Complete Mathematical Model Research Articles

Numerical simulation of entropy generation in thermo-magnetic convection in an inverted T-shaped porous enclosure under thermal radiation

PurposeThermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.Design/methodology/approachThe mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.FindingsThe graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.Practical implicationsSuch complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.Originality/valueTo the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

Синтез адаптивной робастной системы управления трикоптером с поворотными винтами в условиях неопределенных аэродинамических коэффициентов, частично неопределенной матрицы входа, влияния внешних возмущений и ограничения входных воздействий

In this article, an adaptive robust control system for a tricopter equipped with three rotary propellers is developed and studied under the following conditions: a) uncertain aerodynamic coefficients; b) partially uncertain input matrix; c) influence of unknown external disturbances; and d) input constraints. When constructing a complete nonlinear mathematical model of the dynamics of a tricopter with rotary propellers in the form of Lagrange-Euler equations, the input constraints are taken into account. The synthesis of an adaptive robust control system for a tricopter with rotary propellers is carried out on the basis of the modified computed torque control (Li–Slotine method) and the function approximation technique to eliminate the influence of uncertainty. Unknown external disturbances are compensated by a smooth sliding mode control using an adaptive estimate of the upper bound of the sum of external disturbances and approximation errors of uncertain functions in the mathematical model. To compensate for the negative effects of input constraints, an auxiliary dynamic system is constructed, the state variables of which are used to synthesize the control law. The robustness of the adaptive system and the desired tracking accuracy of the reference signals are proven using the Lyapunov function method. Simulation results using MatLab/Simulink are presented to illustrate the effectiveness of the proposed control law.

Синтез нелинейной и адаптивно-робастной систем со скользящими режимами в управлении динамикой трикоптера с поворотными винтами при действии неизвестных внешних возмущений

The article develops a complete nonlinear mathematical model of tricopter dynamics with rotary propellers in the form of Lagrange-Euler equations and two systems of nonlinear and adaptive-robust control with sliding modes, operable under the action of unknown external disturbances. The nonlinear control system with sliding modes and constant controller parameters is synthesized based on the Lyapunov function method. The adaptive-robust system is developed on the basis of the Lyapunov function method with a smooth sliding mode control and using an adaptive estimate of the upper bound of external disturbances. The performance of the proposed control systems under the action of unknown external disturbances and variations in aerodynamic coefficients is investigated. A comparative study of the constructed control systems is conducted in the MatLab/Simulink software environment.

A complete mathematical modelling of robots actuated by epicyclic-gear

The industrial robots often use planetary gear system to have high joint torques; therefore, the influence of the rotary inertia of the number of the equally spaced planet-gears on the dynamical behavior of the robot is very important. The main objective of this paper is to develop the dynamic modeling of robot actuated by (n) equally spaced planet-gears in the case where the planet-carrier is fixed, no closed solution has been reported for this dynamic modeling, and to compare between the dynamic behavior of robot actuated by (n+1) and (n) equally spaced planet-gears for a same trajectory planning. The authors derive the explicit dynamic model for an elbow down of 2-R manipulator holding an external mass. Finally, the obtained simulation results of the dynamic modeling are verified by modeling the same robot and using an advanced simulation via SolidWorks.

SEAM: An integrated activation-coupled model of sentence processing and eye movements in reading

Models of eye-movement control during reading, developed largely within psychology, usually focus on visual, attentional, lexical, and motor processes but neglect post-lexical language processing; by contrast, models of sentence comprehension processes, developed largely within psycholinguistics, generally focus only on post-lexical language processes. We present a model that combines these two research threads, by integrating eye-movement control and sentence processing. Developing such an integrated model is extremely challenging and computationally demanding, but such an integration is an important step toward complete mathematical models of natural language comprehension in reading. We combine the SWIFT model of eye-movement control (Seelig et al., 2023) with key components of the Lewis and Vasishth sentence processing model (Lewis and Vasishth, 2005). This integration becomes possible, for the first time, due in part to recent advances in successful parameter identification in dynamical models, which allows us to investigate profile log-likelihoods for individual model parameters. We present a fully implemented proof-of-concept model demonstrating how such an integrated model can be achieved; our approach includes Bayesian model inference with Markov Chain Monte Carlo (MCMC) sampling as a key computational tool. The integrated Sentence-Processing and Eye-Movement Activation-Coupled Model (SEAM) can successfully reproduce eye movement patterns that arise due to similarity-based interference in reading. To our knowledge, this is the first-ever integration of a complete process model of eye-movement control with linguistic dependency completion processes in sentence comprehension. In future work, this proof of concept model will need to be evaluated using a comprehensive set of benchmark data.

