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20 pages, 17284 KiB  
Article
Fault-Line Selection Method in Active Distribution Networks Based on Improved Multivariate Variational Mode Decomposition and Lightweight YOLOv10 Network
by Sizu Hou and Wenyao Wang
Energies 2024, 17(19), 4958; https://doi.org/10.3390/en17194958 (registering DOI) - 3 Oct 2024
Abstract
In active distribution networks (ADNs), the extensive deployment of distributed generations (DGs) heightens system nonlinearity and non-stationarity, which can weaken fault characteristics and reduce fault detection accuracy. To improve fault detection accuracy in distribution networks, a method combining improved multivariate variational mode decomposition [...] Read more.
In active distribution networks (ADNs), the extensive deployment of distributed generations (DGs) heightens system nonlinearity and non-stationarity, which can weaken fault characteristics and reduce fault detection accuracy. To improve fault detection accuracy in distribution networks, a method combining improved multivariate variational mode decomposition (IMVMD) and YOLOv10 network for active distribution network fault detection is proposed. Firstly, an MVMD method optimized by the northern goshawk optimization (NGO) algorithm named IMVMD is introduced to adaptively decompose zero-sequence currents at both ends of line sources and loads into intrinsic mode functions (IMFs). Secondly, considering the spatio-temporal correlation between line sources and loads, a dynamic time warping (DTW) algorithm is utilized to determine the optimal alignment path time series for corresponding IMFs at both ends. Then, the Markov transition field (MTF) transforms the 1D time series into 2D spatio-temporal images, and the MTF images of all lines are concatenated to obtain a comprehensive spatio-temporal feature map of the distribution network. Finally, using the spatio-temporal feature map as input, the lightweight YOLOv10 network autonomously extracts fault features to achieve precise fault-line selection. Experimental results demonstrate the robustness of the proposed method, achieving a fault detection accuracy of 99.88%, which can ensure accurate fault-line selection under complex scenarios involving simultaneous phase-to-ground faults at two points. Full article
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18 pages, 6879 KiB  
Article
Data-Driven Control Method Based on Koopman Operator for Suspension System of Maglev Train
by Peichen Han, Junqi Xu, Lijun Rong, Wen Wang, Yougang Sun and Guobin Lin
Actuators 2024, 13(10), 397; https://doi.org/10.3390/act13100397 - 3 Oct 2024
Abstract
The suspension system of the Electromagnetic Suspension (EMS) maglev train is crucial for ensuring safe operation. This article focuses on data-driven modeling and control optimization of the suspension system. By the Extended Dynamic Mode Decomposition (EDMD) method based on the Koopman theory, the [...] Read more.
The suspension system of the Electromagnetic Suspension (EMS) maglev train is crucial for ensuring safe operation. This article focuses on data-driven modeling and control optimization of the suspension system. By the Extended Dynamic Mode Decomposition (EDMD) method based on the Koopman theory, the state and input data of the suspension system are collected to construct a high-dimensional linearized model of the system without detailed parameters of the system, preserving the nonlinear characteristics. With the data-driven model, the LQR controller and Extended State Observer (ESO) are applied to optimize the suspension control. Compared with baseline feedback methods, the optimization control with data-driven modeling reduces the maximum system fluctuation by 75.0% in total. Furthermore, considering the high-speed operating environment and vertical dynamic response of the maglev train, a rolling-update modeling method is proposed to achieve online modeling optimization of the suspension system. The simulation results show that this method reduces the maximum fluctuation amplitude of the suspension system by 40.0% and the vibration acceleration of the vehicle body by 46.8%, achieving significant optimization of the suspension control. Full article
(This article belongs to the Special Issue Advanced Theory and Application of Magnetic Actuators—2nd Edition)
18 pages, 1266 KiB  
Article
Finite-Time Mass Estimation Using ℋ and Sliding Mode Control for a Multicopter
by Carlos Augusto Arellano-Muro, Guillermo Luis Osuna-González and Riccardo Cespi
Mathematics 2024, 12(19), 3100; https://doi.org/10.3390/math12193100 - 3 Oct 2024
Abstract
Nonlinear control theory applied to unmanned aeronautical vehicles is an engineering topic that has received higher and higher popularity during the last decade. Model-based control approaches have shown increased performance in flight control accuracy and robustness compared to model-free proposals based on parameter [...] Read more.
