System Model Research Articles

Design and modeling of three-mode nonlinear hybrid piezoelectric-electromagnetic vibration energy harvester for harvesting multi-band vibration energy on the freight wagon axle box

Abstract With the rapid development of rail transit system, it is becoming more demanding for structural health monitoring (SHM) of the train. It is crucial to supply power for sensing devices on the freight wagon to ensure the safe operation of rail transit systems. Three-mode nonlinear hybrid piezoelectric-electromagnetic vibration energy harvester (TNHVEH) with a three-layer pickup system has been designed and applied to efficiently harvest vibration energy on the axle box of freight wagons for providing the power of the sensors for online SHM. Dynamic coupling model of the vehicle-harvester system is built to devote the relationship between the operation bandwidth and the nonlinear degree of TNHVEH for broadening the operation frequency band. Simulation and experimental results demonstrate that the resonant frequencies of the three pickup systems of TNHVEH are concentrated around 27, 70, and 120 Hz, matching the representative frequencies of axle box vibrations. A maximum output voltage of 2.97 V and output power of 29.4 μW under an optimal load of 300 kΩ at 0.5 g acceleration is achieved. It successfully lights up 53 LEDs with ‘ECJTU’ patterns, providing a solution to the power supply problem of microelectronic devices on freight wagons.

Warranty-driven reliability analysis: a stochastic model for continuous solar power supply system with two photovoltaic cells and an inverter

Warranty-driven reliability analysis: a stochastic model for continuous solar power supply system with two photovoltaic cells and an inverter

Application of an Improved State Feedback Control in the Selective Catalytic Reduction Denitrification Systems of Coal Power Units Under Variable Load Conditions

Selective catalytic reduction (SCR) flue gas denitrification systems are inherently complex, typically embodying characteristics of non-linearity, significant time delays, and susceptibility to multiple disturbances. In the context of coal power units engaging in deep load cycling and rapid frequency adjustment, conventional proportional-integral-derivative (PID) control struggles to meet the demands of effective control. This study introduces a control strategy that incorporates a “state observer + Linear Quadratic Regulator (LQR) state feedback + Improved Quantum Genetic Algorithm (IQGA) optimized PID”. Initially, local linear mathematical models of an SCR denitrification system at 340 MW, 450 MW, and 540 MW loads were used to design state observer and LQR state feedback control parameters for each operational condition. At a single load point, the IQGA was employed to optimize the outer loop PID parameters, followed by simulation experiments of load increases and decreases between 340 MW and 540 MW. The results demonstrated that, compared to two other strategies, the proposed approach reduced the overshoot by a minimum of 1.5% and shortened the adjustment time by 31.7% under conditions of step disturbances and internal perturbations. Throughout variable operational conditions, the strategy consistently exhibited minimal output fluctuations, rapid adjustment capabilities, strong disturbance rejection, and robust stability. This algorithm proves to be an effective method for controlling NOx concentrations, offering insights for precise ammonia injection control in future applications.

Presenting a Model for the Evaluation of the Quality of e-learning at Payam Noor University

The current study aims to design a quality evaluation model of the electronic education system at Payam Noor University by applying a mixed methodology. The statistical population of the qualitative section includes twelve professors, researchers, and experts in the field of e-learning, who were selected by selective sampling. The conceptual model of the research was collected after conducting in-depth semi-structured interviews. The quantitative data based on a questionnaire designed by the researcher was collected from 274 professors and students with experience teaching or studying in the electronic education system of Payam Noor University. The data was analyzed using the structural equation modeling method in PLS3 software. The research results show that quality is a concept consisting of four categories behavioral, scientific, cognitive ability, and virtual learning experience. The study’ findings also reveal that cultural, pedagogical, learner, communication, infrastructural, and institutional factors affect the quality of Payam Noor University's electronic education system. Also, the results show that these characteristics will help universities achieve the four outcomes of competitiveness, job opportunities, economy, and reputation by establishing a quality education system. The ideal model for evaluating the quality of e-learning at Payam Noor University is a process approach in which the three dimensions of factors, quality indicators, and outputs are examined and measured. In other words, electronic education is successful when it can create a valuable experience of virtual education while empowering the learners scientifically, behaviorally, and cognitively to let all the stakeholders of higher education benefit from a valuable electronic education.