Numerical simulation on underwater vertical launching process under effect of initial gas

The exiting-tube process is the basis and premise of the underwater vertical launching process. which is a multiphase, rapid, nonlinear, complex issue. Based on RANS method, combined the VOF multiphase flow model, high-resolution interface capture (HRIC) and overlapping grid (zero gap) technology, a complete mathematical model to describe the underwater exiting-tube process of the vehicle is established. The effects of the initial gas and launch parameters on the flow field and the load characteristics of the vehicle are systematically obtained. The research results indicated that: With the increase of the initial pressure of the initial gas, the force period of the vehicle increases, and the evolution process of the initial gas slows down. The initial gas pulsation period can be shortened by increasing the launch depth, while increasing the pressure at the shoulder of the vehicle and suppressing the natural cavitation of the vehicle. The increase of the lateral flow velocity will significantly increase the lateral force and deflection moment of the vehicle. The initial gas's pulsation process has a greater influence on the deflection moment and lateral force of the vehicle.

Numerical modeling of magnetohydrodynamic buoyancy-driven convection for enhanced energy applications

In the realm of thermal management for electronic systems, the efficacy of heat dissipation serves as a major predictor of the reliability and operational lifespan of electronic components. Simultaneously, within the realm of geothermal energy utilization, where harnessing the Earth’s inherent heat reservoirs is employed for power generation and direct heating applications, an intricate comprehension of temperature gradients and the dynamics governing heat transfer stands as an imperative prerequisite for optimizing the extraction of thermal energy. This work offers a complete mathematical model aimed at understanding the principles governing energy transfer inside naturally convected flows subjected to the impact of an external magnetic field. The analytical inspection involves a broad parametric study of the flow system, comprising variations in buoyancy-driven factors, as well as the magnetic field parameter, indicated as the Hartmann number (Ha), ranging from 0 to 50. This multifaceted study unveils the profound impact of magnetic fields on critical aspects of the flow, including isotherm alignment, velocity distributions, thereby paving the way for the development of advanced cooling systems poised to deliver elevated energy efficiency and enhanced performance in electronic devices. The computational analysis digs into the complicated temperature distributions, velocity profiles, and vorticity patterns. It is found that increment of the external magnetic force limits the variations in fluid’s horizontal and vertical velocities. Convective heat transfer is decreased with increasing Hartmann number at cold and hot sections of the fluid chamber. While for Rayleigh number this behavior is reversed.

Resource Allocation Method of Edge IoT Agent Based on Deep Reinforcement Learning

Reasonable allocation of resources is an important guarantee for efficient support of power business in edge IoT agents. Facing the above problems of the current power Internet of Things, this paper proposes a resource optimization allocation method based on deep Q-learning. This method first comprehensively considers the communication performance and network security. Involving indicators such as latency and service satisfaction, a complete and reliable mathematical model of the edge Internet of Things proxy network is constructed to achieve efficient and reliable modeling of the power Internet of Things (pIoT), aiming to better fit the practical interaction needs for efficient and secure communication. The Q-learning network model is optimized, and the method combining Reinforcement learning and deep learning is used to solve the model. Used by this network, the optimization and improvement of the deep network model is realized, so that the status, action and other parameters of the network model can be solved in a timely manner, so as to better support the reliable and efficient information interaction of the communication network. The test results prove that the delay of the proposed method can be maintained within 12[Formula: see text]ms in more complex scenarios, and the interaction success rate reaches 0.975, confirming that the proposed method can provide good information interaction guarantee services.

Passivity-Based Control of Three-Phase PWM AC-DC Converters with Close to Unity Power Factor and RL Load

In the present work, a strategy is proposed to control the pulse width modulation signals of the power devices of high switching of a three-phase alternating current to direct current converter as well as the current of a load type RL guaranteeing that the power factor of the supply be the unity, which is achieved by taking advantage of the properties that the complete mathematical model has in the two-phase synchronous frame of reference. Likewise, a formal stability analysis of the complete closed-loop system is presented, thereby demonstrating that the proposed scheme guarantees global asymptotic stability with all bounded internal signals.

