Mathematical Model Of System Research Articles

Modelling and Testing the Dynamic Properties in a Submachine Gun-Man System

This work was an attempt at an analysis of the interaction between a firearm and a human, exemplified by a cal. 9 mm submachine gun (SMG), PM-98 GLAUBERYT and a trained, professional shooter - a Police special team operator. The results of the analysis made it possible to develop several guidelines aimed at designing the dynamic performance of SMGs to improve their aiming accuracy. In connection with this work, experimental tests were performed at a firing range, where the process of firearm discharge was recorded using a Phantom slow-motion digital camera. What followed was the analysis of the video record using the Tema dedicated computer software. The SMG’s dynamic performance was adjusted to reduce the hit scatter. Based on the results of the empirical tests at the firing range, physical and mathematical models of the SMG-operator system were formulated. The SMG-operator system was simulated in the Scilab software, which provided time-based variation trends of the kinematic quantities that characterised the movements of individual modelled objects. The variation trends determined included displacement, velocity and acceleration of the SMG, its bolt assembly, and the human operator as a function of time. The results of the theoretical analysis were compared to the empirical test results from the firing range. It was found that in the virtual modelling space, the SMG model had a performance similar to that of its real counterpart. With the theoretical model verified, several performance parameters of the SMG were modified and guidelines were developed that could improve the aim.

Efficient parameter generation for constrained models using MCMC

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model’s parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

Protection Design and Effectiveness Verification of High-temperature Fire for Civil Aviation Emergency Locator Transmitter

Considering the coupling between the heat of emergency locator transmitter and the external high-temperature fire environment, a thermal protection system for external insulation and internal heat absorption is proposed. The external insulation layer consists of flexible nanofiber heat insulation film and quartz ceramics to withstand the thermal impact of the external environment. The internal heat absorption layer is composed of microcapsulated paraffin, which is used to absorb the heat transmitted through the insulation layer and the heat generated by emergency locator transmitter. Using the enthalpy method to establish a transient heat transfer mathematical model of thermal protection system, and the protection performance of the system in high-temperature fire is analyzed. The calculation results show that the system can withstand a high-temperature fire for at least 15 minutes, during which the temperature of emergency locator transmitter is controlled below 60℃. After the fire is over, under the coupling of the waste heat of the incoming system and the heat of emergency locator transmitter, the temperature of emergency locator transmitter continues to rise to a maximum of 107℃. Then, as the influence of the waste heat of the incoming system weakens, the temperature of emergency locator transmitter gradually decreases. Finally, the accuracy of the simulation model and the effectiveness of the thermal protection system are verified through destructive experiments.

To the question of the description of the internal combustion engine in the mathematical model of the lifting system of the hovercraft (on the example of the ZMZ-51432.10 CRS engine)

Introduction. It is known that about one third of the total capacity of the power plant of the hovercraft (SVP) is spent on the creation of an air cushion that ensures the rise of the main hull of the vessel. At the same time, in SVP, the source of mechanical energy, as a rule, is a diesel internal combustion engine (ICE). This article discusses one of the issues related to the creation of a mathematical model of the lifting system of the SVP, using: ICE, hydraulic transmission, axial fans and an air cushion nozzle scheme. Since in the vast majority of cases, the internal combustion engine performs its work in partial load modes, it becomes necessary to effectively control the power of the internal combustion engine in order to achieve its high efficiency in partial load modes.
 AIMS. The purpose of this study is to develop a mathematical description of the operation of the internal combustion engine both in external and partial modes of operation, for use in a mathematical model of the operation of the lifting system of the SVP.
 Methods. In this study, a ZMZ-51432.10 CRS diesel engine is used for the lifting system of the hovercraft.
 Results. Using the data obtained using the DIESEL-RK program for this ICE, in the Microsoft Excel environment, the corresponding trend lines were obtained for them by approximating the points that identify the partial characteristics of the engine with fourth-order polynomials, as well as the dependence of the coefficients of these polynomials on the control parameter of the ICE operation mode .
 Conclusion. The developed mathematical description of engine operation can be integrated with various load models when simulating real systems using internal combustion engines as energy sources. This means that it can also be used in mathematical modeling of the SVP lifting system in the MATLAB Simulink package.The approach proposed in this article makes it possible to build mathematical models of various systems using internal combustion engines, simplifying the study and saving computational time. Also, the results obtained can be of reference value.

