Pub Date : 2023-10-24DOI: 10.3390/fractalfract7110773
Rashid Ali, Ahmed S. Hendy, Mohamed R. Ali, Ahmed M. Hassan, Fuad A. Awwad, Emad A. A. Ismail
In this research work, we investigate the complex structure of soliton in the Fractional Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study involves the development of soliton solutions using the modified Extended Direct Algebraic Method (mEDAM). This approach involves a key variable transformation, which successfully transforms the model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series form solution, the NODE is turned into a system of algebraic equations, allowing us to construct soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures. The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional, three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects such as optical fibre research, plasma physics, and a variety of applied sciences.
{"title":"Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity","authors":"Rashid Ali, Ahmed S. Hendy, Mohamed R. Ali, Ahmed M. Hassan, Fuad A. Awwad, Emad A. A. Ismail","doi":"10.3390/fractalfract7110773","DOIUrl":"https://doi.org/10.3390/fractalfract7110773","url":null,"abstract":"In this research work, we investigate the complex structure of soliton in the Fractional Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study involves the development of soliton solutions using the modified Extended Direct Algebraic Method (mEDAM). This approach involves a key variable transformation, which successfully transforms the model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series form solution, the NODE is turned into a system of algebraic equations, allowing us to construct soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures. The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional, three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects such as optical fibre research, plasma physics, and a variety of applied sciences.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"8 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first prove a new parameterized identity. Based on this identity we establish some parametrized Simpson-like type symmetric inequalities, for functions whose first derivatives are s-tgs-convex via Reimann–Liouville frational operators. Some special cases are discussed. Applications to numerical quadrature are provided.
{"title":"Fractional Simpson-like Inequalities with Parameter for Differential s-tgs-Convex Functions","authors":"Meriem Merad, Badreddine Meftah, Hamid Boulares, Abdelkader Moumen, Mohamed Bouye","doi":"10.3390/fractalfract7110772","DOIUrl":"https://doi.org/10.3390/fractalfract7110772","url":null,"abstract":"In this paper, we first prove a new parameterized identity. Based on this identity we establish some parametrized Simpson-like type symmetric inequalities, for functions whose first derivatives are s-tgs-convex via Reimann–Liouville frational operators. Some special cases are discussed. Applications to numerical quadrature are provided.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"20 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135315874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.3390/fractalfract7110774
Imed Bachar
Our goal is to address the question of existence and uniqueness of a positive continuous solution to some semipositone fractional boundary value problems on the half-line. Global estimates on this solution are given. This kind of problems, where the nonlinearity is allowed to be sign-changing, are often difficult to solve analytically and becomes more challenging specially when we are looking for positive solutions. The main result is obtained by means of the properties of the Green function and fixed point theorem.
{"title":"Positive Solutions for Some Semipositone Fractional Boundary Value Problems on the Half-Line","authors":"Imed Bachar","doi":"10.3390/fractalfract7110774","DOIUrl":"https://doi.org/10.3390/fractalfract7110774","url":null,"abstract":"Our goal is to address the question of existence and uniqueness of a positive continuous solution to some semipositone fractional boundary value problems on the half-line. Global estimates on this solution are given. This kind of problems, where the nonlinearity is allowed to be sign-changing, are often difficult to solve analytically and becomes more challenging specially when we are looking for positive solutions. The main result is obtained by means of the properties of the Green function and fixed point theorem.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-23DOI: 10.3390/fractalfract7100771
Igor Pantic, Nikola Topalovic, Peter R. Corridon, Jovana Paunovic
Fractal analysis (FA) is a contemporary computational technique that can assist in identifying and assessing nuanced structural alterations in cells and tissues after exposure to certain toxic chemical agents. Its application in toxicology may be particularly valuable for quantifying structural changes in cell nuclei during conventional microscopy assessments. In recent years, the fractal dimension and lacunarity of cell nuclei, considered among the most significant FA features, have been suggested as potentially important indicators of cell damage and death. In this study, we demonstrate the feasibility of developing a random forest machine learning model that employs fractal indicators as input data to identify yeast cells treated with oxidopamine (6-hydroxydopamine, 6-OHDA), a powerful toxin commonly applied in neuroscience research. The model achieves notable classification accuracy and discriminatory power, with an area under the receiver operating characteristics curve of more than 0.8. Moreover, it surpasses alternative decision tree models, such as the gradient-boosting classifier, in differentiating treated cells from their intact counterparts. Despite the methodological challenges associated with fractal analysis and random forest training, this approach offers a promising avenue for the continued exploration of machine learning applications in cellular physiology, pathology, and toxicology.
{"title":"Oxidopamine-Induced Nuclear Alterations Quantified Using Advanced Fractal Analysis: Random Forest Machine Learning Approach","authors":"Igor Pantic, Nikola Topalovic, Peter R. Corridon, Jovana Paunovic","doi":"10.3390/fractalfract7100771","DOIUrl":"https://doi.org/10.3390/fractalfract7100771","url":null,"abstract":"Fractal analysis (FA) is a contemporary computational technique that can assist in identifying and assessing nuanced structural alterations in cells and tissues after exposure to certain toxic chemical agents. Its application in toxicology may be particularly valuable for quantifying structural changes in cell nuclei during conventional microscopy assessments. In recent years, the fractal dimension and lacunarity of cell nuclei, considered among the most significant FA features, have been suggested as potentially important indicators of cell damage and death. In this study, we demonstrate the feasibility of developing a random forest machine learning model that employs fractal indicators as input data to identify yeast cells treated with oxidopamine (6-hydroxydopamine, 6-OHDA), a powerful toxin commonly applied in neuroscience research. The model achieves notable classification accuracy and discriminatory power, with an area under the receiver operating characteristics curve of more than 0.8. Moreover, it surpasses alternative decision tree models, such as the gradient-boosting classifier, in differentiating treated cells from their intact counterparts. Despite the methodological challenges associated with fractal analysis and random forest training, this approach offers a promising avenue for the continued exploration of machine learning applications in cellular physiology, pathology, and toxicology.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"286 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135413012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.3390/fractalfract7100770
Vetlugin Dzhabrailovich Beybalaev, Abutrab Aleksandrovich Aliverdiev, Jordan Hristov
The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically.
{"title":"Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition","authors":"Vetlugin Dzhabrailovich Beybalaev, Abutrab Aleksandrovich Aliverdiev, Jordan Hristov","doi":"10.3390/fractalfract7100770","DOIUrl":"https://doi.org/10.3390/fractalfract7100770","url":null,"abstract":"The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.3390/fractalfract7100766
Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr, Liliana Guran
In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.
在本文中，我们提出了几种类型的插值近端收缩映射，包括reich - rus - ciric型插值-型收缩和kannan型插值-型收缩。此外，考虑到上述映射，我们证明了最佳的接近点结果。这些结果是对已有文献结果的扩展和概括。此外，我们还提供了几个非平凡的例子，一个求积分方程解的应用，以及一个非线性分数阶微分方程来证明主要结果的有效性。
{"title":"Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications","authors":"Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr, Liliana Guran","doi":"10.3390/fractalfract7100766","DOIUrl":"https://doi.org/10.3390/fractalfract7100766","url":null,"abstract":"In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135778837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.3390/fractalfract7100769
Erdem Ilten
This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.
{"title":"Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System","authors":"Erdem Ilten","doi":"10.3390/fractalfract7100769","DOIUrl":"https://doi.org/10.3390/fractalfract7100769","url":null,"abstract":"This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.3390/fractalfract7100767
Hui Yang, Chunmei Zhang, Ran Li, Huiling Chen
This paper focuses on the equilibrium problem of an urban public transportation system with time delay. Time delay, multi-weights, and stochastic disturbances are considered in the urban public transportation system. Hence, one can regard the urban public transportation system as a stochastic multi-weighted delayed complex network. By combining graph theory and the Lyapunov method, the global Lyapunov function is constructed indirectly. Moreover, the response system can realize synchronization with the drive system under the adaptive controller. In other words, the urban public transportation system is balanced in the actual running traffic network. Finally, numerical examples about the Chua system and small-world network are presented to confirm the accuracy and validity of the theoretical results.