Nonlinear control theory applied to unmanned aeronautical vehicles is an engineering topic that has received higher and higher popularity during the last decade. Model-based control approaches have shown increased performance in flight control accuracy and robustness compared to model-free proposals based on parameter adaptation and estimation. However, model-based structures need more computational efforts in terms of spatial and temporal variables. To avoid these constraints, the latest drone flight controls are based on quaternion models, ensuring more advanced computational performances. To this aim, this paper deals with a flight control algorithm of a quadrotor, in which the mathematics model of the plant is defined in terms of quaternions. Additionally, when aerial vehicles are used in specific applications such as slung load transportation and agriculture fields, among others, the variation of the mass receives high importance since it could make the entire system unstable. In the same line of ideas, this paper presents a H strategy, combined with a Super-Twisting Sliding-Mode Control, ensuring the control objective of the mass variations identification, and trajectory tracking, to be solved. The stability analysis of the proposed control approach is also discussed, and the quality and performances of the presented control strategy are tested by simulations, in an interesting case in which mass variations and external perturbations cannot be negligible. Full article
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17 pages, 5608 KiB  
Article
Probabilistic Loss Assessment for the Typology of Non-Ductile Reinforced Concrete Structures with Flat Slabs, Embedded Beams, and Unreinforced Infill Masonry
by Mauricio Guamán-Naranjo, José Poveda-Hinojosa and Ana Gabriela Haro-Báez
Buildings 2024, 14(10), 3158; https://doi.org/10.3390/buildings14103158 - 3 Oct 2024
Abstract
Quito, the capital of Ecuador, a development pole, has experienced a population growth of 9% in the last five years. The structural system commonly chosen for housing is reinforced concrete frames with flat slabs, embedded beams, and masonry infill. This typology covers approximately [...] Read more.
Quito, the capital of Ecuador, a development pole, has experienced a population growth of 9% in the last five years. The structural system commonly chosen for housing is reinforced concrete frames with flat slabs, embedded beams, and masonry infill. This typology covers approximately 60% of the residential buildings in the city. Adding to the site’s seismic hazard, this fact results in a city with a high seismic risk. The research presented here is carried out within a probabilistic framework to determine the economic consequences of the main structural typology in the city. The methodology defines the seismic hazard by scaling a database of 200 records to the design spectrum. It models the typology to capture the variability between structures with a solid parametric study. Each capacity curve is analyzed through a nonlinear time history analysis using an equivalent one-degree-of-freedom system. The results show an average annual loss ratio of 0.16%. This metric indicates the vulnerability of the typology and the high repair costs of buildings that will be observed in case of an earthquake. The practical implications of these findings are significant as they contribute to urban planning and policy decisions. Finally, it is observed that the probabilistic method used efficiently generates fragility and vulnerability curves, saving computational time and obtaining expected results. Full article
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22 pages, 6295 KiB  
Article
Blast-Induced Progressive Collapse Analysis: Accounting for Initial Conditions and Damage
by Benyam Melkeneh, Bedilu Habte and Girum Solomon Urgessa
Appl. Mech. 2024, 5(4), 696-717; https://doi.org/10.3390/applmech5040038 - 3 Oct 2024
Abstract
Abstract: The paper presents the progressive collapse analysis of structures, focusing on the impact of the initial conditions (particularly initial velocity) and the damage. It proposes a method that calculates the residual axial load capacity and damage of columns based on their strain [...] Read more.
