High Voltage Direct Current (HVDC) transmission lines to collectively enhance both the system's stability and the capacity of its transmission lines. To optimize the PIλ(1+PDF) controller parameters, Zebra Optimization Algorithm (ZOA) is employed utilizing an Integral Time Absolute Error (ITAE) objective function. The proposed controller is tested on a four-area power system integrated with a wind turbine, photovoltaic (PV) panels, a biodiesel generator, and a hydrogen aqua electrolyzer fuel cell, representing a high penetration of RESs in modern power systems. The results are compared with those obtained using Proportional-Integral-Derivative (PID) and Fractional Order Proportional Integral Derivative (FOPID) controllers. Sensitivity analysis and robustness tests are also performed to verify the stability of the power network by changing system parameters and under randomly chosen loading conditions. The proposed PIλ(1+PDF) controller tuned with ZOA outperforms PID and FOPID controllers by minimizing settling time for frequency changes by 62 %, eliminating overshoot, and reducing undershoots for frequency and tie-line power changes by 73 % and 55 %, respectively. Simulation results demonstrate that the proposed controller outperforms PID and FOPID controllers by effectively damping frequency and tie-line deviations, resulting in reduced frequency overshoots, undershoots, and shorter settling times.

A Novel Multilevel Inverter for Renewable Energy Applications with Optimized Controller and Reduced Switches

Multilevel converters have the capability of handling high power as well as deliver output with reduced harmonics. So they can be implemented with renewable energy sources to produce multilayer output with symmetric cascade arrangement with reduced switches. Here the control technique is developed in such a way to reduce the harmonics in the grid integrated PV system. The paper proposes optimized Fractional Order Proportional Integral Derivative (FOPID) controller for a seven level reduced switch multilevel inverter. The War Strategy Optimization Algorithm (WSOA) which utilizes optimizing the strategic movements of armed forces (assault and defend) towards the final optimal value is used to optimize the FOPID controller. This WSOA algorithm is used to adjust the gain parameters of the FOPID controller there by improving the system performance. The characteristics of grid connected PV system are regulated by implementing this suggested technique. The projected approach is incorporated using MATLAB / Simulink and the performances are evaluated and compared with the conventional techniques like GA – PID and WSOA – PID controllers.

Design of fractional MOIF and MOPIF controller using PSO algorithm for the stabilization of an inverted pendulum‐cart system

AbstractThe topic of this paper is the design of two fractional order schemes, based on a state feedback for linear integer order system. In the first one of the state feedback is associated with a fractional order integral () controller. In the second structure the state feedback is associated with a fractional order proportional integral () controller. With such controllers, the closed loop system with state feedback described by the state equations splits in n‐subsystems with different fractional orders derivatives of the state variable. In order to find the optimal parameters value of both controllers () and (), a multi‐objective particle swarm optimization algorithm is used, with the integral of absolute error, the overshoot , the Buslowicz stability criterion are considered as objective functions. The multi‐objective integral fractional order controller and the multi‐objective proportional integral fractional order controller are applied to stabilize the inverted pendulum‐cart system (IP‐C), and their performance is compared to the fractional order controller. The simulation results of these innovative controllers are also compared with those obtained by conventional proportional–integral–derivative and fractional order proportional–integral–derivative controllers. The robustness of the proposed controllers against disturbances is investigated through simulation runs, considering the non‐linear model of the IP‐C system. The obtained results demonstrate that our approach not only leads to high effectiveness but also showcases remarkable robustness, supported by both simulation and experimental results.

Frequency regulation of interconnected hybrid power system with Assimilation of electrical vehicles

