Mathematical Model Of System Research Articles

SIMULATION OF THE AUTOMATIC CONTROL SYSTEM OF A HORIZONTAL-AXIAL WIND POWER PLANT

We considered the results of modelling the operating modes of an electric power generation system of a horizontal-axial wind turbine. The system consist of an aerodynamic blades of a wind wheel connected by an elastic shaft to a generator through a multiplier. Engineering part of the automatic control system (ACS) is the mechanism of rotation of the blades relative to the angle of wind flow. A method for optimizing the main parameters: geometric, dynamic and ACS coefficients is proposed. The method allows a comprehensive assessment of the operation of wind turbines. The value of the average annual electricity generation was used as an optimization criterion. As a result, a deep optimization of the adjustment depth coefficient was carried out. Secondly, we investigated the system in dynamics. A stochastic wind model was used as a disturbing effect. We constructed the system by mathematic simulation methods. As a reference control algorithm, a direct linear dependence of the angular velocity of the turbine rotation on the wind speed with restrictions on the minimum and maximum values was used. Also we described the mathematical model of system and the initial results of the theoretical calculations of algorithms for controlling. The versatility of the calculation system makes it possible to use any aerodynamic profiles of the blades in its composition. The characteristics of aerodynamic moments for the calculation of force moments are obtained by converting Lilienthal curves as initial data for the considered aerodynamic profiles.

Design, modeling, manufacturing, and control of dual axis stabilized system

Recently, Inertial Stabilized Systems (ISS) are widely spread either in military or civilian applications. It’s used to stabilize and point the onboard sensors. Therefore, the accurate modeling and control is a crucial factor to design a suitable control system. In this work, two axes gimbal system is designed, modeled, manufactured, and controlled. Firstly, the stabilized system is built using solid work software. Secondly, the system mathematical model is derived for the physical system with its actuators and encoders. Thirdly, the designed model is manufactured and integrated with the suitable motors; the overall open loop system model is implemented in MATLAB (Simulink). Finally, a modified PI-D structure is designed to stabilize the ISS in an efficient manner, the simulation results show the superiority of the designed controller’s performance and robustness compared to the classical PID in transient and steady state responses.

Assessment of managed aquifer recharge in saline confined aquifers for freshwater storage and improved recovery: A 3D tank study under various operational conditions

Aquifer Storage and Recovery (ASR), a subset of Managed Aquifer Recharge (MAR) techniques, is a promising technique to address water scarcity issues by recharging depleted aquifers. The application of ASR in saline groundwater regions is challenging due to mixing of recharged freshwater with the ambient saline groundwater, decreasing the recoverable amount of freshwater. This paper aimed to investigate the feasibility of ASR techniques for freshwater storage and recovery in saline confined aquifers using a laboratory scale physical model (100 cm length x 30 cm width x 60 cm depth). The study then explored the impact of operational factors (freshwater storage duration, injected freshwater volume, number of injection/extraction cycles etc.) on freshwater recovery from an applied ASR. Firstly, the behaviour of stored freshwater in a saline-confined aquifer was investigated, and in the next step, the impact of ASR operational parameters on the recovery efficiency (RE) was evaluated. Along with the physical model, these effects were studied using a mathematical model (MODFLOW linked with SEAWAT) for the representative aquifer system. The movement and spreading of the stored freshwater were monitored over time. The experimental results presented in this study suggested that several factors significantly influence the efficiency of ASR systems. A negative correlation between ambient groundwater salinity and average recovery efficiency (ARE) was confirmed, with decreasing ARE observed as the salinity level increased. The injection volume of freshwater was found to have a positive influence on ARE, although the relationship was non-linear, a polynomial trend was observed. The longer freshwater was stored in the aquifer, the lower ARE was reported, indicating a negative impact of storage duration on ASR performance. Finally, the number of successive cycles of ASR operation was found to have a positive influence on ARE, but the effect decreased with each subsequent cycle. This research provided valuable insights into the application of ASR techniques for freshwater storage and its enhanced recovery in saline confined aquifers.

Implementation of the method of structural-parametric optimization of graph models of organizational-technical systems

Subject of research: possibility of realization of structural and parametric transition between different states of organizational and technical systems taking into account the properties and features of the processes realized in them.
 Purpose of research: the need to develop and implement methods aimed at solving optimization problems, which are associated with structural transformations of models of organizational and technical systems, and allowing to take into account their intermediate states during the transition from the initial state to the required state.
 Objects of research: mathematical models of organizational and technical systems in the form of sign weighted oriented graphs built on the basis of selected types of relations between elements in terms of conflict theory.
 Methods of research: the method of system analysis is used, associated with the allocation of types of relations between the elements of the studied systems in terms of conflict theory, as well as the formalization of the solution of optimization problems on the basis of structural-parametric representation of research objects.
 Main results of research: models of organizational-technical systems in structural-parametric relation with regard to the selected types of relations between their elements from the point of view of the conflict theory are given; a method is developed, which is based on the formation of tuples of operations necessary for the structural transformation of the systems under study, and which allows taking into account the ways of indirect transition from the initial state of the system to the required (optimal) one; an auxiliary algorithm is developed, which is based on the use of a database containing a set of tuples of augmentations An example of implementation of the proposed method on the model of communication network is given, which shows how the structural-parametric optimization of organizational and technical systems can be carried out.

Simulation investigates on operation characteristics of free piston internal combustion generator

To study the influence of the free piston generator structure on its stable operation, this paper chose the combining mathematical and physical methods to build a simulation model to investigate the influence factors. According to the dynamic and thermodynamic equation, the mathematical model of the free piston internal combustion generator system was established. the simulation model was built with the help of MATLAB/Simulink software, and the validity of the model was verified. Based on this, the influences of ignition position and piston group mass on the operation characteristics of free piston generator were investigated. The simulation results show that the factors such as ignition position, piston group mass have significant effects on the compression ratio, cylinder pressure, maximum acceleration, etc. of the free piston generator, which provides a theoretical basis for the stable operation control of the free piston internal combustion generator.

Research on the mathematical model and design of a three loop controller for the oscillating scanning system of a laser line scanning galvanometer

The scanning vibration mirror system drives the scanning mirror fixed to it through the oscillation of the motor shaft, so as to control the reflected light to form a dynamic variable light path. The vibration mirror scanning system has higher controllability than the fixed optical path system and has been widely used.In this dissertation, after establishing the models of the core components of the scanning vibration mirror system, the mathematical model of the whole system is established.On this basis, simulation and theoretical analysis show that the system has some shortcomings, such as small bandwidth, low dynamic tracking accuracy, and the comprehensive dynamic performance of the system is easily affected by the input of external interference branches. A series correction controller and three closed-loop controller are designed for the above problems, respectively, and the control effects of the two controllers on the scanning vibration mirror system are studied through simulation experiments. By comparing the output response results of the system under the action of sinusoidal signals of different frequencies, it can be seen that the comprehensive effect of the three closed-loop controllers is better. Under the action of step signals, the overshoot of the three closed-loop correction controller correction system is 21.5% higher than that of the series controller correction system, the adjustment time is 82.7% less, and the steady-state error is significantly smaller. Therefore, it indicates that the three closed-loop correction system has good rapidity and steady-state accuracy.

Analysis of Nodal Multiflows in a Multiuser System with Equalizing Control Strategies

Within the framework of computational experiments on a mathematical model of a multiuser network communication system, the dynamics of changes in the indicators of the functioning of a telecommunications network are studied. The proposed algorithmic scheme makes it possible to sequentially form component-by-component nondecreasing vectors of permissible outgoing nodal multiflows. The model assumes that the transmission of interstitial flows of different types is carried out simultaneously from all nodes by all nodes along all routes with the minimum number of edges. During the calculations, resources are distributed in equal shares at each step until the network is fully loaded. The results obtained during the experiments make it possible to trace changes in the values of quotas distributed to the nodes for transmitting a certain type of flow. The found vectors of allowable outgoing nodal multiflows can be considered as guaranteed multicriterial estimates of the functioning of a multiuser system. Networks with different structural features and equal total capacity are analyzed. Special diagrams are provided.

Research on the modeling and control mechanism of three-phase cascade rectification stage of non-power frequency transformer

Non-power frequency transformers are essential and important devices for new energy generation and smart grid construction. This article analyzes the working principle of voltage cascade rectifier stage, constructs a mathematical model of three-phase cascade rectifier stage system, and simplifies its model. Finally, the idea of overall control of the voltage loop in the rectifier stage system was derived, and the traditional control method of rectification was directly transplanted into the overall control system of the cascade rectifier stage. At the same time, the characteristics of voltage loop and current loop of cascade rectifier stage system are analyzed, and the relevant control structure block diagram and controller design idea are given, which lays an important theoretical foundation for in-depth study of non-power frequency transformer.

CONFIGURATIONS OF ULTRASONIC EMITTER RESONANCE MODES FOR UNILATERAL ACCESS TO AN OBJECT

Link for citation: Azin A.V., Bogdanov E.P., Vasilyev A.V., Ponomarev S.A., Ponomarev S.V., Rikkonen S.V. Configurations of ultrasonic emitter resonance modes for unilateral access to an object. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 10, рр. 199-209. In Rus. Relevance. To prepare high-viscosity oil for transport, a number of methods are used in practice: thermal, chemical and the method of physical influences. Ultrasonic exposure of hydrocarbon raw materials is one of the physical methods. It is necessary to develop an effective method for tuning an ultrasonic emitter for maximum energy transfer into a multilayer technological medium. Aim: to study resonant operating modes of an ultrasonic emitter in a multilayer system with unilateral access to the object with simplified design of a resonance type ultrasonic emitter. Objects: oscillating system of an ultrasonic resonant type emitter, multilayer system, physical model of a system «ultrasonic emitter – multilayer system». Methods: mathematical modeling of linear oscillating system to determine the properties of oscillating system influence and technological factors on the form of vibration oscillations and on the amplitude-frequency characteristics of the system; experimental research on the basis of the physical model «ultrasonic emitter – multilayer system». Results. The authors have revealed a physical feature of the oscillatory system operation, which consists in the fact that at resonance the form of oscillations of the force signals of a multilayer piezoactor and vibration acceleration signals are purely harmonic in nature. This effect extends to operation of a resonant-type ultrasonic emitter in a short-circuit mode on a multilayer system. It was found that force and vibration acceleration amplitude-frequency characteristics of a multilayer piezoactor are similar to each other. Based on the analysis of theoretical and experimental data, the authors developed the method for adjusting the resonant operating modes of an ultrasonic emitter with unilateral access to an object. This allows simplification and reduction in the emitter design cost. The method for setting up oscillatory systems is applicable for laboratory and industrial installations. Conclusion. The research results show that in practice, harmonic shape of acceleration and force signals, as well as force amplitude of a multilayer piezoactor can be used as criteria for determining and adjusting the resonance of an oscillatory system. The oscillatory system of a resonant-type ultrasonic emitter can be tuned to resonance according to the shape and amplitude of the signal from the force sensor of the multilayer piezoactor. The force sensor is located in series with the multilayer piezoactor and does not require additional structural elements for its fastening. The ultrasonic emitter design is greatly simplified due to the absence of a vibration acceleration sensor. The method of adjusting the resonance of an oscillatory system using only a force sensor is also applied when operating a resonant-type ultrasonic emitter to a multilayer mechanical system. The developed design and technique for tuning the oscillatory system of a resonant-type ultrasonic emitter can be conveniently used when influencing process fluids through the walls of tanks and storage tanks.

Hybridized Renewable Energy for Smart Vehicle-to-Grid (V2G) Systems

Wind and sunlight are increasingly being exploited as energy supplies that never run out. Additionally, renewable energy resources, including sun, wind, and geothermal heat, are being used for different technologies. It was considered the use of hybridized wind-solar energy resources in smart vehicle technology. A thorough understanding of an integrated framework of the hybridized renewable energy for smart vehicle-to-grid (V2G) systems is essential and required to further identify and perhaps maximize existing opportunities. Aiming to develop a vehicle-to-grid (V2G) system where the smart vehicle runs on stored sunshine and wind energy, and vehicle batteries store energy and release it to the electricity grid in peak demand periods. To achieve this aim, mathematical models for solar and wind systems were created and entire 24-h simulations were run for case studies of three smart vehicles, which were assessed for different scenarios and circumstances, using the MATLAB/SIMULINK environment. The estimated values obtained were home load 10 MW, power factor 0.15 MVA, industrial load 0.16 MVA, and smart car-to-grid, solar panel farm, and wind farm power of 4 MW, 8 MW, and 4.5 MW, respectively. Therefore, the hybridized wind-solar energy sources were applicable for all three smart vehicles considered.

Negative pressure protection of water supply systems with multi-undulating terrain by one-way surge tanks

Abstract The protection of negative pressures generated by the hydraulic transient process in the water supply system is crucial to safe and stable operation. In this study, a mathematical model of a pipeline hydraulic transient system with multi-undulating terrain was established based on the method of characteristics (MOC). The generation and development of water hammer negative pressures were analyzed, and double one-way surge tank protection schemes were proposed. It proved that the first surge tank should be located at the initial negative pressure point, and the second surge tank should be located at the second-highest point rather than the highest point. Additionally, compared with the theoretical minimum height, there was an optimization margin for the total surge tank height, which was reduced by 21% in this study. Meanwhile, the applicability of protection schemes and the influence of the one-way surge tank number on the total height were analyzed. The total height reduced with the increase of one-way surge tank number and tended to a minimum value. By comprehensively considering the engineering investment and negative pressure protection effect, the optimal surge tank number could be determined. This research represents an advance in negative pressure protection in multi-undulating terrain and provides support for further engineering studies.

A Mathematical Model for a Hybrid Ignition System

In the operation of a car's ignition system, the primary ignition coil is responsible for generating a high voltage that typically ranges from around 100V to 300V. However, this self-induced electromotive force (emf) can lead to certain negative effects such as switch breakdown, inductive noise, and secondary voltage drop. This article introduces a novel hybrid ignition system designed for a 4-cylinder engine. This innovative system is a combination of capacitive discharge ignition system (CDI) and induction discharge ignition (IDI) system. The excess electromagnetic force energy (emf) generated during the induction ignition stage will be used in the capacitive ignition. Thereby contributing to limiting the negative effects as mentioned. Forming and solving the mathematical model for the hybrid ignition system mentioned above enables us to analyze the transient responses of the primary current (i1) and primary voltage (V1). These instantaneous responses are crucial in understanding the behavior of the composite ignition circuit and calculating key parameters such as ignition energy during the inductive and capacitive ignition stages, as well as the magnitude of the maximum secondary voltage (V2m). Furthermore, the article also presents experimental results from the hybrid ignition system to complement the theoretical analysis.

Efficient and geometry-matching two-stage annular thermoelectric generator for tubular solid oxide fuel cell waste heat recovery

Tubular solid oxide fuel cell (TSOFC) converts a great part of chemical energy within fuel into high-grade waste heat, leading to a decrease in overall fuel efficiency. In this paper, a steady-state hybrid system model based on TSOFC and two-stage annular thermoelectric generator (TATEG) is proposed. Considering various kinds of irreversible effects, mathematical model for the hybrid system is explicitly formulated and verified to guarantee the accuracy. Energetic and exergetic performance indexes of the hybrid system and subsystems are obtained, and the corresponding performance characteristics are revealed. Calculation results display that the power density, energetic and exergetic efficiencies of TSOFC-TATEG hybrid system can be 15.29 %, 11.25 % and 11.25 % higher than that of stand-alone TSOFC, respectively. The power density, energetic efficiency and exergetic efficiency of TSOFC-TATEG hybrid system are all increased by 5.65 % compared to that of TSOFC-ATEG hybrid system. Furthermore, this study reveals that enhancing the performance of the hybrid system is attainable through regulating variables, such as elevated operating temperatures, optimal quantities of thermoelectric elements, appropriate ratios between thermoelectric element numbers, well-considered thermocouple thickness, suitable thermocouple radial width, and the judicious selection of parameters like annular shape or height ratio.

Mathematical Modeling of a Novel PVT-Fin System for Maximum Energy Yield

Mathematical Modeling of a Novel PVT-Fin System for Maximum Energy Yield

Evaluation of Biogas and Solar Energy Coupling on Phase-Change Energy-Storage Heating Systems: Optimization of Supply and Demand Coordination

Biogas heating plays a crucial role in the transition to clean energy and the mitigation of agricultural pollution. To address the issue of low biogas production during winter, the implementation of a multi-energy complementary system has become essential for ensuring heating stability. To guarantee the economy, stability, and energy-saving operation of the heating system, this study proposes coupling biogas and solar energy with a phase-change energy-storage heating system. The mathematical model of the heating system was developed, taking an office building in Xilin Hot, Inner Mongolia (43.96000° N, 116.03000° E) as a case study. Additionally, the Sparrow Search Algorithm (SSA) was employed to determine equipment selection and optimize the dynamic operation strategy, considering the minimum cost and the balance between the supply and demand of the building load. The operating economy was evaluated using metrics such as payback period, load ratio, and daily rate of return. The results demonstrate that the multi-energy complementary heating system, with a balanced supply and demand, yields significant economic benefits compared to the central heating system, with a payback period of 4.15 years and a daily return rate of 32.97% under the most unfavorable working conditions. Moreover, the development of a daily optimization strategy holds practical engineering significance, and the optimal scheduling of the multi-energy complementary system, with a balance of supply and demand, is realized.

Quality analysis of diffraction grating based 3D light field display system: Identifying optimal system parameters

Revealing the relationship between the parameters and display performance metrics is crucial to designing a high-quality three-dimensional (3D) light field display (LFD) system. However, there is currently no such analysis available for the diffraction grating (DG)-based 3D LFD system. In this paper, the light field mathematical model of the DG-based 3D LFD system is established and the influence of the main parameters of the DG-based 3D LFD system on the display quality is analyzed. A quality analysis methodology for the reconstructed light field of the DG-based 3D LFD system is proposed. This quality analysis methodology can be adopted as a design criterion for the DG-based 3D LFD system.

Scientific Activity and Contribution of Voldemārs Dāle (1922–2008), Honorary Doctor of the Latvian Academy of Sciences, to the Development of Power Engineering

Honorary Doctor (Dr. h. c.) of the Latvian Academy of Sciences (LAS), long-time leading researcher of the Institute of Physical Energetics, Professor Voldemārs Dāle (1922–2008) devoted his entire working life to science. The most important field of V. Dāle’s research was the use of mathematical methods and computer technology in the dynamic optimization of power engineering development. The main areas of his scientific work include planning and forecasting methods of power system development; research on development problems of the Latvian and Baltic energy systems; methods of mathematical modelling of power systems considering the environmental factors. A monograph on research results in the optimization of electrical network development published in 1964 written by a group of three scientists, including V. Dāle, received the State Prize of the Latvian Soviet Socialist Republic (LSSR), which was awarded in 1965.

A reliable stochastic computational procedure to solve the mathematical robotic model

The current work presents the numerical solutions of the robotic system in the process of coronavirus. The stochastic performances using the modeling of Gudermannian neural networks (GDMNNs) are provided along with the global search genetic algorithm (GA) and rapid interior-point scheme (IPS), i.e., GDMNNs-GAIPS. An error function using the differential form of the model is created and then optimized by applying the hybridization of GA-IPS. The correctness and accuracy of the stochastic procedure GDMNNs-GAIPS is examined by using the comparison of the proposed and reference results. The reliability and substantiation of the proposed GDMNNs-GAIPS is authenticated by using the statistical operators based on the mean square error, Theil inequality coefficient and variance account for. Forty numbers of independent trials along with ten numbers of hidden neurons have been used to solve the mathematical model of robotic system to detect the positive cases of COVID-19.

Research and concept design of wave energy converter on ocean squid jigging ship

Wave power capture applied on a squid jigging ship is assessed in this paper; this would decrease the operating cost of ships and reduce carbon emissions. Firstly, the history of wave energy devices and wave energy generation on ships are briefly reviewed. Then, a new wave energy device on an ocean squid jigging ship is designed. The linear mathematical system model of the device, and WAMIT software are used to calculate wave energy captured. The floating bodies of the device is designed to take advantage of resonance. By comparing wave capture width ratio of the float with arm hinged on the ship, it is found that wave capture width ratio of the device is highest when the arm length is half a wavelength. The numerical method is validated by experimental tests which are presented in details from setup, data treatment to wave energy capture ratio calculated. Based on a resonance criterion, 20 wave energy device layouts of the ocean squid jigging ship are designed. From numerical simulation the optimum radius of the floating body is 2 m, and the maximum annual average power among these devices is 136 kW at Northwest Pacific fishery ground, which can provide about 10 % of the power consumption for the ocean squid jigging ship.

Алгоритмы дискретной фильтрации на основе модифицированной взвешенной ортогонализации Грама –Шмидта для дискретных стохастических систем с мультипликативными и аддитивными шумами

Discrete-time stochastic systems with multiplicative and additive noises describe a wide class of mathematical models of complex systems, for example, industrial-technological, energy, economic, telecommunication, aerospace systems, etc. An important class of algorithms for processing measure ment information in complex systems are Kalman-type discrete-time filtering algorithms. Purpose. Construction of new discrete-time filtering algorithms for discrete-time linear systems with multiplicative and additive noises based on numerically stable modified weighted Gram – Schmidt orthogonalization (MWGS). Methodology. The methods of computational linear algebra were used, namely, the direct procedu re of MWGS-orthogonalization, the theory of Kalman filtering, methods of scientific programming in MATLAB. Findings. New LD-algorithms for discrete-time filtering in covariance and informational form for discrete-time stochastic systems with multiplicative and additive noises are constructed. The algorithms have an extended array form allowing updates for all necessary filter values. The method employs numerically stable modified weighted Gram – Schmidt orthogonalization. Algebraic equiva lence of LD-filters to Kalman-type covariance and informational algorithms for linear discrete time stochastic systems with multiplicative and additive noises is proved. The conducted numerical experiments have shown the effectiveness of the proposed algorithms using the example of solving the problem of parametric estimation of a model of almost rectilinear motion, as well as their savings in computation time compared to previously constructed UD filters. Value. New discrete-time filtering LD-algorithms can be used as a reliable computational alterna tive to the Kalman-type “standard algorithms” since they have the property being numerically stable to machine round-off errors due to the use of the MWGS orthogonalization computational procedure at each iteration of the algorithm. The results can be used to solve problems of measurement information processing in discrete-time systems with multiplicative and additive noise.