Parameters Of Fractional Order PID Controller Research Articles

Robust fractional-order PID controller assisted by active disturbance rejection control for the first-order plus time-delay systems

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

Nature‐ınspired algorithms for optimizing fractional order PID controllers in time‐delayed systems

AbstractTime‐delayed systems frequently appear, especially in sectors such as fluid flow processes, chemical procedures, and the food industry. This paper addresses the optimization of parameters for a fractional order PID (FOPID) controller, which is used to control a time‐delayed system, using five distinct algorithms inspired by nature. These algorithms are NewBAT, Cuckoo search (CS), Firefly (FF), Gray Wolf Optimizer (GWO), and Whale optimization algorithm (WOA). The FOPID controller parameters, namely KP, KI, KD, λ and μ, have been optimized using these algorithms. During the optimization process, the integral of the time absolute error (ITAE) was considered as the primary measurement criterion. In addition to this value, the maximum overshoot, settling time, time to reach the maximum value, and error values were examined. Simulations conducted with the obtained parameters tested the system's resilience to disturbances introduced at the output, and the controller responses were also evaluated during these tests. The reactions of the determined parameters to different reference inputs were analyzed, and the results are presented in graphs and tables. The efficiency and reliability of the optimization algorithms were substantiated by comprehensive statistical analyses. These analyses play a critical role in algorithm selection and objective evaluation of the results. Simulation studies were conducted in the Matlab and Simulink environments. The FOMCON Toolbox was used for fractional‐order processes.

Data-Driven Robust Servo Tuning Method Using Fractional-Order PID Controller

This paper proposes a data-driven method using a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. The proposed method simultaneously obtains FOPID controller and reference model parameters to achieve tracking performance and specified robust stability from only one-shot closed-loop input-output data. The proposed control law is designed by solving an optimization problem, subject to the constraint condition of using the maximum value of the sensitivity function. Therefore, the proposed method provides trade-off design between tracking performance for the reference input and robust stability by selecting robust stability. By comparing numerical example results obtained for FOPID and integer-order controllers, it is shown that the use of the FOPID controller is effective in improving tracking performance for reference output.

Optimal control of DC motor using leader-based Harris Hawks optimization algorithm

Direct Current (DC) motor is considered a very critical component of various industrial drive equipment. This is due to their unique advantages including reasonable cost, speed-torque characteristics, ease of control, etc. While most DC motor drive applications often employ PID controllers to regulate the speed of the machine, selecting the optimal design parameters for the controllers used in these applications often posed a serious challenge. Moreover, as the complexity of the industrial process increases, the need for precise speed and position tracking becomes necessary. This current study proposes a novel Leader-based Harris Hawks Optimization (LHHO) algorithm for the design of Proportional-Integral-Derivative (PID) and Fractional Order Proportional-Integral-Derivative (FOPID) controllers to achieve optimal speed regulation of DC motors. The LHHO algorithm is an innovative meta-heuristic algorithm that draw inspiration from the cooperative hunting behavior and leadership prowess of the Harris Hawks called the “seven pounds”. While several error functions were tested in this study, the integral of time multiplied absolute error (ITAE) has been adopted as the error function for obtaining the parameters of PID and FOPID controllers using the LHHO algorithm. Through quantitative evaluations and comparisons with existing techniques, the proposed controllers (LHHO-PID and LHHO-FOPID) have revealed significant improvements in key performance metrics, including rise time, settling time, and maximum overshoot during transient periods when ITAE is used as the error function. Furthermore, the stability response and robustness analyses were carried out by varying the parameters of the DC motor under eight scenarios, which confirmed competitive performance in system response and transient behavior.