Enhancing collaborative advantage through critical systems thinking: An augmented viable system model intervention in a cross‐sector partnership social policy context

AbstractCross‐sector partnerships are essential for addressing wicked problems but are typically ineffective because of messy human and organisational dynamics. Systemic approaches are needed to re‐design collaborations for a collaborative advantage. While the Viable System Model (VSM) is suited to this task, little guidance is provided on managing multiple perspectives or marginalisation in VSM interventions. Hence, we trial and evaluate the utility of a novel multimethodology approach combining the VSM with Team Syntegrity (TS), which is a workshop protocol for supporting fair dialogue and stakeholder pluralism. Our findings show this combination supports joined‐up thinking about improvements for viability and synergies from combining these methodologies. We propose that before a VSM diagnosis, an understanding of ‘what a system does’ and existence of VSM functions is established to ensure more meaningful selection of intervention participants and consideration of the VSM's insights. We also identify four avenues for marginalisation that need careful consideration in critical systems interventions.

Dual-Sliding-Surface Robust Control for the PEMFC Air-Feeding System Based on Terminal Sliding Mode Algorithm

The proton exchange membrane fuel cell (PEMFC) is the most widely used fuel cell, but it also has some limitations. One of the research pain points is controlling the oxygen content in PEMFCs. A moderate excess of oxygen boosts electrochemical reaction efficiency, while an appropriate oxygen content ensures system stability. In this paper, a fourth-order nonlinear mathematical model of a PEMFC stack air supply system is established to solve the problem of optimal oxygen excess ratio (OER) control under dynamic load conditions. Based on the model, a nonsingular terminal sliding mode controller (NTSMC) based on a sliding mode observer (SMO) is proposed. The NTSM exhibits superior robustness and performance compared to other sliding mode structures. Meanwhile, the SMO accurately predicts system states, facilitating precise control actions. Additionally, the dual sliding mode surfaces enhance system stability against parameter uncertainties and external disturbances. Our results demonstrate that the proposed controller outperforms traditional ones in terms of robustness and performance, which significantly enhances PEMFC system efficiency and stability.

Equivalent Heat Source Model of Thermal Relay Contact Based on Surface Roughness of Silver–Magnesium–Nickel Contact

In a sealed electromagnetic relay, the change in the surface roughness mainly depends on the collision wear between the contact and the moving reed and the ablation effect of the arc on the contact surface based on the strong correlation between the contact resistance and the surface roughness of the Ag-Mg-Ni contact. With a change in contact resistance, the contact temperature increase in a hermetically sealed electromagnetic relay (HSER) is greatly affected. Under extreme overload conditions, the contact surface is severely ablated by the arc, and the roughness increases rapidly with the number of cycles, which greatly affects the contact resistance of the contact surface and the reliability of the relay. A thermal model of a relay contact system based on the surface roughness of Ag-Mg-Ni contacts was established in this paper by analyzing the effect of an arc on the surface roughness of Ag-Mg-Ni contacts under heavy overload conditions. The arc image of the Ag-Mg-Ni contact was recorded using a double-axis arc photographing platform, and the moving track of the arc center under overload conditions was drawn. This paper explored the patterns of arc center movement on the contact surface and the effects of the arc on the surface roughness of the contacts by analyzing the probabilities of the arc center appearing in various locations. A mathematical model correlating the number of contact cycles with contact resistance was established. Subsequently, a finite element simulation model for the equivalent heat source of the contact was developed. The theoretical model error was less than 10%. The accuracy of the equivalent heat source model was verified by comparing the measured data with the simulation results.

Concept model and realization of object orientied system with metaprogramming

The purpose of the research is to develop a conceptual model of an object oriented system and implement it using a functional language with metaprogramming support. Methods. A conceptual model of an object oriented system was developed based on a dynamic object system with message passing and dynamic dispatch. The developed object oriented system includes functions for creating and deleting classes, creating and deleting object instances of a class, functions for working with object properties, functions for adding methods to a class and passing messages. Inheritance is also possible, when a child class will have the properties of the parent class and its own properties. Results. The object oriented system was implemented using a set of macros and helper functions. The basic data structure was a hash table with key access capabilities, which was also implemented using macros. When a class is created, an instance constructor is automatically generated, setting the initial values of the object’s fields. Inheritance is implemented as the inclusion of fields of a parent class in a child object. Polymorphism is implemented as dynamic dispatch: when processing a message, a handler method is searched. The resulting object oriented system, together with the hash table module, occupies 97 lines. Conclusion. As a result of the work, a conceptual model of an object oriented system was created and implemented, which includes the main functions of the object oriented programming paradigm. It has been shown that macros can be used to create a compact object oriented system without the need to add any new functions or capabilities to the functional language interpreter.