Abstract: The paper presents the progressive collapse analysis of structures, focusing on the impact of the initial conditions (particularly initial velocity) and the damage. It proposes a method that calculates the residual axial load capacity and damage of columns based on their strain profile and considers the effects of multiple blast locations. The methodology involves the conventional design of a three-story moment-resisting frame, selecting blast parameters, calculating blast pressures, and performing structural and progressive collapse analyses. The findings reveal that the Alternate Load Path Method (APM) overestimates the capacity compared to a benchmark blast–structure interaction analysis, especially when unsuitable initial conditions and damage properties are used. To address this limitation, the paper concludes the recommendations for incorporating appropriate initial conditions and damage considerations for a relatively accurate progressive collapse analysis. Full article
35 pages, 958 KiB  
Article
Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation
by Willy Hereman and Ünal Göktaş
Math. Comput. Appl. 2024, 29(5), 91; https://doi.org/10.3390/mca29050091 - 3 Oct 2024
Abstract
In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the [...] Read more.
In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica, but can be adapted for major computer algebra systems. Full article
(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
24 pages, 14371 KiB  
Article
An Enhanced Transportation System for People of Determination
by Uma Perumal, Fathe Jeribi and Mohammed Hameed Alhameed
Sensors 2024, 24(19), 6411; https://doi.org/10.3390/s24196411 - 3 Oct 2024
Abstract
Visually Impaired Persons (VIPs) have difficulty in recognizing vehicles used for navigation. Additionally, they may not be able to identify the bus to their desired destination. However, the bus bay in which the designated bus stops has not been analyzed in the existing [...] Read more.
Visually Impaired Persons (VIPs) have difficulty in recognizing vehicles used for navigation. Additionally, they may not be able to identify the bus to their desired destination. However, the bus bay in which the designated bus stops has not been analyzed in the existing literature. Thus, a guidance system for VIPs that identifies the correct bus for transportation is presented in this paper. Initially, speech data indicating the VIP’s destination are pre-processed and converted to text. Next, utilizing the Arctan Gradient-activated Recurrent Neural Network (ArcGRNN) model, the number of bays at the location is detected with the help of a Global Positioning System (GPS), input text, and bay location details. Then, the optimal bay is chosen from the detected bays by utilizing the Experienced Perturbed Bacteria Foraging Triangular Optimization Algorithm (EPBFTOA), and an image of the selected bay is captured and pre-processed. Next, the bus is identified utilizing a You Only Look Once (YOLO) series model. Utilizing the Sub-pixel Shuffling Convoluted Encoder–ArcGRNN Decoder (SSCEAD) framework, the text is detected and segmented for the buses identified in the image. From the segmented output, the text is extracted, based on the destination and route of the bus. Finally, regarding the similarity value with respect to the VIP’s destination, a decision is made utilizing the Multi-characteristic Non-linear S-Curve-Fuzzy Rule (MNC-FR). This decision informs the bus conductor about the VIP, such that the bus can be stopped appropriately to pick them up. During testing, the proposed system selected the optimal bay in 247,891 ms, which led to deciding the bus stop for the VIP with a fuzzification time of 34,197 ms. Thus, the proposed model exhibits superior performance over those utilized in prevailing works. Full article
(This article belongs to the Section Intelligent Sensors)
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22 pages, 1109 KiB  
Review
Exploring Evolutionary Algorithms for Optimal Power Flow: A Comprehensive Review and Analysis
by Harish Pulluri, Vedik Basetti, B. Srikanth Goud and CH. Naga Sai Kalyan
Electricity 2024, 5(4), 712-733; https://doi.org/10.3390/electricity5040035 - 3 Oct 2024
Abstract
It has been more than five decades since optimum power flow (OPF) emerged as one of the most famous and frequently used nonlinear optimization problems in power systems. Despite its long-standing existence, the OPF problem continues to be widely researched due to its [...] Read more.