Vibration Control of Marine Flexible Riser with Uncertain Model

When flexible risers in the ocean are subjected to various environmental loads in the ocean, vibration will inevitably occur. Due to the nonlinearity and uncertainty of the actual riser system, it is impossible to obtain an accurate mathematical model of the riser system. The existing control algorithms designed based on the precise model of the riser system cannot meet the actual control requirements. A flexible riser boundary control method based on fuzzy control algorithm is proposed to suppress the vibration of marine flexible riser systems with uncertain models. Firstly, the dynamic models of existing marine flexible risers were studied. In response to the uncertainty of the riser system model, the control experience was transformed into an automatic control strategy in the form of fuzzy language control rules to improve the adaptability of the controller. Then, combining boundary control technology with fuzzy control, a boundary controller is constructed to stabilize the riser in a small neighborhood of its original position and reduce fatigue damage to the riser. Finally, the effectiveness of the designed fuzzy boundary control algorithm was verified through MATLAB simulation results, and the vibration suppression effect of the algorithm on the vertical tube was better than that of traditional PD control.

Mathematical Description of Systems for Space Stabilization of Equipment Assigned for Operation on Moving Vehicles

The article deals with the development of mathematical description of systems for stabilization of measurement and observation equipment assigned for operation at moving vehicles of the wide class such as land, marine, and air moving vehicles. Mathematical descriptions of one-axis, two-axis, and three-axis stabilization systems are represented including kinematical relations and dynamics models. The general mathematical descriptions and the appropriate models in the space of states are given. The basic approaches to linearization of the generalized models are represented. The sets of turns in the inertial space for two-axial and three-axial stabilizations systems are represented. The obtained mathematical model for one-axis stabilization system has been used for the robust structural synthesis of the system assigned for stabilization of the observation equipment mounted at the land moving vehicles. The obtained results can be spread on moving vehicles of the different type.

An Approach to Robust Control of Aircraft Motion

The article deals with approaches to designing aircraft control systems based on the robust synthesis. The mathematical model of the aircraft control system both for deterministic and stochastic cases is considered. The Dryden filter models are represented. The state-space conception is applied. The concept of robust designing based on H-infinity synthesis, function of the mixed sensitivity, and loop shaping is represented. The features of Robust Control Toolbox necessary for automated designing of aircraft control systems are studied. The weighting transfer functions are proposed. Results of simulation of the synthesized robust control system are shown in the form of transient processes in lateral and longitudinal motions. The proposed approach is directed on providing the possibility of the aircraft to function in conditions of influence of disturbances. The possible applications of obtained results is control of aircraft motion in civil aviation.

Моделирование динамических режимов работы электроприводов с системой векторного управления синхронным двигателем

Purpose: The purpose of the work is a comparative assessment of dynamic processes in electric drives with a vector control system for permanent magnets synchronous motors and various methods of stator voltage modulation. To achieve this purpose, a mathematical description of a synchronous motor in a rotating dq coordinate system is given, and a mathematical model of a vector control system is developed. The model of the vector control system takes into account the decoupling of stator current control loops and proposes two options for generating a current reference along the d-axis, ensuring the efficiency of energy conversion processes at rotation speeds below the nominal value, depending on the design of the motor rotor. Algorithms for scalar pulse-width and space-vector modulation of motor stator voltage for a frequency converter with a two-level autonomous voltage inverter are presented. Methods: When developing mathematical models and algorithms, methods from the theory of electric drive and the theory of automatic control have been used. The developed mathematical models and algorithms are implemented in the Matlab Simulink software package. Results: The results of modeling dynamic processes in electric drives (mechanical characteristics, stator currents, stator current total harmonic distortion) are presented, which have shown the performance of the developed models and algorithms. Practical significance: The choice of modulation type does not affect the mechanical characteristics of the electric drive, but does affect the harmonic composition of the stator current. The greatest effect from the use of space-vector modulation algorithms is manifested at reduced values of the frequency of the stator current and partial load torque on the rotor shaft.

Modeling and analysis for group delay mismatch effect on wideband adaptive spatial interference cancellation

The adaptive interference cancellation technique has been widely utilized in radar, GPS, data link, etc., systems to address challenges from external interference, such as co-site and hostile interference. Since the anti-jamming performance of the adaptive interference cancellation technique is sensitive to group delay mismatch between channels, the group delay mismatch becomes one of the main factors that limit the system’s anti-jamming capability. However, the traditional adaptive interference cancellation system’s mathematical model cannot quantitatively characterize the group delay mismatch effect on the wideband interference cancellation performance. In this paper, the mathematical model of the wideband adaptive spatial interference cancellation (ASIC) system is established, which considers the group delay mismatch, to quantitatively analyze the impact of group delay mismatch on the hostile interference cancellation. The mathematical model utilizes the weighted multi-tone signals to fit the wideband interference, and then, delay differences are attached to each tone signal to simulate the group delay mismatch. Then, the analytic expressions of weight and interference cancellation ratio are derived, which consider the interference bandwidth and group delay mismatch, to quantitatively analyze the group delay mismatch effect on the anti-jamming performance of the wideband ASIC system. Simulation results indicate that the theoretical analysis based on the mathematical model of wideband ASIC system are accurate, which can achieve the quantitative analysis of the group delay mismatch effect on the WIC performance.

Numerical Simulation of Chemical Propulsion Systems: Survey and Fundamental Mathematical Modeling Approach

This study deals with the mathematical modeling and numerical simulation of chemical propulsion systems (CPSs). For this, we investigate and summarize a comprehensive collection of the simulation modeling developments of CPSs in academic works, applications, and industrial fields. Then, we organize and analyze the simulation modeling approaches in several ways. After that, we organize differential-algebraic Equations (DAEs) for fundamental mathematical modeling consisting of the governing Equations (ordinary differential equations, ODEs) for the components and other equations derived from several physical rules or characteristics (algebraic equations or phenomenological equations, AEs) and then synthesize and summarize the fundamental structures of analytic mathematical modeling by types (liquid-propellant rocket engines, solid-propellant rocket motors, and hybrid-propellant rocket motors) of CPSs.

An adaptive impedance control method for polishing system of an optical mirror processing robot

AbstractTo solve the constant contact force control problem between the end tool of a 5 degrees of freedom hybrid optical mirror processing robot and a workpiece, an adaptive impedance control method for the pneumatic servo-polishing system of the robot is designed. Firstly, the pneumatic servo-polishing control system at the end of the robot is set up. Secondly, the impedance control method for contact force is investigated based on the mathematical model of the pneumatic servo-polishing control system. Additionally, the causes of steady-state error of impedance control are analyzed theoretically, and the calculation method for steady-state error of impedance control is deduced. Finally, an indirect adaptive impedance controller based on Lyapunov Stability Principle is developed to estimate the environmental stiffness and position online, so as to reduce steady-state error and realize the tracking of polishing contact force. The simulation and experimental results suggest that the adaptive impedance control method not only recognizes that the contact force of the robot is relatively constant during the polishing process but also has high control accuracy for the force, fast-tracking response for the abrupt force, and considerable adaptability to the variable environmental stiffness.

Fuzzy control of temperature in gas flow control system based on mixed cold and hot gases

This study proposes a novel high-temperature gas flow temperature simulation system based on the mixing of cold and hot gas flow. The outlet gas flow temperature is controlled by adjusting the flow rate of the cold gas flow. To achieve consistent control of high-precision and wide-range temperature control of the system. The system mathematical model was constructed and the system characteristics were analyzed. However, traditional PID control suffers from inconsistencies in control performance at high and low temperatures, as well as inconsistent responses during temperature increasing and decreasing processes. To address these issues, fuzzy PID control was introduced, but its parameter tuning proved challenging, resulting in poor consistency of control performance. To expand the adaptability of fuzzy control, a function-based and fuzzy inference-based variable universe fuzzy PID controller was proposed. Experimental and simulation results demonstrate that the fuzzy inference-based variable universe fuzzy PID controller exhibits good dynamic and static performance under different operating conditions. The max settling time and static error are 16.5 s and ± 4 K, respectively. Compared with PID controller, the settling time and static error are reduced by 56.2% and 67.5% respectively. The fuzzy inference-based variable universe fuzzy PID controller overcomes the performance discrepancies during temperature increasing and decreasing processes, different operate temperatures, and various step amplitudes. Consequently, highly accurate simulation of system outlet gas flow temperature is realized. This methodology can be widely applied to control systems with strong nonlinearity and asymmetry, improving the consistency of the system control performance.

Vibroconverter mathematical model based on the levitation effect

Modern requirements for the safe operation of nuclear power plants dictate the need to introduce systems for early reactor plants state diagnosis. Vibrations have always been a threat to the safe nuclear power plants operation, therefore, solving the issues of improving the nuclear power plants vibronoise diagnostics accuracy, especially in the field of ultra-low frequencies, is an urgent task. The most promising way to solve the problem of flexible guides in electromechanical vibration transducers is the levitation effect, which makes it possible to completely eliminate mechanical contact and, accordingly, reduce the sensitivity threshold of the transducer. The article presents an analysis of existing vibration transducers and offers analogue and digital mathematical models of the magnetic levitation system, taking into account the influence of the electromagnetic force nonlinearity. The characteristics of such a nonlinear system are studied using the method of harmonic linearization, which makes it possible to obtain an equivalent linear system. At the same time, the third order terms of the electromagnetic force expansion in the Taylor series are taken into account, which made it possible to obtain a more accurate analogue the vibration transducer model. For the developed vibration transducer digital model, using the z-form method, a system function and the corresponding difference equation were obtained. Expressions and graphs of transient, pulse and frequency characteristics are derived for both analogue and digital vibration converter models, which allow us to conclude about the accuracy and adequacy of the developed digital model. Using obtained vibration transducer digital models will make it easier to model its operation and reasonably select the vibration transducer initial parameters.

Simulation-Based Model-Updating Method for Linear Dynamic Structural Systems

The dynamic characteristics of buildings and their behavior under various dynamic loads play a crucial role in civil engineering applications, particularly for earthquake-resistant structural design. Employing a precise mathematical model of the structural system makes it possible to accurately predict the actual structural performance under dynamic loads, such as winds and earthquakes. Given this perspective, finite element model-updating approaches in structural systems have gained significant attention in recent decades. This paper proposes a simulation-based model-updating technique that utilizes measured free vibration responses to the correct structural parameters of multi-degree-of-freedom systems. A five-degree-of-freedom building model is subjected to shaking table tests to demonstrate the effectiveness of the proposed method. The experimental data for this method consists of the dynamic behavior of the system under the seismic excitation of the El Centro 1940 earthquake and the results of the free vibration tests. The MATLAB/Simulink parameter estimation tool is employed to establish a correlation between the analytical model and the measured dynamic response from the building model. Compared to the measured structural responses, the updated analytical model, which incorporates the proposed simulation-based model-updating technique, demonstrates high accuracy in predicting the responses through effective corrections of stiffness and damping coefficients.