Recent widespread connections of renewable energy resource (RESs) in place of fossil fuel supplies and the adoption of electrical vehicles in place of gasoline-powered vehicles have given birth to a number of new concerns. The control architecture of linked power networks now faces an increasingly pressing challenge: tie-line power fluctuations and reducing frequency deviations. Because of their nature and dependence on external circumstances, RESs are analogous to continually fluctuating power generators. Using a fractional order-based frequency regulator, this work presents a new method for improving the frequency regulation in a two-area interconnected power system. In order to deal with the frequency regulation difficulties of the hybrid system integrated with RES, the suggested controller utilizes the modified form of fractional order proportional integral derivative (FOPID) controller known as FOI-PDN controller. The new proposed controllers are designed using the white shark optimizer (WSO), a current powerful bioinspired meta heuristic algorithm which has been motivated by the learning abilities of white sharks when actively hunting in the environment. The suggested FOI-PDN controller's performance was compared to that of various control methodologies such as FOPID, and PID. Furthermore, the WSO findings are compared to those of other techniques such as the salp swarm algorithm, sine cosine algorithm and fitness dependent optimizer. The recommended controller and design approach have been tested and validated at different loading conditions and different circumstances, as well as their robustness against system parameter suspicions. The simulation outcomes demonstrate that the WSO-based tuned FOI-PDN controller successfully reduces peak overshoot by 73.33%, 91.03%, and 77.21% for region-2, region-1, and link power variation respectively, and delivers minimum undershoot of 89.12%, 83.11%, and 78.10% for both regions and tie-line. The obtained findings demonstrate the new proposed controller's stable function and frequency controlling performance with optimal controller parameters and without the requirement for a sophisticated design process.

Implementation of FOPID controller with modified harmony search optimization for precise modelling and auto-tuning of nonlinear systems

This research aims to optimize the fractional order proportional integral derivative (FOPID) controller for nonlinear process tests. Instead of relying on the traditional trial-and error method for dynamic parameter selection, this proposes a modified harmony search optimization method to compute the optimal dynamic parameters. Based on the physical parameters, using mathematical modelling techniques system transfer function is determined. Additionally, the delay of the control scheme is determined using the Open Loop Transfer Function (OLTF) response. The dynamic parameters of the FOPID controller are evaluated using the Harmonic Search Algorithm – Fractional Order Proportional Integral Derivative (HAS_FOPID) optimization technique, which aims to minimize the system's Integral Square Error (ISE). Time responses, including rise time, peak time, and peak overshoot, are obtained and optimized through the HAS_FOPID algorithm. To verify systems stability, the output response is analysed using various techniques such as bode plots, pole placement, and Nyquist plots. Furthermore, the HAS_FOPID optimization technique is compared with other natural optimization techniques to assess its effectiveness. The research also evaluates the system's robustness by supply/ load disturbances. The objective is to demonstrate that, the optimized HAS_FOPID technique, has significantly enhanced control performance, stability, and robustness of nonlinear systems compared to natural and alternative optimization approaches.

Enhancing Power Quality with PDO-FOPID Controller in Unified Power Quality Conditioner for Grid-Connected Hybrid Renewables

Addressing the pressing research problem of power fluctuations and grid harmonics in the integration of renewable energy, our proposed control strategy utilizes the Prairie Dog Optimization Fractional Order Proportional Integral Derivative (PDO-FOPID) controller within a Unified Power Quality Conditioner (UPQC) system. This innovative approach is tailored to mitigate harmonics and meet load requirements in grid-connected hybrid renewables. The UPQC system is instrumental in regulating coupling point voltage, countering voltage and current harmonics to enhance overall power quality. The PDO-FOPID controller dynamically adapts control parameters to system dynamics and load changes, ensuring a stable power supply despite the variability of renewable sources. Simulations in MATLAB/ Simulink confirm its superiority over traditional control strategies, such as PI, sliding mode, and fuzzy control, in harmonics mitigation, load fulfilment, and power stability. By effectively addressing these challenges, our proposed solution not only contributes to resolving a critical research problem but also advances the seamless integration of Hybrid Renewable Energy Sources (HRES) into power systems, thereby enhancing overall grid performance and the efficacy of renewable energy integration.

Passivity-based Rieman Liouville fractional order sliding mode control of three phase inverter in a grid-connected photovoltaic system.