Influence of dynamic complexity on serial robots with joint clearance based on a nonlinearity measure

Conditional monitoring and diagnosis of serial robots depend not only on the method used but also on the dynamic complexity of the robotic system itself. Previously, researchers have focused mainly on the analysis of dynamic behaviors with different parameters of a mechanical system with clearance. Although the indicators such as Root Mean Square (RMS), spectrum kurtosis (SK), Entropy have the potentiality to express the specific trend by different parameters, it can be noticed that they mainly depend on the values of the dynamic responses and neglect the information of the nonlinear characteristics in the responses of mechanical systems. In this paper, a nonlinearity measure-based method is proposed to analyze the impact of dynamic complexity on serial robots with joint clearance. The kinetic equations of a serial robot with joint clearance are established by considering the contact forces in the joint. The dynamic model of the robotic system is validated by experiments. A quantization method for dynamic complexity analysis is established based on the nonlinearity measure, and the influences of parameters on the dynamic complexity are analyzed via numerical computations for the validated dynamical models of the robotic system. A relationship is developed among the clearance radius, friction coefficient, and dynamic complexity. This shows that a larger clearance radius will lead to a more complex system and that friction coefficients within a certain range can reduce the dynamic complexity of the system. These results can guide methodological choices for condition monitoring and diagnosis of serial robotic systems.

Anti-disturbance adaptive cruise control method based on H∞ robust controller with optimized safe velocity and following time headway

Abstract To alleviate driver workload, many vehicles are now equipped with adaptive cruise control (ACC) systems. However, ACC performance can significantly deteriorate in real-world conditions due to disturbances such as sensor measurement errors, system uncertainties, and modeling errors. Therefore, an innovative anti-disturbance ACC method is proposed based on H ∞ robust controller with optimized safe velocity and following time headway to overcome the above problems. Initially, we analyze the longitudinal following characteristics that are undergoing disturbances and establish the ACC system model. Then, the optimization models for the safe velocity and the following time headway during ACC are designed. Subsequently, based on H ∞ theory, the design criterion of the H ∞ robust controller for ACC is established by utilizing the linear matrix inequality technique. Finally, two typical experiment scenarios are given for hardware-in-the-loop simulation to demonstrate the effectiveness of the proposed method.

Sensing equivalent kinematics enables robot-assisted mirror rehabilitation training via a broaden learning system

IntroductionRobot-assisted mirror therapy has been widely developed to help remodeling of premotor cortex for patients suffering from motor disability of limbs. Nevertheless, it is difficult to achieve real-time adaptive control in robot-assisted mirror rehabilitation training, particularly for patients with varying levels of limb impairment.MethodsThis paper proposes an equivalent kinematics control framework based on the Broaden Learning System model for active robotic mirror rehabilitation, where people’s bilateral upper limbs actively perform mirror movements to enhance the impaired limb’s participation. The framework accommodates a broaden learning model from sensing multi-kinematic features to adjust the robotic damping coefficient in assisting human participants to complete mirror-symmetry training. Besides, in order to adapt to inter-patients’ variability with different disability levels, a challenge-level modification interface is also fused for safer training. This model is verified by additional symmetry indicator such as position trajectory error and force.ResultsExperimental results show that the weaker subjects can also maintain mirror movement with the stronger subjects under the help of this model and verify the performance of framework in mirror-symmetry effects and movement smoothness. This leads us to believe that the framework can safely and efficiently assist human participants in completing mirror-symmetry movement.DiscussionThe framework has the potential to improve outcomes in smoother and safer mirror-symmetry training by sensing multi-kinematic features. Future studies are necessary to involve clinical trials with actual patients.

Tropical Interbasin Interaction as Effective Predictors of Late-Spring Precipitation Variability in the Southern Great Plains