It has been more than five decades since optimum power flow (OPF) emerged as one of the most famous and frequently used nonlinear optimization problems in power systems. Despite its long-standing existence, the OPF problem continues to be widely researched due to its critical role in electrical network planning and operations. The general formulation of OPF is complex, representing a large-scale optimization model with nonlinear and nonconvex characteristics, incorporating both discrete and continuous control variables. The inclusion of control factors such as transformer taps and shunt capacitors, and the integration of renewable energy sources like wind power further complicates the system’s design and solution. To address these challenges, a variety of classical, evolutionary, and improved optimization techniques have been developed. These techniques not only provide new solution pathways but also enhance the quality of existing solutions, contributing to reductions in computational cost and operational efficiency. Multi-objective approaches are frequently employed in modern OPF problems to balance trade-offs between competing objectives like cost minimization, loss reduction, and environmental impact. This article presents an in-depth review of various OPF problems and the wide array of algorithms, both traditional and evolutionary, applied to solve these problems, paying special attention to wind power integration and multi-objective optimization strategies. Full article
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22 pages, 312 KiB  
Article
Existence and Stability Results for Thermodiffusion Laminated Beam System with Delay Feedback
by Zineb Khalili, Djamel Ouchenane, Ali Krelifa, Imene Laribi, Salah Boulaaras and Ahmed Himadan Ahmed
Mathematics 2024, 12(19), 3097; https://doi.org/10.3390/math12193097 - 3 Oct 2024
Abstract
In this paper, a one-dimensional thermodiffusion laminated beam system with delay feedback is studied. The existence of a solution for our system is discussed within the context of the semigroup approach. In addition, under different boundary conditions, two results of stability properties independent [...] Read more.
In this paper, a one-dimensional thermodiffusion laminated beam system with delay feedback is studied. The existence of a solution for our system is discussed within the context of the semigroup approach. In addition, under different boundary conditions, two results of stability properties independent of initial data are investigated. Full article
14 pages, 7238 KiB  
Article
Generic and Specific Models for Volume Estimation in Forest and Savanna Phytophysiognomies in Brazilian Cerrado
by Yanara Ferreira de Souza, Eder Pereira Miguel, Adriano José Nogueira Lima, Álvaro Nogueira de Souza, Eraldo Aparecido Trondoli Matricardi, Alba Valéria Rezende, Joberto Veloso de Freitas, Hallefy Junio de Souza, Kennedy Nunes Oliveira, Maria de Fátima de Brito Lima and Leonardo Job Biali
Plants 2024, 13(19), 2769; https://doi.org/10.3390/plants13192769 - 3 Oct 2024
Viewed by 180
Abstract
The Cerrado has high plant and vertebrate diversity and is an important biome for conserving species and provisioning ecosystem services. Volume equations in this biome are scarce because of their size and physiognomic diversity. This study was conducted to develop specific volumetric models [...] Read more.
The Cerrado has high plant and vertebrate diversity and is an important biome for conserving species and provisioning ecosystem services. Volume equations in this biome are scarce because of their size and physiognomic diversity. This study was conducted to develop specific volumetric models for the phytophysiognomies Gallery Forest, Dry Forest, Forest Savannah, and Savannah Woodland, a generic model and a model for Cerrado forest formation. Twelve 10 m × 10 m (100 m²) (National Forest Inventory) plots were used for each phytophysiognomy at different sites (regions) of the Federal District (FD) where trees had a diameter at breast height (DBH; 1.30 m) ≥5 cm in forest formations and a diameter at base height (Db; 0.30 m) ≥5 cm in savanna formations. Their diameters and heights were measured, they were cut and cubed, and the volume of each tree was obtained according to the Smalian methodology. Linear and nonlinear models were adjusted. Criteria for the selection of models were determined using correlation coefficients, the standard error of the estimates, and a graphical analysis of the residues. They were later validated by the chi-square test. The resultant models indicated that fit by specific phytophysiognomy was ideal; however, the generic and forest formation models exhibited similar performance to specific models and could be used in extensive areas of the Cerrado, where they represent a high potential for generalization. To further increase our understanding, similar research is recommended for the development of specific and generic models of the total volume in Cerrado areas. Full article
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22 pages, 7802 KiB  
Article
Study on Bionic Design and Tissue Manipulation of Breast Interventional Robot
by Weixi Zhang, Jiaxing Yu, Xiaoyang Yu, Yongde Zhang and Zhihui Men
Sensors 2024, 24(19), 6408; https://doi.org/10.3390/s24196408 - 3 Oct 2024
Viewed by 161
Abstract
Minimally invasive interventional surgery is commonly used for diagnosing and treating breast cancer, but the high fluidity and deformability of breast tissue reduce intervention accuracy. This study proposes a bionic breast interventional robot that mimics the scorpion’s predation process, actively manipulating tissue deformation [...] Read more.
Minimally invasive interventional surgery is commonly used for diagnosing and treating breast cancer, but the high fluidity and deformability of breast tissue reduce intervention accuracy. This study proposes a bionic breast interventional robot that mimics the scorpion’s predation process, actively manipulating tissue deformation to control target displacement and enhance accuracy. The robot’s structure is designed using a modular method, and its kinematics and workspace are analyzed and solved. To address the nonlinear breast tissue deformation problem, a hierarchical tissue method is proposed to simplify the three-dimensional problem into a two-dimensional one. A two-dimensional tissue deformation solver is established based on the minimum energy method for quick resolution. The problem is treated as quasi-static, deriving the displacement relationship between external manipulation points and internal tissue targets. The method of active manipulation of tissue deformation is simulated using MATLAB (2019-b) software to verify the feasibility of the method. Results show maximum errors of 1.7 mm for prostheses and 2.5 mm for in vitro tissues in the X and Y directions. This method improves intervention accuracy in breast surgery and offers a new solution for breast cancer diagnosis and treatment. Full article
(This article belongs to the Collection Biomedical Imaging & Instrumentation)
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21 pages, 2184 KiB  
Article
Design of a High-Power Nanosecond Electromagnetic Pulse Radiation System for Verifying Spaceborne Detectors
by Tianchi Zhang, Zongxiang Li, Changjiao Duan, Lihua Wang, Yongli Wei, Kejie Li, Xin Li and Baofeng Cao
Sensors 2024, 24(19), 6406; https://doi.org/10.3390/s24196406 - 2 Oct 2024
Viewed by 180
Abstract
The Spaceborne Global Lightning Location Network (SGLLN) serves the purpose of identifying transient lightning events occurring beneath the ionosphere, playing a significant role in detecting and warning of disaster weather events. To ensure the effective functioning of the wideband electromagnetic pulse detector, which [...] Read more.
The Spaceborne Global Lightning Location Network (SGLLN) serves the purpose of identifying transient lightning events occurring beneath the ionosphere, playing a significant role in detecting and warning of disaster weather events. To ensure the effective functioning of the wideband electromagnetic pulse detector, which is a crucial component of the SGLLN, it must be tested and verified with specific signals. However, the inherent randomness and unpredictability of lightning occurrences pose challenges to this requirement. Consequently, a high-power electromagnetic pulse radiation system with a 20 m aperture reflector is designed. This system is capable of emitting nanosecond electromagnetic pulse signals under pre-set spatial and temporal conditions, providing a controlled environment for assessing the detection capabilities of SGLLN. In the design phase, an exponentially TEM feed antenna has been designed firstly based on the principle of high-gain radiation. The feed antenna adopts a pulser-integrated design to mitigate insulation risks, and it is equipped with an asymmetric protective loading to reduce reflected energy by 85.7%. Moreover, an innovative assessment method for gain loss, based on the principle of Love’s equivalence, is proposed to quantify the impact of feed antenna on the radiation field. During the experimental phase, a specialized E-field sensor is used in the far-field experiment at a distance of 400 m. The measurements indicate that at this distance, the signal has a peak field strength of 2.2 kV/m, a rise time of 1.9 ns, and a pulse half-width of 2.5 ns. Additionally, the beamwidth in the time domain is less than 10°. At an altitude of 500 km, the spaceborne detector records a signal with a peak field strength of approximately 10 mV/m. Particularly, this signal transformed into a nonlinear frequency-modulated signal in the microsecond range across its frequency spectrum, which is consistent with the law of radio wave propagation in the ionosphere. This study offers a stable and robust radiation source for verifying spaceborne detectors and establishes an empirical foundation for investigating the impact of the ionosphere on signal propagation characteristics. Full article
(This article belongs to the Section Electronic Sensors)
23 pages, 3109 KiB  
Article
Phase Error Correction in Sparse Linear MIMO Radar Based on the Equivalent Phase Center Principle
by Wenyuan Shao, Jianmin Hu, Yicai Ji, Jun Pan and Guangyou Fang
Remote Sens. 2024, 16(19), 3685; https://doi.org/10.3390/rs16193685 - 2 Oct 2024
Viewed by 236
Abstract
Multiple-input multiple-output (MIMO) technology is widely used in the field of radar imaging. Array sparse optimization reduces the hardware cost of MIMO radar, while virtual aperture and the equivalent phase center (EPC) principle simplify the radar signal model and reduce the computation and [...] Read more.