Photovoltaic (PV) system parameters are always non-linear due to variable environmental conditions. The Maximum power point tracking (MPPT) is difficult under multiple uncertainties, disruptions and the occurrence of time-varying stochastic conditions. Therefore, Passivity based Fractional order Sliding-Mode controller (PBSMC) is proposed to examine and develop a storage function in error tracking for PV power and direct voltage in this research work. A unique sliding surface for Fractional Order Sliding Mode Control (FOSMC) framework is proposed and its stability and finite time convergence is proved by implementing Lyapunov stability method. An additional input of sliding mode control (SMC) is also added to a passive system to boost the controller performance by removing the rapid uncertainties and disturbances. Therefore, PBSMC, along with globally consistent control efficiency under varying operating conditions is implemented with enhanced system damping and substantial robustness. The novelty of the proposed technique lies in a unique sliding surface for FOSMC framework based on Riemann Liouville (R-L) fractional calculus. Results have shown that the proposed control technique reduces the tracking error in PV output power, under variable irradiance conditions, by 81%, compared to fractional order proportional integral derivative (FOPID) controller. It is reduced by 39%, when compared to passivity based control (PBC) and 28%, when compared to passivity based FOPID (EPBFOPID). The proposed technique led to the least total harmonic distortion in the grid side voltage and current. The tracking time of PV output power is 0.025 seconds in PBSMC under varying solar irradiance, however FOPID, PBC, EPBFOPID, have failed to converge fully. Similarly the dc link voltage has tracked the reference voltage in 0.05 seconds however the rest of the methods either could not converge, or converged after significant amount of time. During solar irradiance and temperature change, the photovoltaic output power has converged in 0.018 seconds using PBSMC, however remaining methods failed to converge or track fully and the dc link voltage has minimum tracking error due to PBSMC as compared to the other methods. Furthermore, the photovoltaic output power converges to the reference power in 0.1 seconds in power grid voltage drop, whereas other methods failed to converge fully. In addition power is also injected from the PV inverter into the grid at unity power factor.

Black-hole optimisation algorithm with FOPID-based automation intelligence photovoltaic system for voltage and power issues

ABSTRACT The article discusses the challenges related to voltage and power management in automated intelligent photovoltaic (PV) systems. It suggests that Fractional Order Proportional Integral Derivative (FOPID) controllers can help address these challenges effectively. The research aims to create a highly adaptable and precise automated intelligent PV system that focuses on managing voltage and power issues. It introduces a novel approach using the Black Hole Optimization (BHO) algorithm and leverages the advantages of FOPID controllers for automation. The study also considers thermal models for batteries within the automated intelligent PV system and explores different options to handle voltage and power issues stemming from PV panels. It involves fine-tuning 15 parameters using the BHO algorithm and concludes that one configuration (Instance 1) is preferable due to its superior accuracy and scalability. This choice is supported by objective validation. In essence, your abstract is about improving the performance and automation of PV systems, particularly in dealing with voltage and power challenges, through the application of FOPID controllers and the innovative BHO algorithm.

ANFIS-based FOPID controller to enhanced stability of cascaded converter for electric vehicle (EV) charger

In an electric vehicle (EV) charger system, a two-stage conversion process is integrated and cascaded with a voltage source converter (VSC) and a Dual active bridge converter (DAB). These impedances VSC outputs impedance (ZoutVSC(s)) and DAB have input impedance (ZinDAB(s)) interact, leading to voltage fluctuation and power loss. To address the cascaded converter’s impedance interaction, the modified controller that combines an adaptive Neuro-fuzzy inference system (ANFIS) based fractional order proportional integral derivative (FOPID) controller is used with effective active damping (AD). The modified controller (ANFIS + FOPID + AD) uses ANFIS’s skills to capture and predict the system’s nonlinear behaviour, using its trained data to guide the FOPID’s parameter. The presence of AD ensures the sorting out of impedance interaction problems. Compared to the PID controller, the FOPID controller includes two more degrees of freedom and offers superior adaptability and performance. The effectiveness of the modified controller is tested via frequency response analysis and time domain simulations. Time domain simulations underscore the advantage of the modified controller (ANFIS + FOPID + AD), revealing a remarkable 30% settling time and a 25% overshoot compared to the (FOPID + AD) controller. It is better regarding flexibility, faster response time, and improved system stability. The system performance has been validated and compared by simulation process and HIL technique OPAL RT OP44512.