Abstract The southern Great Plains experience fluctuating precipitation extremes that significantly impact agriculture and water management. Despite ongoing efforts to enhance forecast accuracy, the underlying causes of these climatic phenomena remain inadequately understood. This study elucidates the relative influence of the tropical Pacific and Atlantic basins on April–May–June precipitation variability in this region. Our partial ocean assimilation experiments using the Community Earth System Model unveil the prominent role of interbasin interaction, with the Pacific and Atlantic contributing approximately 70% and 30%, respectively, to these interbasin contrasts. Our statistical analyses suggest that these tropical interbasin contrasts could serve as a more reliable indicator for late-spring precipitation anomalies than El Niño–Southern Oscillation. The conclusions are reinforced by analyses of seven climate forecasting systems within the North American Multi-Model Ensemble, offering an optimistic outlook for enhancing real-time forecasting of late-spring precipitation in the southern plains. However, the current predictive skills of the interbasin contrasts across the prediction systems are hindered by the lower predictability of the tropical Atlantic Ocean, pointing to the need for future research to refine climate prediction models further. Significance Statement Agriculture and infrastructure in the southern plains face challenges from severe late-spring precipitation extremes. Traditional predictors like El Niño–Southern Oscillation (ENSO) lose effectiveness during the critical spring-to-summer transition, creating a forecasting gap. This study introduces the concept of tropical interbasin interactions, known to enhance seasonal predictability for late-spring precipitation in the southern plains. Novel climate model experiments highlight contributions from the tropical Pacific and Atlantic, offering a promising predictability that potentially surpasses the limitations of ENSO-based predictions. These outcomes hold the potential for developing operational forecasts of late-spring precipitation anomalies in the southern plains, enabling proactive risk management.

Prediction of automotive response using supervised machine learning in antilock braking systems and comparison with different models for improved vehicle safety

Abstract Previous research on predicting automotive response in antilock braking systems faced several common drawbacks. Limited availability of high-quality datasets and computational constraints hindered the models' ability to generalize and perform effectively in real-time. Additionally, integrating these models into existing vehicle systems is challenging, often requiring extensive calibration and testing to ensure reliability and safety. This study focuses on enhancing automotive safety through the integration of machine learning with advanced braking systems. An antilock braking system model is developed using MATLAB, accounting for key parameters such as speed, mass, wheel radius, and moment of inertia. Various probability ranges are simulated to evaluate the system's real-time response in dynamic environments. A supervised machine learning approach is applied, with lasso regression used for model validation. Braking response was evaluated at three speeds: 25 km/h, 45 km/h, and 65 km/h. To assess model accuracy, error analysis was conducted using metrics such as mean absolute percentage error (MAPE), mean absolute error (MAE), root mean squared error (RMSE), and mean squared error (MSE). Results showed a significant improvement in prediction accuracy, with MAPE reduced to 3.2%, MAE to 0.15 seconds, RMSE to 0.25 seconds, and MSE to 0.06 seconds.A comparative analysis is done using the Python Jupyter Framework, further validating the findings. The machine learning model successfully forecasts braking response times, and validates its prediction against random datasets.

Climate change mitigation and adaptation for rice-based farming systems in the Red River Delta, Vietnam

Abstract Background Rice is a major contributor to anthropogenic greenhouse gas (GHG) emissions, primarily methane, and at the same time will be negatively impacted by regional climate changes. Identifying rice management interventions to reduce methane emissions while improving productivity is, therefore, critical for climate change mitigation, adaptation, and food security. However, it can be challenging to conduct multivariate assessments of rice interventions in the field owing to the intensiveness of data collection and/or the challenges in testing long-term changes in meteorological and climate conditions. Process-based modeling, evaluated against site-based data, provides an entry point for evaluating the impacts of climate change on rice systems and assessing the impacts, co-benefits, and trade-offs of interventions under historical and future climate conditions. Methods We leverage existing site-based management data to model combined rice yields, methane emissions, and water productivity using a suite of process-based coupled crop-soil model experiments for 83 growing sites across the Red River Delta, Vietnam. We test three rice management interventions with our coupled crop-soil model, characterized by Alternate Wetting and Drying (AWD) water management and other principles representing the System of Rice Intensification (SRI). Our simulations are forced with historical as well as future climate conditions, represented by five Earth System Models for a high-emission climate scenario centered on the year 2050. We evaluate the efficacy of these interventions for combined climate change mitigation and adaptation under historical and future climate change. Results Two SRI interventions significantly increased yields (one by over 50%) under historical climate conditions while also reducing (or not increasing) methane emissions. These interventions also increase yields under future climate conditions relative to baseline management practices, although climate change decreases absolute yields across all management practices. Generally, where yield improved, so did crop water-use efficiency. However, impacts on methane emissions were mixed across the sites under future climate conditions. Two of the interventions resulted in increased methane emissions, depending on the baseline management point of comparison. Nevertheless, one intervention reduced (or did not significantly increase) methane under both historical and future climate conditions and relative to all baseline management systems, although there was considerable variation across five selected climate models. Conclusions SRI management principles combined with high-yielding varieties, implemented for site-specific conditions, can serve climate change adaptation and mitigation goals, although the magnitude of future climate changes, particularly warming, may reduce the efficacy of these interventions with respect to methane reductions. Future work should better bracket important sensitivities of coupled crop-soil models and disentangle which management and climate factors drive the responses shown. Furthermore, future analyses that integrate these findings into socio-economic assessment can better inform if and how SRI/AWD can potentially benefit farmer livelihoods now and in the future, which will be critical to the adoption and scaling of these management principles.