HYDRO TURBINE SPEED CONTROL SYSTEM

The article presents a mathematical model of an hydro turbine speed control system. In the world and domestic practice of creating hydraulic turbine equipment, there is a clear tendency to create computer-based rotor speed control systems for hydraulic turbines. Computer systems provide an opportunity to implement the introduction of effective algorithms using software that improve the static and dynamic characteristics of the system. This in turn increases the importance of mathematical modeling both at the design stage and during commissioning. The analysis of the performed works devoted to the mathematical description of the elements of the hydraulic drive of the regulator showed that they are reduced to linearized equations without taking into account a number of important factors that will increase the accuracy of the mathematical model. Improvement of static and dynamic characteristics and the system as a whole can be achieved by solving the scientific problem of studying its dynamics based on the development of a more complete mathematical model. To reduce friction and hysteresis, to prevent obliteration, the electrohydraulic converter plunger in the lower part is equipped with a segner wheel. Improving the dynamic characteristics of hydraulic turbine speed controllers requires the development of nonlinear mathematical models with subsequent analysis of transients in the hydraulic drive of the speed controller. Evaluation of the quality of transient processes and subsequent adjustment of parameters allows to achieve a reduction in the duration of transients, increase the speed and accuracy of positioning at small movements of the servo motor. A number of unaccounted factors during the preparation of the mathematical model of the electro-hydraulic converter makes it possible to increase its adequacy to the real object of study and increase the speed of the control system of the rotor speed of the hydraulic turbine.

Closed loop operation and testing with processor-in-loop (PIL) simulation of an asymmetrical six-phase open-ended winding synchronous machine

This paper presents a simple closed loop indirect field-oriented controlled operation for an asymmetrical six-phase open-ended winding synchronous motor in a newly defined two-axis (M-T) coordinate system, in which the common mutual leakage coupling between the two stator winding sets has been considered. Phasor diagram of the vector-controlled motor is developed under steady-state. Performance of a six-phase synchronous machine is presented in all four quadrant operations. A complete mathematical model is developed and controlled in a closed loop on Matlab/Simulink environment. Suitability and practical validity of the proposed control scheme are shown by conducting a test using processor-in-loop (PIL) by employing the STM32F407G board. An efficient data transfer at a high baud rate was obtained between the target board and host through an externally connected serial communication interface by using a USB-USART converter i.e. FT32RL board.

Design and implementation of shape‐adaptive and multifunctional robotic gripper

AbstractThis paper presents a multifunctional underactuated two fingered adaptive grippers for grasping a wide range of objects in different working scenarios. Two layered‐based novel multifunctional gripper design is proposed by stacking a multijointed closed‐chain mechanism over a multijointed double parallelogram mechanism to achieve a maximum number of grasping techniques. The multijointed closed‐chain mechanism is employed to perform power, shape‐adaptive grasping, and a multijointed double parallelogram mechanism is used to perform scooping, parallel, and pinch grasping. For stable shape‐adaptive/power grasping, the proposed design allows more contact points between the object and the contact surface of fingers as compared to previous gripper mechanisms. Moreover, a complete mathematical model relating the contact forces at the links of each finger to the linear actuation force and spring torque is developed to conduct stability analysis of the proposed gripper design. Finally, simulations and several experiments are performed using real objects in a reconfigurable environment to demonstrate and validate the stable grasping capabilities of the proposed gripper.

Theory of gravitational lensing on a curved cosmic string

It is discussed in detail the complete mathematical model of gravitational lensing on a single cosmic string (CS) of general shape and position with respect to the line of sight. CS are one-dimensional extended objects assuredly predicted by modern cosmology. The presence of CS changes the global geometry of the Universe, could clarify the properties of the early Universe, including inflation models, and could serve as a unique proof of higher-dimensional theories. Despite the fact that CS have not yet been reliable detected, there are several strong independent indications of the existence of the CS, based of CMB analysis and search of gravitational lens chains with special properties (The recent new indication of the existence of the CSs is the nHz gravitational waves in the NANOGrav and other PTA Collaborations data.) However, early considered models of straight CS presented only a small fraction of the general CS-configurations to be observed. Now we propose model which could significantly increase the possibilities of CS observational search. It is considered more realistic models have necessarily include the inclinations and bends of the CS. Besides, the recent analysis of observational data on the search for gravitational-lens candidates, shows a large number of pairs that could be explained by the complex geometry of the CS.

OPTIMIZATION OF OPERATING MODES OF POWER UNITS OF NUCLEAR POWER PLANTS

The materials of the article consider the main methodological provisions of calculations and optimization of NPP power unit equipment parameters using mathematical modeling methods. For the effective implementation of tasks related to determining the optimal parameters and structures of NPP power unit equipment using mathematical modeling and well-developed multifactor optimization methods, it is necessary to fulfill a number of requirements at their productions. Practice shows that it is impractical to optimize with the help of a single mathematical (simulation) model the entire set of parameters characterizing a given power unit, because with such a formulation, the optimization tasks are often mutually incorrect due to a significant discrepancy in the accuracy of various source information, unequal influence of parameters on the target function, specific differences in the mathematical description of various units and elements of the power unit. In order to effectively optimize the parameters of NPP power units, it is necessary to create a system of interconnected mathematical models, which include: a group of detailed mathematical models of individual units and elements of power unit equipment; more generalized mathematical models for the main equipment of power units built on their basis; complete mathematical model of power units.

Cascade nonlinear observer design for large amplitude of slosh variables in spacecraft maneuver with liquid propellant tank

Slosh dynamics in a liquid propellant tank during a spacecraft maneuver can have an effect on the system stability and potentially lead to critical problems for the mission operation. In particular, the fuel sloshing problem has drawn significant attention in aerospace applications where a large portion of the gross weight is comprised of liquid fuel. Recently, many active control methods have been introduced as alternatives to passive approaches. However, the majority of these methods basically require the full-state condition. To guarantee the availability of the full-state condition, this paper proposes a cascade nonlinear state observer based on the sliding mode theory for estimating the unmeasurable slosh variables in a planar model. Additionally, for large amplitude estimation, a complete nonlinear mathematical model with a pendulum analogy is formulated without a linearization process. The stability analysis is theoretically proven by Lyapunov method. The effectiveness is demonstrated through simulations, and the performance comparison with a different observer method is also presented in the results.

Novel design of thermo-electric air conditioning system integrated with PV panel for electric vehicles: Performance evaluation

Traditional air conditioning may be inappropriate for electric vehicles due to its moving parts noise besides using chlorofluorocarbons that harm the environment. In addition, it consumes a significant portion of the stored energy in batteries, reducing the vehicle's driving range. So, in this paper, a novel design of thermo-electric cooling (TEC) system coupled with a photovoltaic (PV) panel replacing the vehicle roof is studied. This system consists of a sandwich of PV panel outside the vehicle and TEC inside with a heat sink system integrated between them. The air temperature variation in the cabin during the daytime is predicted by solving a complete mathematical transient thermal model of the whole system before and after mounting the cooling system. The air streams through the vehicle moving are exploited to improve the TEC and PV system performance. The system performance is investigated for different cases during the day with and without including the PV output power and for the vehicle parks inside or outside. The results indicate that, for each scenario, the number of used TEC modules influences the system performance where the best number varies between 128 and 98. Coupling the PV panel with the TEC system reduces the daily required energy from batteries by about 19%. Running the TEC system during parking from 8 to 10 am decreases the cabin air temperature from 47.5 to 34°C while the input power declines by about 45%, which reduces the interior temperature to 25°C in 10 min (transition time). The contribution of the PV panel based on the studied conditions can increase the range of the vehicle by 10.4 km/day and about 160kWh/year energy saving. The reduction in the input power during transition time reaches 27.8% when the vehicle speed increases from 30 to 60 km/h, while this ratio declines to 10.8% as the vehicle speed rises from 60 to 90 km/h. During vehicle moving, powering the TEC system by the PV panel only can prevent the cabin temperature from rising over 40°C, whereas during parking, there is an optimum fan air velocity that gives the maximum reduction of the cabin temperature.

Attitude Control of Ornithopter Wing by Using a MIMO Active Disturbance Rejection Strategy.

This work proposes a mathematical solution for the attitude control problem of an ornithopter wing. An ornithopter is an artificial bird or insect-like aerial vehicle whose flight and lift movements are produced and maintained by flapping wings. The aerodynamical drag forces responsible for the flying movements are generated by the wing attitude and torques applied to its joints. This mechanical system represents a challenging problem because its dynamics consist of MIMO nonlinear equations with couplings in the input variables. For dealing with such a mathematical model, an Active Disturbance Rejection Control-based (ADRC) method is considered. The cited control technique has been studied for almost two decades and its main characteristics are the use of an extended state observer to estimate the nonmeasurable signals of the plant and a state-feedback control law in standard form fed by that observer. However, even today, the application of the basic methodology requires the exact knowledge of the plant's control gain which is difficult to measure in the case of systems with uncertain parameters. In addition, most of the related works apply the ADRC strategy to Single Input Single Output (SISO) plants. For MIMO systems, the control gain is represented by a square matrix of general entries but most of the reported works consider the simplified case of uncoupled inputs, in which a diagonal matrix is assumed. In this paper, an extension of the ADRC SISO strategy for MIMO systems is proposed. By adopting such a control methodology, the resulting closed-loop scheme exhibits some key advantages: (i) it is robust to parametric uncertainties; (ii) it can compensate for external disturbances and unmodeled dynamics; (iii) even for nonlinear plants, mathematical analysis using Laplace's approach can be always used; and (iv) it can deal with system's coupled input variables. A complete mathematical model for the dynamics of the ornithopter wing system is presented. The efficiency of the proposed control is analyzed mathematically, discussed, and illustrated via simulation results of its application in the attitude control of ornithopter wings.

Physically informed data-driven modeling of active nematics

A continuum description is essential for understanding a variety of collective phenomena in active matter. However, building quantitative continuum models of active matter from first principles can be extremely challenging due to both the gaps in our knowledge and the complicated structure of nonlinear interactions. Here, we use a physically informed data-driven approach to construct a complete mathematical model of an active nematic from experimental data describing kinesin-driven microtubule bundles confined to an oil-water interface. We find that the structure of the model is similar to the Leslie-Ericksen and Beris-Edwards models, but there are appreciable and important differences. Rather unexpectedly, elastic effects are found to play no role in the experiments considered, with the dynamics controlled entirely by the balance between active stresses and friction stresses.

Smart Energy Management for a Microgrid System Based on Echo State Networks─Gray Wolf Optimizer Hybrid Algorithm

This work present a smart energy management system for a microgrid based on a hybrid intelligent adaptive algorithm composed of an echo state network and gray wolf optimizer techniques. The microgrid connected to the grid is composed of renewable sources such as photovoltaic and wind conversion associated with a hybrid battery hydrogen fuel generation storage system. An adaptive intelligent control unit is developed to manage the power flow between the hybrid power sources and other devices in the system. The controller chooses the optimal operating mode of power sources ensuring the continuous supply of the injecting power in the grid and maintaining the battery state of charge at acceptable levels as the hydrogen tank level. Complete mathematical modeling for the proposed system is implemented in MATLAB/Simulink to track the microgrid performance. Numerical and graphical results are presented to show the effectiveness of the proposed control system

MATHEMATICAL MODEL OF THE ELECTRO-HYDRAULIC CONVERTER OF THE HYDRAULIC TURBINE SPEED CONTROL SYSTEM

Presents a mathematical model of an electro-hydraulic converter with proportional control. In the world and domestic practice of creating hydraulic turbine equipment, there is a clear tendency to create computer-based rotor speed control systems for hydraulic turbines. Computer systems provide an opportunity to implement the introduction of effective algorithms using software that improve the static and dynamic characteristics of the system. This in turn increases the importance of mathematical modeling both at the design stage and during commissioning. The analysis of the performed works devoted to the mathematical description of the elements of the hydraulic drive of the regulator showed that they are reduced to linearized equations without taking into account a number of important factors that will increase the accuracy of the mathematical model. Improvement of static and dynamic characteristics and the system as a whole can be achieved by solving the scientific problem of studying its dynamics based on the development of a more complete mathematical model. To reduce friction and hysteresis, to prevent obliteration, the electrohydraulic converter plunger in the lower part is equipped with a segner wheel. Improving the dynamic characteristics of hydraulic turbine speed controllers requires the development of nonlinear mathematical models with subsequent analysis of transients in the hydraulic drive of the speed controller. Evaluation of the quality of transient processes and subsequent adjustment of parameters allows to achieve a reduction in the duration of transients, increase the speed and accuracy of positioning at small movements of the servo motor. A number of unaccounted factors during the preparation of the mathematical model of the electro-hydraulic converter makes it possible to increase its adequacy to the real object of study and increase the speed of the control system of the rotor speed of the hydraulic turbine.