LUS-TLBO Optimized Load Frequency Control for EV-Thermal-Hydro System Using Cascaded 3DOFPID-FOPID-FOPD-TID Controller

This study unveils the application of cascaded-three degree of freedom proportional integral derivative -fractional order proportional integral derivative-fractional order proportional derivative-tilted integral derivative (CC-3DOFPID-FOPID-FOPD-TID) controller optimized by local unimodal sampling –teaching learning based optimization (Lus-TLBO) algorithm for frequency stability. Conventional controller under reformed operating situations, are not giving reasonable performances as compared to cascaded controller in terms of robustness towards system non-linearities. Hence, a novel optimal 3DOFPID-FOPID-FOPD-TID controller is exploited for 4-area hydro thermal power systems considering system non lineraities. Further batteries of electric vehicles (EVs) are conformed here in the control areas to speedily incarcerated frequency oscillations following load demands to improve the stability of the system. Frequent simulations are directed to substantiate the robustness and superiority of EVs and the recommended control strategy over prevailing approaches. A hybrid Lus-TLBO algorithm is introduced here to optimize the controller parameters. The supremacy of dynamic performances of Lus-TLBO optimized controller is accomplished with teaching learning based optimization (TLBO) based for EV with system and without system through extensive simulations. Moreover the preeminence of cascade 3DOFPID-FOPID-FOPD-TID controller is executed in comparison with 3DOFPID-FOPID-TID, 3DOFPID-FOPID and 3DOFPID-TID controllers. Finally the robustness of this cascade is performed under random load fluctuation.

A novel metaheuristic algorithm based FOPID approach for decentralized control of vibration of a railway vehicle

This article investigates a 27-degree-of-freedom dynamic model of a full-scale railway vehicle. The controlling action is performed by developing a decentralized control structure with five independent Fraction Order Proportional Integral Derivative (FOPID) controllers three types of random track irregularities, vertical profile, lateral alignment, and cross-level. A novel metaheuristic optimization technique named hybrid Particle Swarm Optimization-Gray Wolf Optimization (hybrid PSO-GWO) is proposed to optimize active force for an active suspension system. The simulated results show that the hybrid metaheuristic algorithm outperforms with a significant reduction in vehicle vibration ensuring enhanced ride comfort of the car body.

Fractional Order Modeling and Control of an Articulated Robotic Arm

This paper presents a fractional order system modeling of a robotic arm and the development of a Fractional Order PID (FOPID) controller applied to the system. The controller technique originated from non-integer calculus, which improves the robotic arm's overall stability and positioning. The robotic arm system is modeled using the non-integer order technique in order to improve system accuracy. Thus, a non-integer order Proportional Integral Derivative (PID) control method is implemented to stabilize the plant positioning. Using MATLAB/Simulink the FOPID controller simulations were confirmed and compared to the Integer Order PID (IOPID) controller for tracking the robotic arm positioning. Simulation outcomes imply that the proposed non-integer controller increases the system stability and position with/without external disturbances being present in the environment.

Improved Load Frequency Control in Power Systems Hosting Wind Turbines by an Augmented Fractional Order PID Controller Optimized by the Powerful Owl Search Algorithm

The penetration of intermittent wind turbines in power systems imposes challenges to frequency stability. In this light, a new control method is presented in this paper by proposing a modified fractional order proportional integral derivative (FOPID) controller. This method focuses on the coordinated control of the load-frequency control (LFC) and superconducting magnetic energy storage (SMES) using a cascaded FOPD–FOPID controller. To improve the performance of the FOPD–FOPID controller, the developed owl search algorithm (DOSA) is used to optimize its parameters. The proposed control method is compared with several other methods, including LFC and SMES based on the robust controller, LFC and SMES based on the Moth swarm algorithm (MSA)–PID controller, LFC based on the MSA–PID controller with SMES, and LFC based on the MSA–PID controller without SMES in four scenarios. The results demonstrate the superior performance of the proposed method compared to the other mentioned methods. The proposed method is robust against load disturbances, disturbances caused by wind turbines, and system parameter uncertainties. The method suggested is characterized by its resilience in addressing the challenges posed by load disturbances, disruptions arising from wind turbines, and uncertainties surrounding system parameters.

Optimal control of the electro-hydraulic actuator for variable pitch variable speed wind turbine: Performance enrichment

The wind energy generation system is complex because of varying wind speeds and its control systems to improve its ability of energy harvesting. This paper considers a hydraulic actuator-based variable-pitch angle control of a 1.5 MW wind turbine. The existing control systems of the pitch mechanism of the wind turbines are complex and bulky size. This study applied Genetic Algorithm based Proportional Integral Derivative Controller (GA-PID), Fractional Order Proportional Integral Derivative (FOPID), and Genetic Algorithm based Fractional Order Proportional Integral Derivative (GA-FOPID) controllers to adjust the pitch angle of the wind turbine blade. The performance of GA-FOPID, FOPID, and GA-PID controlled pitch angle is compared by considering different wind speeds. The GA-FOPID controller reduced the variation in mechanical power to 0.08% concerning the rated value and the variation in mechanical torque to 1.51% in comparison to the rated value. Therefore, the GA-FOPID controller shows better performance than the conventional PID.

Control of self-excited induction generator based wind turbine using current and voltage control approaches

The self-excited induction generator (SEIG) is widely applied in the wind energy conversion system (WECS) to enhance power generation. The power generation from WECS is varied in terms of varying wind speed. Hence, to improve the working of SEIG-based WECS, the multi-stage coati optimized proportional integral (CPI) fractional order proportional integral derivative (FOPID) controller is proposed in this work. The proposed coati optimized proportional integral - fractional order proportional integral derivative controls the SEIG’s grid side converter and generator side converter. The coati optimization algorithm optimizes the controller parameters of a proposed multi-state controller. The proposed CPI-FOPID controls both the voltage at the grid side converter and the current at a generator side converter. Moreover, the pitch angle of the wind turbine (WT) is controlled by the fuzzy-based tilt integral derivative (F-TID) controller. The proposed work will be implemented on the Matlab/Simulink platform, and the THD of 0.63% has proven the efficacy of the proposed methodology.

Distributed leader-follower based adaptive consensus control for networked microgrids

Networked microgrids (NMGs) provide a promising solution for accommodating various distributed energy resources (DERs) and enhance its performance. However, the coordinated operation of the system with integration of a large number of DERs is major challenge. Therefore, this article aims to provide a distributed control strategy (DCS) based on a leader-follower framework for the coordination of multiple DERs in NMGs. A fuzzy optimized Recurrent Hopfield Neural Network (F-HNN) designed self-adaptive fractional order proportional integral derivative (FOPID) controller is proposed for distributed frequency control of NMGs. Initially, a Lyapunov-based objective function is derived for weight updation of the proposed network. The fuzzy approach is used to optimize the output of the HNN based on its gradients. The proposed F-HNN based DCS is implemented in MATLAB/Simulink and validated for frequency regulation of NMGs through hardware-in-the-loop simulation (HIL) using OPAL-RT. The results obtained are compared with the conventional FOPID HNN tuned and other classical controls. The self-adaptiveness of the controller is demonstrated for change in renewable power generation. Furthermore, the resiliency of the controller is tested with communication failures and, plug and play operation of MGs. The results obtained showed that the frequency of the NMG system is well regulated within the band of ±0.2 Hz. Also, the transient and steady state performance reveals that the proposed DCS is more significant than other techniques.

Neural Fractional Order PID Controllers Design for 2-Link Rigid Robot Manipulator

The robotic manipulator is considered one of the complex systems that include multi-input, multi-output, non-linearity, and highly coupled. The uncertainty in the parameters and external disturbances have a negative influence on the performance of the system. Therefore, the controllers that will be designed for these systems must be able to deal with these complexities and difficulties. The Proportional, Integral, and Derivative (PID) controller is known to be simple and well robust, while the neural network has a solid ability to map complex functions. In this paper, we propose six control structures by combining the benefits of PID controller with integer and fractional order and the benefits of neural networks to produce hybrid controllers for a 2-Link Rigid Robot Manipulator (2-LRRM) handling with the problem of trajectory tracking. The Gorilla Forces Troops Optimization algorithm (GTO) was used to tune the parameters of the proposed controller schemes to minimize the Integral of Time Square Error (ITSE). In addition, the robustness of the performance of the suggested control systems is tested by altering the initial position, external disturbances and parameters and carried out using MATLAB. The best performance of the proposed controllers was the Neural Network Fractional Order Proportional Integral Derivative Controller (NNFOPID).