Extension of a 3D Geological Entity Modeling Method for Discontinuous Deformation Analysis

AbstractWith the development of 3D discontinuous deformation analysis (DDA) in precise stress fields and crack propagation problems, it has also demonstrated outstanding capabilities in solving continuous–discontinuous problems. However, currently, 3D DDA modeling primarily focuses on generating rock joint networks and developing 3D cutting algorithms. Correspondingly, 3D geological modeling methods are not yet mature, and establishing 3D models often demands substantial time. The lack of supporting preprocessing modeling methods and corresponding visual operation interfaces significantly hampers the development of 3D DDA. This method builds upon advanced research achievements in unmanned aerial vehicle oblique photography, 3D reconstruction, 3D cutting, computer graphics, and visualization program design. This research establishes a 3D geological entity modeling method for 3D DDA and constructs a comprehensive program using relevant C++ libraries and C language interfaces. In this method, a 3D geological model that incorporates geological elements such as strata and faults is initially established using non‐uniform rational B‐splines (NURBSs) surfaces as the boundary of the solid model. Subsequently, finite element meshing is applied, followed by corresponding topology transformation, resulting in a 3D block system model suitable for 3D DDA calculation. To cater for diverse application scenarios, continuous–discontinuous models integrated with subblocks and models of arbitrary polyhedra can be established. The proposed method has been validated through several typical modeling examples, showing its ability to rapidly and generate 3D high‐precision geological reality models suitable for 3D DDA calculations. Additionally, some techniques used in this method can be extended for modeling other numerical simulation methods, warranting further research.

A decision support system to increase the compliance of diagnostic imaging examinations with imaging guidelines: focused on cerebrovascular diseases.

Diagnostic imaging decision support (DI-DS) system has emerged as an innovative evidence-based solution to decrease inappropriate diagnostic imaging. The aim of the present study was to design and evaluate a DI-DS system for cerebrovascular diseases. The present study was an applied piece of research. First, the conceptual model of the DI-DS system was designed based on its functional and non-functional requirements. Afterwards, to create the system's knowledge base, cerebrovascular diseases diagnostic imaging algorithms were extracted from the American College of Radiology Appropriateness Criteria (ACR-AC). Subsequently, the system was developed based on the obtained conceptual model and the extracted algorithms. The software was programmed by means of the C#. After debugging the system, it was evaluated regarding its performance and also the users' satisfaction with it. Assessing the users' satisfaction with the system demonstrated that all the evaluation criteria met the acceptable threshold (85 %). The retrospective evaluation of the system's performance indicated that from among 76 imaging examinations, which had previously been performed for 30 patients, 12 (15.78 %) were deemed inappropriate. And, the system accurately identified all the inappropriate physicians' decisions. The concurrent evaluation of the system's performance indicated that the system's recommendations helped the physicians remove 100 % (4 out of 4) of the inappropriate and 40 % (2 out of 5) of the inconclusive imaging examinations from their initial choices. A DI-DS system could increase the compliance of the physicians' decisions with diagnostic imaging guidelines, and also improve treatment outcomes through correct diagnosis and providing timely care.

Tutorial on Molecular Latent Space Simulators (LSSs): Spatially and Temporally Continuous Data-Driven Surrogate Dynamical Models of Molecular Systems.