{"title":"Equilibrium Problem for the Stochastic Multi-Weighted Urban Public Transportation System with Time Delay: A Graph-Theoretic Method","authors":"Hui Yang, Chunmei Zhang, Ran Li, Huiling Chen","doi":"10.3390/fractalfract7100767","DOIUrl":"https://doi.org/10.3390/fractalfract7100767","url":null,"abstract":"This paper focuses on the equilibrium problem of an urban public transportation system with time delay. Time delay, multi-weights, and stochastic disturbances are considered in the urban public transportation system. Hence, one can regard the urban public transportation system as a stochastic multi-weighted delayed complex network. By combining graph theory and the Lyapunov method, the global Lyapunov function is constructed indirectly. Moreover, the response system can realize synchronization with the drive system under the adaptive controller. In other words, the urban public transportation system is balanced in the actual running traffic network. Finally, numerical examples about the Chua system and small-world network are presented to confirm the accuracy and validity of the theoretical results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135778883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.3390/fractalfract7100768
Ashish Bhoria, Anju Panwar, Mohammad Sajid
The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a point in the complex plane belongs to the set or not. In this article, the fractals of higher importance, i.e., Julia sets and Mandelbrot sets, are visualized using the Picard–Thakur iterative procedure (as one of iterative methods) for the complex sine Tc(z)=asin(zr)+bz+c and complex exponential Tc(z)=aezr+bz+c functions. In order to obtain the fixed point of a complex-valued sine and exponential function, our concern is to use the fewest number of iterations possible. Using MATHEMATICA 13.0, some enticing and intriguing fractals are generated, and their behavior is then illustrated using graphical examples; this is achieved depending on the iteration parameters, the parameters ‘a’ and ‘b’, and the parameters involved in the series expansion of the sine and exponential functions.
{"title":"Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration","authors":"Ashish Bhoria, Anju Panwar, Mohammad Sajid","doi":"10.3390/fractalfract7100768","DOIUrl":"https://doi.org/10.3390/fractalfract7100768","url":null,"abstract":"The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a point in the complex plane belongs to the set or not. In this article, the fractals of higher importance, i.e., Julia sets and Mandelbrot sets, are visualized using the Picard–Thakur iterative procedure (as one of iterative methods) for the complex sine Tc(z)=asin(zr)+bz+c and complex exponential Tc(z)=aezr+bz+c functions. In order to obtain the fixed point of a complex-valued sine and exponential function, our concern is to use the fewest number of iterations possible. Using MATHEMATICA 13.0, some enticing and intriguing fractals are generated, and their behavior is then illustrated using graphical examples; this is achieved depending on the iteration parameters, the parameters ‘a’ and ‘b’, and the parameters involved in the series expansion of the sine and exponential functions.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.3390/fractalfract7100765
Muhyaddin Rawa, Sultan Alghamdi, Martin Calasan, Obaid Aldosari, Ziad M. Ali, Salem Alkhalaf, Mihailo Micev, Shady H. E. Abdel Aleem
In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated.
{"title":"Disturbance Rejection-Based Optimal PID Controllers for New 6ISO AVR Systems","authors":"Muhyaddin Rawa, Sultan Alghamdi, Martin Calasan, Obaid Aldosari, Ziad M. Ali, Salem Alkhalaf, Mihailo Micev, Shady H. E. Abdel Aleem","doi":"10.3390/fractalfract7100765","DOIUrl":"https://doi.org/10.3390/fractalfract7100765","url":null,"abstract":"In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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