Multiple-input multiple-output (MIMO) technology is widely used in the field of radar imaging. Array sparse optimization reduces the hardware cost of MIMO radar, while virtual aperture and the equivalent phase center (EPC) principle simplify the radar signal model and reduce the computation and complexity of imaging algorithms. However, the application of sparse array structure and the EPC principle produces a non-negligible phase error, which affects the imaging quality. This paper simplifies the MIMO radar signal model based on the phase center approximation, analyzes the phase error generated by this method, and proposes an improved phase error correction method to solve the problem that the target cannot be well-focused at non-reference distance during imaging. In addition, this paper designs a sparse linear MIMO array with a periodic structure, which reduces the number of transmitting and receiving units, system complexity, and hardware costs. The proposed phase correction method was combined with the wavenumber domain algorithm to simulate and experiment on the designed antenna array, and good experimental results were obtained to verify the effectiveness of the proposed method. Full article
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18 pages, 2623 KiB  
Article
Design and Applicability of Two-Step Fractional Newton–Raphson Method
by Naseem Zulfiqar Ali, Awais Gul Khan, Muhammad Uzair Awan, Loredana Ciurdariu and Kamel Brahim
Fractal Fract. 2024, 8(10), 582; https://doi.org/10.3390/fractalfract8100582 - 2 Oct 2024
Viewed by 352
Abstract
Developing two-step fractional numerical methods for finding the solution of nonlinear equations is the main objective of this research article. In addition, we present a detailed study of convergence analysis for the methods that have been proposed. By comparing numerically, we can see [...] Read more.
Developing two-step fractional numerical methods for finding the solution of nonlinear equations is the main objective of this research article. In addition, we present a detailed study of convergence analysis for the methods that have been proposed. By comparing numerically, we can see that the proposed methods significantly improve convergence rate and accuracy. Additionally, we demonstrate how our main results can be applied to basins of attraction. Full article
(This article belongs to the Special Issue Fractional Systems, Integrals and Derivatives: Theory and Application)
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15 pages, 5019 KiB  
Article
Optimization of PID Control Parameters for Belt Conveyor Tension Based on Improved Seeker Optimization Algorithm
by Yahu Wang, Ziming Kou and Lei Wu
Electronics 2024, 13(19), 3907; https://doi.org/10.3390/electronics13193907 - 2 Oct 2024
Viewed by 356
Abstract
Aiming to address the problems of nonlinearity, a large time delay, poor adjustment ability, and a difficult parameter setting process of the tension control system of belt conveyor tensioning devices, an adaptive Proportional-Integral-Derivative (PID) parameter self-tuning algorithm based on an improved seeker optimization [...] Read more.
Aiming to address the problems of nonlinearity, a large time delay, poor adjustment ability, and a difficult parameter setting process of the tension control system of belt conveyor tensioning devices, an adaptive Proportional-Integral-Derivative (PID) parameter self-tuning algorithm based on an improved seeker optimization algorithm (ISOA) is proposed in this paper. The algorithm uses inertia weight random mutation to determine step size. An improved boundary reflection strategy avoids the defect of a large number of out-of-bound individuals gathering on the boundary in a traditional algorithm, and projects the individual reflection beyond the boundary into the boundary, which increases the diversity of the population and improves the convergence accuracy of the algorithm. To improve the system response speed and suppress the overshoot problem of the control target, coefficients related to the proportional term are introduced into the fitness function to accelerate the convergence of the algorithm. The improved algorithm is tested on three test functions such as Sphere and compared with other classical algorithms, which verify that the proposed algorithm is better in accuracy and stability. Finally, the interference and tracking performance of the ISOA-PID controller are verified in industrial experiments, which show that the PID controller optimized using the ISOA has good control quality and robustness. Full article
(This article belongs to the Section Systems & Control Engineering)
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