The inherently serial nature and requirement for short integration time steps in the numerical integration of molecular dynamics (MD) calculations place strong limitations on the accessible simulation time scales and statistical uncertainties in sampling slowly relaxing dynamical modes and rare events. Molecular latent space simulators (LSSs) are a data-driven approach to learning a surrogate dynamical model of the molecular system from modest MD training trajectories that can generate synthetic trajectories at a fraction of the computational cost. The training data may comprise single long trajectories or multiple short, discontinuous trajectories collected over, for example, distributed computing resources. Provided the training data provide sufficient sampling of the relevant thermodynamic states and dynamical transitions to robustly learn the underlying microscopic propagator, an LSS furnishes a global model of the dynamics capable of producing temporally and spatially continuous molecular trajectories. Trained LSS models have produced simulation trajectories at up to 6 orders of magnitude lower cost than standard MD to enable dense sampling of molecular phase space and large reduction of the statistical errors in structural, thermodynamic, and kinetic observables. The LSS employs three deep learning architectures to solve three independent learning problems over the training data: (i) an encoding of the high-dimensional MD into a low-dimensional slow latent space using state-free reversible VAMPnets (SRVs), (ii) a propagator of the microscopic dynamics within the low-dimensional latent space using mixture density networks (MDNs), and (iii) a generative decoding of the low-dimensional latent coordinates back to the original high-dimensional molecular configuration space using conditional Wasserstein generative adversarial networks (cWGANs) or denoising diffusion probability models (DDPMs). In this software tutorial, we introduce the mathematical and numerical background and theory of LSS and present example applications of a user-friendly Python package software implementation to alanine dipeptide and a 28-residue beta-beta-alpha (BBA) protein within simple Google Colab notebooks.

Enhancing load frequency control and automatic voltage regulation in Interconnected power systems using the Walrus optimization algorithm.

This paper introduces the Walrus Optimization Algorithm (WaOA) to address load frequency control and automatic voltage regulation in a two-area interconnected power systems. The load frequency control and automatic voltage regulation are critical for maintaining power quality by ensuring stable frequency and voltage levels. The parameters of fractional order Proportional-Integral-Derivative (FO-PID) controller are optimized using WaOA, inspired by the social and foraging behaviors of walruses, which inhabit the arctic and sub-arctic regions. The proposed method demonstrates faster convergence in frequency and voltage regulation and improved tie-line power stabilization compared to recent optimization algorithms such as salp swarm, whale optimization, crayfish optimization, secretary bird optimization, hippopotamus optimization, brown bear optimization, teaching learning optimization, artificial gorilla troop optimization, and wild horse optimization. MATLAB simulations show that the WaOA-tuned FO-PID controller improves frequency regulation by approximately 25%, and exhibits a considerable faster settling time. Bode plot analyses confirm the stability with gain margins of 5.83 dB and 9.61 dB, and phase margins of 10.8 degrees and 28.6 degrees for the two areas respectively. The system modeling and validation in MATLAB showcases the superior performance and reliability of the WaOA-tuned FO-PID controller in enhancing power system stability and quality under step, random step load disturbance, with nonlinearities like GDC and GDB, and system parameter variations.

Mathematical Techniques in the Design of Robust Control Systems

Solid control frameworks are exceptionally imperative for making beyond any doubt that energetic frameworks remain steady and work well in a parcel of diverse circumstances and with a parcel of questions. This diagram tells you everything you wish to know about the numerical strategies utilized to form steady control systems. Strong control tries to bargain with issues like unknowns within the system model, stuns from the exterior, and changes within the system's parameters. It does this to form beyond any doubt that the framework keeps working well and remaining steady in spite of these issues. Lyapunov soundness hypothesis and the H-infinity (H∞) optimization strategy are two of the foremost critical arithmetic apparatuses. Lyapunov steadiness hypothesis gives us a way to see at how steady a framework is, and H∞ minimizes the worst-case pick up from unsettling influence to yield. State-space representations are moreover utilized to show and ponder multi-input multi-output (MIMO) frameworks, which makes control plan more organized. When making controls that guarantee steady execution, strategies like Direct Framework Disparities (LMIs) and Riccati conditions are utilized. The thought of unwavering quality limits is additionally displayed to degree how well the framework can handle factors. The solid control plan incorporates frequency-domain apparatuses, such as the Nyquist and Bode plots, to see at how the framework acts at distinctive frequencies. This makes it simpler to form controllers that can bargain with high-frequency occasions. We conversation around progressed strategies like α-synthesis and strong shaft situation that can offer assistance with certain control problems in dubious settings. Down to earth illustrations appear how these scientific strategies can be used, showing how vital they are in numerous building areas, such as the airplane, vehicle, and prepare control industries. The unique emphasizes how imperative these numerical strategies are for making beyond any doubt that solid control frameworks can handle the challenges of the genuine world, which improves system security, execution, and steadfastness in a wide run of circumstances. The abstract's objective with this outline is to provide you a basic idea of the math that's critical to the field of solid control framework plan.

A study for analysing predator–prey ecological system using Legendre polynomial

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB.