Mathematical Model Of System Research Articles

Event-Triggered Sliding Mode Control Versus Time-Triggered Sliding Mode Control: A Comparative Study

unlike continuously triggered techniques, event-triggered strategies update the control actions based on specific conditions. Consequently, the energy consumption will be reduced while maintaining performance and stability. Compared to the traditional (periodic) implementation of SMC, event-triggered sliding mode controller (ET-SMC) requires 101 control action modifications, 33.9 % less than periodic SMC implementation. The proposed triggering rule technique is shown to be feasible and closed-loop stable. A positive lower bound for inter-event execution time prevents Zeno-type behavior. The mathematical model of a linear time invariant system which is chosen to be a Direct Current servo motor (DC servo motor) is simulated to show the advantages of the recommended technique over conventional sliding mode technique. The Direct Current servo motor (DC servo motor) is chosen as the mathematical model of a linear time invariant system which simulated to show the advantages of the recommended technique over conventional sliding mode technique. Index Terms— Event control, Triggered control, Sliding mode, Event triggered control, Aperiodic control, DC servo motor.

Mathematical model of a battery energy storage for a standalone solar photovoltaic plant

Relevance. One of the priority areas for modern energy development is the active use of renewable energy technologies, the leading position among which in terms of the volume of commissioned generating capacity and areas of practical application is occupied by photovoltaics. In recent years, solar photovoltaic plants are increasingly being used as part of autonomous power supply systems, which is largely facilitated by a significant reduction in the cost of their components due to improved technology. Autonomous power supply systems can vary significantly in power, operating conditions, requirements for uninterrupted power supply and many other factors. This determines the high importance of the task of choosing the composition of the main electrical equipment that ensures optimal technical and economic indicators of the designed energy system. To make a reasonable choice of the equipment of an autonomous photovoltaic power plant, simulation models of all its main components are required that adequately reflect their performance characteristics under real operating conditions. An important component of autonomous photovoltaic plants is the energy storage device, which includes a battery and a solar controller that manages the energy balance of the power plant. The settings of the solar controller largely determine the operating modes of the photovoltaic power plant, on which the service life of the batteries primarily depends. Taking into account the fact that the costs of energy storage constitute a significant share of the costs of the total financial investments in the designed power plant, the problem of reliably assessing the service life of batteries is very relevant. Aim. Development of a mathematical model of energy storage system for the design and optimization of the equipment of autonomous photovoltaic plants. Methods. Mathematical and numerical modeling using the MatLab/Simulink software package. Results. A mathematical model of a battery has been developed, based on the modified Shepherd model and the kinetic model of a rechargeable battery. The model is universal and can be used to simulate the static and dynamic characteristics of different types of batteries. To identify model parameters, only the technical specification data provided by the manufacturer is sufficient. The complex model includes a battery life model, which allows you to dynamically adjust the available maximum battery capacity during operation.

Data-driven identification of stable sparse differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning differential operators that are theoretically linearly stable and have sparsity patterns of common discretization schemes. These differential operators are obtained by solving a constrained regression problem, involving local constraints to ensure the linear stability of the global dynamical system. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

System performance comparison of oxygen consumption and air separation for aircraft fuel tank inerting

To compare the performance of oxygen consumption and air separation inerting systems. This paper established the mathematical models of the oxygen consumption inerting system and air separation inerting system by mass conservation and energy conservation formula, and the equal inerting time method is adopted to assess the overall performance of the two systems. The two system performances, such as volume flow, thermal load, thermal power, mass increment, and additional fuel consumption, are compared. The results show that: The volume flow of the oxygen consumption inerting system is only 22.9% of the air separation system because of its internal circulation air injection characteristics. Furthermore, the thermal load of the oxygen consumption inerting system is reduced by 30% compared to the air separation system. The total additional fuel consumption of the oxygen consumption inerting system is reduced by 93.57% compared to the air separation system.

Hybrid Nonlinear Model Predictive Motion Control of a Heavy-duty Bionic Caterpillar-like Robot

This paper investigates the motion control of the heavy-duty Bionic Caterpillar-like Robot (BCR) for the maintenance of the China Fusion Engineering Test Reactor (CFETR). Initially, a comprehensive nonlinear mathematical model for the BCR system is formulated using a physics-based approach. The nonlinear components of the model are compensated through nonlinear feedback linearization. Subsequently, a fuzzy-based regulator is employed to enhance the receding horizon optimization process for achieving optimal results. A Deep Neural Network (DNN) is trained to address disturbances. Consequently, a novel hybrid controller incorporating Nonlinear Model Predictive Control (NMPC), the Fuzzy Regulator (FR), and Deep Neural Network Feedforward (DNNF), named NMPC-FRDNNF is developed. Finally, the efficacy of the control system is validated through simulations and experiments. The results indicate that the Root Mean Square Error (RMSE) of the controller with FR and DNNF decreases by 33.2 and 48.9%, respectively, compared to the controller without these enhancements. This research provides a theoretical foundation and practical insights for ensuring the future highly stable, safe, and efficient maintenance of blankets.

Finite Speed-Set Model Reference Adaptive System Based on Sensorless Control of Permanent Magnet Synchronous Generators for Wind Turbines

This paper proposes a novel finite speed-set model reference adaptive system (FSS-MRAS) based on the current predictive control (CPC) of a permanent magnet synchronous generator (PMSG) in wind energy turbine systems (WETSs). The mathematical models of wind energy systems (WESs) coupled with a permanent magnet synchronous generator (PMSG) are presented in addition to the implementation of the CPC of PMSGs. The proposed FSS-MRAS is based on eliminating the tuning burden of the conventional MRAS by using a limited set of speeds of the PMSG rotor that are employed to predict the rotor speed of the generator. Consequently, the optimal speed of the rotor is the one resulting from the optimization of a proposed new cost function. Accordingly, the conventional MRAS controller is eliminated and the main disadvantage represented in the tuning burden of the constant-gain proportional-integral (PI) controller has been overcome. The proposed FSS-MRAS observer is validated using MATLAB/Simulink (R2023b) at different operating conditions. The results of the proposed FSS-MRAS have been compared with those of the conventional MRAS, which proved the high robustness and reliability of the proposed observer.

Анализ компромисса между точностью и сложностью идентифицированных моделей динамических систем

One of the rapidly developing areas of the modern control theory is the identification of systems associated with the construction of mathematical models of systems in the form of a set of mathematical relationships that adequately reflect the basic properties of the system. Symbolic regression methods are becoming more and more popular in the problems of structural-parametric identification of systems based on available observations and experimental data, which allow building regression models in the form of codes of mathematical expressions in a symbolic form. Among the known numerical evolutionary methods of symbolic regression, the universally acknowledged “favorite” is the method of genetic programming”, the application of which allows us to describe the search for solving a problem as the construction of a regression model by enumerating various arbitrary superpositions of functions from some predetermined set. In this case, the important indicators determining the quality of identification of the mathematical model of the system are the accuracy and complexity of the identified model. Often, the system model obtained as a result of solving identification problem is not accurate enough or excessively complex. As a result, the solution to the identification problem is inextricably linked to ensuring sufficient accuracy and simplicity of the identified model. In this connection, it is natural to adhere to the principle of balanced identification, which indicates the search for a compromise between the accuracy of reproduction and the measure of complexity of the identified model. The purpose of this paper, which develops the concept of balanced identification, is to analyze the trade-off between the accuracy and complexity of models of dynamic systems identified by genetic programming. In this paper we introduce a functional "accuracy-complexity", which allows us to balance the trade-off between these key indicators of the identified models when solving the identification problem. The effectiveness of the proposed functional is demonstrated on the example of computer identification by genetic programming of a Lorentz dynamical system.

Bridging Continuous and Lattice-Based Models of Two-Dimensional Diffusion: A Systematic Approach for Estimating Transition Probabilities, Grid Size and Diffusivity

Lattice-based models have been broadly applied in mathematical and computational modeling of biological and biomedical systems for which spatial effects are important. These discrete models commonly include diffusion of mobile constituents as a key underlying mechanism. While the direct simulation of diffusion in continuous (off-lattice) domains is possible, it is computationally intensive, particularly when multiple coupled mechanisms are involved. This study presents a systematic approach for connecting continuous models of two-dimensional diffusion with internal obstacles to discrete, lattice-based (surrogate) models of diffusion. Results from continuous model simulations on a representative domain, and over many realizations, are used to develop accurate lattice-based surrogate models by exploiting internal symmetries. Probabilities determined for the lattice-based surrogate models are also connected to theoretical diffusivities for 2D random walks on a square lattice, necessitating the calibration of a spatial grid size. This approach can facilitate the inclusion of more accurate diffusive transport models of complex media within the general framework of lattice-based models that incorporate multiple coupled mechanisms.

Performance evaluation of standalone new solar energy system of hybrid PV/electrolyzer/fuel cell/MED-MVC with hydrogen production and storage for power and freshwater building demand

To achieve zero carbon emissions, increasing the scale of renewable energy implementation is imperative. Hydrogen is considered the prospective solution for sustainable energy due to its dual nature as a carbon-neutral fuel and an efficient storage medium for renewable energy sources. So, in this work, a standalone new hybrid energy system powered by solar energy for yearly power and freshwater production for building demand in New Borg El-Arab, Egypt. The system comprises photovoltaic (PV) panels, a water electrolyzer, multi-effect mechanical vapor compression desalination (MED-MVC), and fuel cells with hydrogen storage. A complete mathematical system model is built and solved by MATLAB/Simulink to study the daily, monthly, and yearly performance and sizing of the different system components based on the location climate conditions. The results indicate that PV panels of an area of 1824 m2, in conjunction with an electrolyzer, 863 fuel cells, and a storage tank capacity of 3013.4 m3can satisfy the annual building requirements of 255.17 MWh electricity, 766.5 m3 hot water and 876 m3 cold water. The maximum hydrogen storage lies between September and October, with maximum consumption between February and March. The average annual efficiency of PV, electrolyzer, fuel cell, electrolyzer output, fuel cell output, and overall hybrid system is 20.7%, 68.2%, 34.6%, 13.4%, 4.4%, and 16.5%, respectively, and the performance ratio (PR) of MED-MVC is 2.61. The system proves its capability to supply the building with electrical and water requirements with a levelized cost of energy (LCOE) equal to 0.712 $/kWh. Additionally, This system shows the potential to include other activities in remote areas or islands besides its contribution to achieving SDGs 6, 7, and 13.

Multi-objective optimization of solar-driven hollow fiber membrane dehumidification system based on MOPSO

The solar-driven hollow fiber membrane dehumidification (SHFMD) system is a renewable, energy-saving, and highly effective dehumidification system. It provides an effective solution to the problem of air-entrained liquid droplets during the traditional solution dehumidification process. The system's mathematical model was established and the reliability of the mathematical model was verified by experimental data. To enhance the comprehensive performance of the system, the multi-objective particle swarm optimization (MOPSO) algorithm is used in this paper to optimize the multi-objective parameters of the system. The objective function is the total exergy destruction of the system and the dehumidification capacity of the system. The optimization variables are cold water temperature, cold water flow rate, solution flow rate, air flow rate, and hot water flow rate. The optimization is performed using the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the Pareto front, and the points of the Pareto front are normalized. Finally, the optimal trade-off point of the Pareto frontier is obtained. Each operating parameter of the optimal point of the Pareto front is also analyzed. The results show that the air flow rate and cold water flow rate have the most influence on the conflict between the total exergy destruction of the system and the dehumidification capacity of the system.

Heat transfer characteristics of topological latent heat storage systems based on optimization objectives

In order to improve the heat storage efficiency and shorten the heat storage/release time in latent heat storage (LHS) systems, topology optimization of heat transfer problems has been applied to LHS systems. The choice of the optimization objective determines the structure of the topology fins. In this paper, the topology generation process was analyzed using the mean temperature, the mean square deviation (MSD) of the mean temperature, and the multi-objective entropy depletion as the optimization objectives. In this way, a method for selecting the optimization objectives according to the design requirements was obtained. The multi-objective topological structure (Case 3) with uniform tree-shaped fins (Case 4) and gradient tree-shaped fins (Case 5) was applied to the LHS system, and the finite element analysis method was used to construct a mathematical model of the LHS system to comprehensively analyze the heat storage/release process. The results showed that the complete melting times for Case 3, Case 4, and Case 5 were 751 s, 1005 s, and 920 s, respectively. At 751 s, the average heat storage capacities for Case 3, Case 4, and Case 5 are 296.81 W, 216.94 W, and 238.92 W, respectively. Compared to Case 4, Case 3 decreased the complete melting time by 25.27 % and increased the average heat storage capacity by 36.82 %. At heat-releasing times of 500 s, 1000 s, 1500 s, and 2000 s, the maximum differences in liquid phase rates for the three models were 10.93 %, 11.97 %, 11.51 %, and 9.57 %, respectively. From the perspective of the field synergy, Case 3 showed a better heat transfer path and the optimal heat transfer effect considering the temperature, liquid phase rate, heat storage/release time, and heat storage/release capacity. In addition, the dimensionless criterion equation affecting the liquid phase rate was obtained by segmented fitting of the heat transfer process of the topology-optimized LHS system. The findings of the study can facilitate the promotion of topology-optimized structures for practical engineering applications in LHS systems.

An Optimized Artificial Neural Network Model of a Limaçon-to-Circular Gas Expander with an Inlet Valve

In this work, an artificial neural network (ANN)-based model is proposed to describe the input–output relationships in a Limaçon-To-Circular (L2C) gas expander with an inlet valve. The L2C gas expander is a type of energy converter that has great potential to be used in organic Rankine cycle (ORC)-based small-scale power plants. The proposed model predicts the different performance indices of a limaçon gas expander for different input pressures, rotor velocities, and valve cutoff angles. A network model is constructed and optimized for different model parameters to achieve the best prediction performance compared to the classic mathematical model of the system. An overall normalized mean square error of 0.0014, coefficient of determination (R2) of 0.98, and mean average error of 0.0114 are reported. This implies that the surrogate model can effectively mimic the actual model with high precision. The model performance is also compared to a linear interpolation (LI) method. It is found that the proposed ANN model predictions are about 96.53% accurate for a given error threshold, compared to about 91.46% accuracy of the LI method. Thus the proposed model can effectively predict different output parameters of a limaçon gas expander such as energy, filling factor, isentropic efficiency, and mass flow for different operating conditions. Of note, the model is only trained by a set of input and target values; thus, the performance of the model is not affected by the internal complex mathematical models of the overall valved-expander system. This neural network-based approach is highly suitable for optimization, as the alternative iterative analysis of the complex analytical model is time-consuming and requires higher computational resources. A similar modeling approach with some modifications could also be utilized to design controllers for these types of systems that are difficult to model mathematically.

Investigation on a novel hybrid system based on radiative sky cooling and split thermoelectric cooler driven by photovoltaic cell

This paper develops a novel cooling and heating system by integrating a novel split thermoelectric cooler (STEC) with photovoltaic power generation and radiative sky cooling. The system uses photovoltaic driven STEC modules to generate cooling and heating combined with radiative sky cooling to improve cooling capacity. By harnessing the distinctive characteristics of photovoltaic technology and radiative sky cooling, the new system is capable of operating continuously for 24 h without requiring any additional energy input. The system mathematical model is established, and the effects of STEC module number, solar illumination intensity, area ratio and ambient temperature on the performance are studied. Results demonstrate that the cooling efficiency of the system is 3.02 and the heating efficiency is 1.86 when the number of STEC modules is 3. In a year, the monthly average heat production of the system fluctuates due to changes in the solar illumination intensity, while the fluctuation of cooling capacity is small. The system cold production is larger than heat production, which is more suitable for application in the area with high demand for year-round refrigeration. The new system has good energy and economic performance with payback time being shorter than that of the photovoltaic-air conditioning system.

Towards sustainable smart cities: Integration of home energy management system for efficient energy utilization

Smart Homes (SHs) play a crucial role in the broader context of smart cities, contributing to the overall efficiency, sustainability, and quality of life for residents. This work presents a computationally efficient mathematical model for Home Energy Management Systems (HEMS) to activate the Demand Side Management (DSM) while minimizing the energy consumption costs of SHs. The proposed model is represented as a standard Mixed-Integer Linear Programming (MILP) optimization problem. The proposed HEMS provides the optimal scheduling of home appliances and plugging time for charging Electric Vehicles (EV) at home. The main objective of this optimization problem is to minimize the electricity bills while improving the load profile of the distribution system in the context of smart cities. In this study, load management for a typical household has been studied considering several electricity tariffs in Portugal. The simulation results confirm that in the presence of the proposed HEMS, the electricity bill will be effectively reduced while consumer behavior is changed. The cost savings that can be attained through only shifting loads is 5.7 %, while it can reach 67.65 % by installing a hybrid energy system at the studied smart home. The weekly cost reduction percentage due to charging the EV at home is around 16.24 % compared to charging the EV using public charging stations regardless of the traveling time and waiting at the public charging stations.

The Groundwater Management in the Mexico Megacity Peri-Urban Interface

Megacities boost peri-urban socioeconomic development but fulfill their high natural resource demands by overexploitation, yielding irreversible environmental damage in surroundings that turn into sacrifice zones. This study reports the effects on the Cuautitlán-Pachuca Valley, the Mexico City main expansion zone at the northeast of the metropolitan area on the Central Mexico plateau, the trend scenarios from 2020 to 2050, and the actions to mitigate the growing water demand that will worsen its aquifer overexploitation. We designed a conceptual archetype to apply the Water Evaluation and Planning System (W.E.A.P.) mathematical model calibrated with 2013–2014 data to calculate groundwater volume demand in future scenarios. The demand output for the international airport and agriculture was less than 5%. The local climate change effect up to 2050 will slightly reduce the infiltration. The most crucial water demand increase (195% in 2050) is due to the population and industrial growth of the Mexico City northern municipalities (89% of the total groundwater extraction volume), and the aquifer will have a notable −2192.3 hm3 accumulated deficit in 2050, while urban sprawl will decrease water infiltration by 2.3%. Mitigation scenarios such as rainwater harvesting may reduce the urban water supply only by 9%, and a leak cutback will do so by 24%, which is still insufficient to achieve sustainable water management in the future. These outcomes emphasize the need to consider other actions, such as importing water from near aquifers and treating wastewater reuse to meet the future water demand.

MATHEMATICAL MODELING OF THE AUTONOMOUS HEAT SUPPLY SYSTEM WITH TUBULAR GAS HEATERS IN BUILDING STRUCTURES WHEN OPERATING IN THE CONDENSATION MODE

Problem statement. The application of modern autonomous heat supply systems is one of the directions of reducing the consumption of natural energy resources. There are many different autonomous systems of heat supply of objects. One of the variants of such systems is the system with tubе gas heaters. A tube gas heater consists of a gas burner, a radiating tube and a fan. One of the technical solutions for such heat supply systems is a tubular heater located inside the building structure. Increase of the efficiency of gas equipment can be achieved by operating this equipment in the condensation mode. Therefore, the operation of tubular gas heaters in building structures in the condensation mode is quite interesting in terms of increasing the efficiency of utilisation of the thermal potential of gaseous fuel and ensuring its saving. For research and practical design of autonomous heat supply systems with gas tube heaters in building structures with regard to the condensation mode of operation it is essential to develop a mathematical model for calculating the thermal and hydraulic modes of the system. The purpose of the article is to develop a mathematical model of an autonomous heat supply system with tubular gas heaters in building structures when operating in the condensation mode. Conclusion. The mathematical model of hydraulic and thermal modes of autonomous heat supply system with tubular gas heaters in building structures when operating in the condensation mode was developed. It is presented in the form of differential equations. The model is based on the equations of conservation of mass, motion and energy for the gas-air mixture inside the canal in two-phase flow, the equation of heat transfer inside the building structure, the equation of heat transfer from the external surface of the heater to the environment. The mathematical model of hydraulic and thermal modes of autonomous heat supply system with tubular gas heaters in building structures when operating in the condensation mode will be used to calculate and design such systems.

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Real time adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural network proportional-integral-derivative controller for nonlinear systems

This paper presents an adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural PID controller for handling the problems of uncertainties in nonlinear systems. The proposed controller combines probabilistic processing with a Takagi-Sugeno-Kang fuzzy neural system to proficiently address stochastic uncertainties in controlled systems. The stability of the controlled system is ensured through the utilization of Lyapunov function to adjust the controller parameters. By tuning the probability parameters of the controller design, an additional level of control is achieved, leading to enhance the controller performance. Furthermore, it can operate without relying on the system's mathematical model. The proposed control approach is employed in nonlinear dynamical plants and compared to other existing controllers to validate its applicability in engineering domains. Simulation and experimental investigations demonstrate that the proposed controller surpasses alternative controllers in effectively managing external disturbances, random noise, and a broad spectrum of system uncertainties.

Оценка пространственного распределения зон локализации риска развития бронхо-легочной патологии на основе математического моделирования воздушно-пылевых потоков в дыхательных путях и легких человека

The article continues the series of studies that describe a mathematical model of the respiratory system developed by the authors and dwell on its use in practice to assess and predict risks for human health caused by negative effects of airborne environmental factors. The mathematical model includes several submodels that describe how an air mixture flows in the air-conducting zone (it includes the nasal cavity, pharynx, larynx, trachea and five generations of bronchi) and the lungs approximated with a continuous two-phase elastically deformed porous medium. The mathematical model is described by using continuum mechanics relationships. It is realized numerically by using engineering software (to investigate processes in the airways) and a self-developed set of programs (to simulate processes in the lungs). Numeric modeling of a non-stationary flow of an air-dust mixture is performed for a personalized three-dimensional geometry of the human respiratory system based on CT-scans. The study provides calculated lines of velocity for a flow of particles in inhaled air in the airways. We have quantified shares of deposited articles with their diameters being 10 µm, 2.5 µm, and 1 µm (РМ10, РМ2,5, РМ1) in the airways; the study also provides trajectories of particulate matter. As particles become smaller and lighter, the share of deposited ones goes down in the airways and grows in the lungs. According to numeric modeling, most (more than 95 %) large particles (PM10) are deposited in the nasal cavity, pharynx and larynx; small particles are able to reach the lower airways and bronchi (most particles that reach the lungs penetrate lobar bronchi predominantly in the right lung). Sites with maximum health risks in the human lungs have been identified relying on assessing changes in an air phase mass within the respiration cycle; they are located in lower lobes of the lungs. When contacting airway walls, particles are able to be deposited and accumulate over time producing irritating, toxic and fibrogenic effects; they can thus cause and / or exacerbate pathological states.

Assessing spatial distribution of sites with a risk of developing bronchopulmonary pathology based on mathematical modeling of air-dust flows in the human airways and lungs

The article continues the series of studies that describe a mathematical model of the respiratory system developed by the authors and dwell on its use in practice to assess and predict risks for human health caused by negative effects of airborne environmental factors. The mathematical model includes several submodels that describe how an air mixture flows in the air-conducting zone (it includes the nasal cavity, pharynx, larynx, trachea and five generations of bronchi) and the lungs approximated with a continuous two-phase elastically deformed porous medium. The mathematical model is described by using continuum mechanics relationships. It is realized numerically by using engineering software (to investigate processes in the airways) and a self-developed set of programs (to simulate processes in the lungs). Numeric modeling of a non-stationary flow of an air-dust mixture is performed for a personalized three-dimensional geometry of the human respiratory system based on CT-scans. The study provides calculated lines of velocity for a flow of particles in inhaled air in the airways. We have quantified shares of deposited articles with their diameters being 10 µm, 2.5 µm, and 1 µm (РМ10, РМ2,5, РМ1) in the airways; the study also provides trajectories of particulate matter. As particles become smaller and lighter, the share of deposited ones goes down in the airways and grows in the lungs. According to numeric modeling, most (more than 95 %) large particles (PM10) are deposited in the nasal cavity, pharynx and larynx; small particles are able to reach the lower airways and bronchi (most particles that reach the lungs penetrate lobar bronchi predominantly in the right lung). Sites with maximum health risks in the human lungs have been identified relying on assessing changes in an air phase mass within the respiration cycle; they are located in lower lobes of the lungs. When contacting airway walls, particles are able to be deposited and accumulate over time producing irritating, toxic and fibrogenic effects; they can thus cause and / or exacerbate pathological states.