Fractional order controller design via gazelle optimizer for efficient speed regulation of micromotors

In this paper, the design of an efficient fractional-order proportional-integral-derivative (FOPID) controller, tailored specifically for the regulation of micro direct current (DC) motors, is explored. A fresh approach is introduced using the gazelle optimization algorithm (GOA), a cutting-edge method set to manage the speed control of these small but vital motors. With the adoption of GOA, fine-tuning the parameters of the FOPID controller is aimed. This is achieved by employing a time-based performance metrics-based cost function as the guiding compass. The GOA is implemented to discover the optimal controller settings for the attainment of peak performance. Through thorough simulations and careful statistical analysis, the worth of GOA-based FOPID controller is demonstrated. Not only are top-notch cost function values achieved, but excellence across various time domain-based performance metrics is also excelled in. The results suggest that the GOA proves to be efficient in fine-tuning of FOPID controller parameters. A comprehensive analysis in the time domain further solidifies the superiority of GOA-based FOPID-controlled micro-DC motor system. Outperformance is observed when compared to alternative algorithms employing different controllers, such as an advanced hybrid stochastic fractal search-based FOPID controller, a grey wolf optimizer-based FOPID controller, a slime mold algorithm-based PID controller, an enhanced arithmetic Harris hawks optimization-based PID controller, and a hybrid atom search optimization and simulated annealing-based PID controller. In essence, the results highlight the potential of the GOA as a powerful tool poised to reshape the optimization of FOPID controllers for micro-DC motor speed regulation.

Performance analysis of buck converter with fractional PID controller using hybrid technique

In this paper, a hybrid technique is proposed for analyzing the performance of buck converters with fractional-order proportional integral derivative (FOPID) controllers. The hybrid approach is a combination of Capuchin Search Algorithm (CapSA) and Golden Jackal Optimization (GJO). The update behavior of Golden Jackal Optimization2 is enhanced with Capuchin Search Algorithm (CapSA) therefore it is called the improved GJO (IGJO) technique. The power converters are hard to manage based on their nonlinear nature and therefore the search for smart and effectual controllers is ongoing and continual. In current years, fractional order controllers have shown greater efficiency in power electronic systems. The IGJO technique is used to establish the optimum design of a fractional-order proportional integral derivative (PID) controller for the buck converter. The FOPID controller parameters are considered to diminish several performance metrics, with a particular focus on the Integral Squared Error (ISE). The proposed method is performed in the MATLAB, and its execution is analyzed by using the existing methods. From the simulation result, the proposed method reduces the error more effectively than existing methods.

Frequency regulation of hybrid shipboard microgrid system using butterfly optimization algorithm synthesis fractional‐order controller

AbstractInclusion of intermittent natured renewable energy resources in microgrid to reduce global warming, especially in shipboard power system and due to highly fluctuating propulsion load, frequency control strategy of isolated shipboard hybrid microgrid (ISHMG) is major point of attraction. Hence, a power system of marine vessel with dish‐stirling solar thermal system (DSTS), wind‐driven generation (WDG), solid oxide fuel cell (SOFC), super‐conducting magnetic energy storage (SMES), two different AC‐loads, and propulsion loads are considered as an ISHMG. The main objective of this paper is reducing the mismatch between generation and demand with the help of fractional‐order proportional integral‐derivative (FOPID) controller. To improve the frequency control, the tuning of the controller coefficients plays a major role as the controller's performance fully dependent on the parameters. Accordingly, the recently developed butterfly optimization algorithm (BOA) has been used to optimize the FOPID controller's parameters. Comparative analysis of several techniques like FA, PSO, GOA, SSA, and BOA used for PID, PI, FOPID controllers' optimization, and sensitivity analysis under different parametric variation has been presented to prove the stability of the ISHMG model. Analyzing all the results, it is found that BOA‐based FOPID controller is performing the frequency control far better than other techniques.

Output power control of nuclear reactor using ant lion optimization-based controller

Power level control is a <span>critical issue in nuclear power stations due to its nonlinear dynamics. One of the most commonly used controllers is fractional order proportional–integral–derivative (FOPID). The FOPID is an enhanced and modern controlling system that has two additional added parameters. In this paper, comparison between particle swarm, gray wolf and ant lion optimization techniques is performed to determine the FOPID controller parameters. The nuclear reactor is a pressurized water reactor which is a fifth order nonlinear reactor model and is simulated using MATLAB software based on the point kinetic model. The integral square error (ISE) performance index is used to evaluate the performance of the three optimization techniques. The simulation results show that ant lion optimization for tuning the FOPID controller parameters gives the best performance and integral square error index better than the two other optimization techniques.</span>

A New Approach of BLDC Motor Using Fuzzy Fractional Order PID

In order to manage the speed of brushless DC (BLDC) motors, this research presents a novel hybrid control method that simultaneously regulates the DC bus voltage of the inverter and the BLDC motor reference current. A fractional-order PID (FOPID) controller manages the BLDC motor reference current, and a fuzzy logic controller manages the inverter DC bus voltage. A modified harmony search (HS) metaheuristic technique is developed for adjusting the FOPID controller parameters. Three separate working scenarios—no load, varying load, and varying speed—are used to test the motor's capabilities. Run the proposed controller at a high speed to verify its efficacy. The suggested hybrid control method has also been put to the test. weighed against FOPID and fuzzy-based speed control techniques The outcomes demonstrate the effectiveness of the suggested control. approach enables more accurate speed control over a wide region.

Optimized fractional-order PID controller based on nonlinear point kinetic model for VVER-1000 reactor

Abstract Nuclear reactor dynamics are nonlinear and time-varying, so the power level control is a challenging problem in nuclear power plants (NPPs) to ensure both its operation stability and efficiency. An important measure to improve the safety of the reactor core of NPP is the implementation of robust control for the core by adjusting the inserted reactivity of the control rods. Thus in the present paper, fractional-order PID (FOPID) controller is developed as it is well known for its simplicity and robustness against disturbances. A Genetic Algorithm (GA) is used to determine FOPID controller parameters to achieve the desired power level for the generation III+ reactor VVER-1000. Implementing the GA, a suitable objective function is proposed to search for the optimal FOPID parameters. The nonlinear model of the VVER-1000 nuclear reactor is presented based on the point kinetic equations with six delayed neutron groups and temperature feedback from lumped fuel and coolant temperatures. Two cases for the VVER-1000 reactor are investigated; the changes in the power loads and the control rod withdrawal that leads to reactivity disturbance. Moreover, the uncertainties that result from model parameters perturbation are added to examine the controller robustness. The simulation results show that the proposed optimized FOPID controller can track the desired power level of the VVER-1000 reactor and robustly cope with any load changes, disturbances, or any parameters uncertainties. Also, it proves the superiority of the proposed optimized FOPID controller over other PID controllers in ensuring the safe and effective operation of the VVER-1000 reactor.

Power Quality Improvement Using Distributed Power Flow Controller with BWO-Based FOPID Controller

The integration of hybrid renewable energy sources (HRESs) into the grid is currently being encouraged to meet the increasing demand for electric power and reduce fossil fuels which are causing environmental-related problems. Integration of HRESs into the grid can create some power quality (PQ) problems. To mitigate PQ problems and improve the performance of grid-connected HRESs some flexible devices should be used. This paper presents a distributed power flow controller (DPFC), as a type of flexible device to mitigate some PQ problems, including voltage sag, swell, disruptions, and eliminating the harmonics in a hybrid power system (HPS). The HPS presented in this work comprises a photo voltaic (PV) system, wind turbine (WT) and battery energy storage system (BESS). As a result, black widow optimization (BWO) with DPFC with real and reactive power (DPFC-PQ) is built in this paper to solve the PQ issues in HRES systems. The main aim of the work is to mitigate PQ problems and compensate for load demand in the HRES scheme. The controller used to drive this DPFC-PQ is a fractional-order PID (FOPID) controller optimized by the black widow optimization (BWO) technique. To assess the capability of BWO in fine-tuning the FOPID controller parameters, twelve optimization techniques were presented: P&O, PSO, Cuckoo, GA, GSA, BBO, Whale, ESA, RFA, ASO, and EVORFA. Additionally, a comparison between the FOPID controller and the classical PI controller is introduced. The results showed that the proposed BWO-FOPID controller for DFPC had mitigated the PQ problems in grid-connected HRESs. The system’s performance with the presented BWO-FOPID controller is compared with eleven optimization techniques used to optimize the FOPID controller and also compared with the conventional PI controller. The design of the proposed system is implemented in the MATLAB/Simulink platform and performances were analyzed.

English

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared to PID controller, the tuning of FOPID is more complex and remains a challenge problem. This paper focuses on the design of FOPID controller using wound healing algorithm (WHA) based on clonal selection principle. The tuning of FOPID controller is formulated as a nonlinear optimization problem, in which the objective function is composed of overshoot, steady-state error, raising time and settling time. WHA algorithm, a newly developed evolutionary algorithm inspired by human immune system, is used as the optimizer to search the best parameters of FOPID controller. The designed WHA-FOPID controller is applied to various systems. Numerous numerical simulations and comparisons with other FOPID/PID controllers show that the WHA-FOPID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.

Optimal Fractional PID Controller for Buck Converter Using Cohort Intelligent Algorithm

The control of power converters is difficult due to their non-linear nature and, hence, the quest for smart and efficient controllers is continuous and ongoing. Fractional-order controllers have demonstrated superior performance in power electronic systems in recent years. However, it is a challenge to attain optimal parameters of the fractional-order controller for such types of systems. This article describes the optimal design of a fractional order PID (FOPID) controller for a buck converter using the cohort intelligence (CI) optimization approach. The CI is an artificial intelligence-based socio-inspired meta-heuristic algorithm, which has been inspired by the behavior of a group of candidates called a cohort. The FOPID controller parameters are designed for the minimization of various performance indices, with more emphasis on the integral squared error (ISE) performance index. The FOPID controller shows faster transient and dynamic response characteristics in comparison to the conventional PID controller. Comparison of the proposed method with different optimization techniques like the GA, PSO, ABC, and SA shows good results in lesser computational time. Hence the CI method can be effectively used for the optimal tuning of FOPID controllers, as it gives comparable results to other optimization algorithms at a much faster rate. Such controllers can be optimized for multiple objectives and used in the control of various power converters giving rise to more efficient systems catering to the Industry 4.0 standards.

Doğadan Esinlenen Optimizasyon Algoritmaları Tabanlı Kesir Dereceli PID Denetleyicilerle Kontrol Edilen Bir Santral Modelinin Performansının İncelemesi

Bu çalışmada, klasik oransal-integral-türev (PID) kontrolörlerin gelişmiş hali olan kesir dereceli oransal-integral-türev (FOPID) kontrolörlerden faydalanılarak basitleştirilmiş gaz türbinli bir santral modeli için denetlemenin hassas şekilde yapılabilmesi sağlanmıştır. Klasik PID kontrolörler (denetleyiciler) üç parametre içerirken, kesir dereceli PID kontrolörler beş parametre içerir. Parametre sayısının fazla olması daha hassas denetlemenin yapılabilmesine olanak sağlar, ancak bu durum kontrolörün optimizasyonunu zorlaştırır. Kesir dereceli PID kontrolörlerin geleneksel matematiksel yöntemler ile optimizasyonu zor olduğu için; bu çalışmada, doğadan esinlenen (meta-sezgisel) optimizasyon algoritmaları arasında yer alan balina optimizasyon algoritması (BOA), salp sürüsü algoritması (SSA), yapay arı kolonisi (YAK) ve atom arama optimizasyon algoritması (AAO) kullanılmıştır. Bu dört farklı algoritmayla optimize edilen FOPID kontrolör parametreleri, basitleştirilmiş gaz türbini enerji santrali modeline uygulanmış ve sistem çıkış sinyallerinin geçici yanıt performansları karşılaştırılmıştır. Bu amaçla yerleşme süresi ve yüzde en büyük aşım, karşılaştırma kriteri olarak kullanılmıştır. Simulasyon sonuçları, yapay arı kolonisi (YAK) algoritmasıyla optimize edilmiş FOPID kontrolörün, bu santral modeli için yerleşme süresi ve yüzde en büyük aşım kriterleri açısından diğer algoritmalarla optimize edilmiş FOPID kontrolörlere göre daha iyi performans sergilediğini göstermektedir.

Design and Tuning of Digital Fractional-Order PID Controller for Permanent Magnet DC Motor

One of the central problems in control theory is related to the design of controllers for the improvement of system performance. The aim of this paper is to design an efficient digital fractional-order proportional-integral-derivative (FO-PID) controller for the speed control of buck converter fed permanent magnet DC (PMDC) motor. Speed control is achieved by a pulse width modulated control. The FO-PID controller parameters (gain and order) are obtained by using the ant colony optimization (ACO) technique. The effectiveness of the proposed control scheme is simulated and verified using MATLAB/Simulink results. The performance comparison shows that the speed control of buck converter fed PMDC motor is improved with proposed FO-PID controller than that of integer-order PID controller.

WITHDRAWN: Optimized FOPID controller for power quality enhancement between feeders using interline dynamic voltage restorer

This paper proposes a novel control scheme for Interline dynamic voltage restorer (IDVR). The optimized fractional order PID (FOPID) controller is used in this work for power quality enhancement such as voltage regulation, harmonics distortion reduction, voltage sag and swells compensation, fault compensation etc. The gain parameters of FOPID controller are tuned by gravitational search algorithm (GSA). The performance of the suggested controller is evaluated by contrasting it with other optimization technique such as particle swarm optimization and cuckoo-search optimization algorithm. These simulation results represents that FOPID with GSA works better than the other techniques in terms of power quality enhancement.

Hybrid Fuzzy Fractional-Order PID-Based Speed Control for Brushless DC Motor

This article presents a novel hybrid control scheme for speed control of Brushless DC (BLDC) motor by simultaneously controlling BLDC motor reference current and inverter DC bus voltage. A fractional-order PID (FOPID) controller is employed to control BLDC motor reference current while a fuzzy logic controller manipulates the inverter DC bus voltage. A modified harmony search (HS) metaheuristic technique is developed for FOPID controller parameters tuning. Three different operating conditions are applied to test the motor, including no-load operation, varying load operation, and varying speed operation to verify the proposed controller’s effectiveness. Furthermore, the proposed hybrid control strategy has been compared to Fuzzy-based and FOPID-based speed control schemes. The obtained results confirm that the proposed control scheme provides better and accurate speed control over a wide range of speeds. Also, the proposed controller decreases the torque ripples under different operating conditions.

A Simplified Fractional Order PID Controller's Optimal Tuning: A Case Study on a PMSM Speed Servo.

A simplified fractional order PID (FOPID) controller is proposed by the suitable definition of the parameter relation with the optimized changeable coefficient. The number of the pending controller parameters is reduced, but all the proportional, integral, and derivative components are kept. The estimation model of the optimal relation coefficient between the controller parameters is established, according to which the optimal FOPID controller parameters can be calculated analytically. A case study is provided, focusing on the practical application of the simplified FOPID controller to a permanent magnet synchronous motor (PMSM) speed servo. The dynamic performance of the simplified FOPID control system is tested by motor speed control simulation and experiments. Comparisons are performed between the control systems using the proposed method and those using some other existing methods. According to the simulation and experimental results, the simplified FOPID control system achieves the optimal dynamic performance. Therefore, the validity of the proposed controller structure and tuning method is demonstrated.

Sine-cosine-algorithm-based fractional order PID controller tuning for multivariable systems

The multivariable systems, used in several industrial processing systems, are controlled using multi-loop controllers. A novel fractional order proportional integral derivative (FOPID) controller design without decoupler for the multivariable system using an optimisation algorithm is proposed. The FOPID controller is employed in each loop of two-input-two-output (TITO) system and their parameters are tuned using sine-cosine algorithm (SCA). The proposed method eliminates the interaction of loops with optimal tuning of FOPID controller parameters. The proposed FOPID design for Wood-Berry TITO system is compared with the recent state-of-the-art literature to verify its overall efficiency. The simulation result demonstrates the superiority of the proposed controller over other controller designs for the TITO system.

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and ωgc as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and ωgc when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.