Stability and passivity analysis of higher‐order differential systems inspired by RLC circuits

SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's linearization method. The relationship between stability and passivity is also given. Meanwhile, we realized that linear system analysis is not a guaranteed way for determining the stability properties of a full system. Finally, the correctness and availability of the proposed approach are verified through simulation results.

Operational characteristics of the super-long gravity heat pipe for geothermal energy exploitation

As a novel geothermal heat transfer technology, the super-long gravity heat pipe (SLGHP) demonstrates great potential for the efficient exploitation of deep geothermal energy. Despite the rapid advances made to the SLGHP technology, its operational characteristics remain to be fully investigated. In this study, the underlying phenomenological mechanisms of the SLGHP are compared with those of normal-size gravity heat pipes (NSGHPs), and the operational characteristics of the SLGHP are analyzed in view of its distinctive geometric features. It is noted that the thermal resistance caused by the vapor flow is negligible in the NSGHPs, while it dominates the overall thermal resistance of the SLGHP. The dominance of the vapor flow thermal resistance allows making the one-dimensional simplification (along the pipe length direction) in the mathematical model of the SLGHP geothermal energy extraction system. Under these circumstances, the temperature gradient along the SLGHP length can be theoretically deduced based on the pressure drop of vapor flow. Close observation of the temperature gradient expression indicates that the desirable SLGHP working fluid should have the following properties: i) large latent heat of vaporization, and ii) a strong dependence of the saturated vapor pressure on the temperature. In cases where the saturated vapor pressure of the working fluid is highly dependent on the temperature, as in the case of ammonia, the working temperature profile of the SLGHP can be formulated as a linear function of the depth. This unique working temperature characteristic offers valuable guidance to determine the length of the SLGHP adiabatic section in practical geothermal applications. The on-site observed operational characteristics provide the necessary theoretical foundation for modeling the multiphase heat transfer process in SLGHP, which will lead to a valuable engineering analysis and design tool supporting the application and commercialization of the SLGHP technology.

Modeling method of a class of 5D Hamiltonian conservative hyperchaotic systems with adjustable signal amplitude

Compared to dissipative chaotic systems, conservative chaotic systems have gained attention because they can avoid reconstruction attacks due to the absence of attractors. This paper reports a general method for constructing 5D Hamiltonian conservative hyperchaotic systems, mainly by coupling three 5D sub-rigid bodies with two identical axes to obtain 5D Euler equations, and then combining Hamiltonian energy and Casimir energy analysis to obtain a 5D conservative hyperchaotic system. This method is general and convenient, and the constructed conservative hyperchaotic system has good performance. In addition, this paper investigates the impact of parameters and initial values on system performance using energy analysis and proposes a simple signal amplitude adjustment method. This method has no restrictions on the mathematical models of chaotic systems, can quickly adjust signal amplitudes, and enhances the hyperchaotic characteristics of the system based on this method. Finally, the correctness of the theoretical and simulation analysis is verified using a DSP hardware platform.

Experimental and numerical study of an energy-efficient building fenestration system with seasonal adaptability

Previous building-integrated solar thermal fenestrations were limited to the single function, either air heating or water heating. Thus, they failed to meet the seasonal thermal needs of buildings. To address this limitation, this paper proposed a novel building fenestration-integrated solar collector. This system is designed to harness solar irradiation on the fenestrations for air heating in winter and recover irradiation for water heating in summer, effectively addressing seasonal thermal demands and improving annual solar utilization efficiency. Firstly, the prototype of the proposed system was fabricated, and its thermal performance was tested. The experimental results indicated the thermal efficiency of 40∼50% for air heating and 39% for water heating. Subsequently, a mathematical model of the proposed system was developed and experimentally validated. Based on the validated model, a comparative performance analysis was conducted between the proposed system and double clear glazing. Additionally, the energy-saving potential and economic viability of the proposed system were predicted. Compared to double clear glazing, the proposed system exhibited a higher solar heat gain coefficient (SHGC) in air heating mode, lower SHGC in water heating mode, and lower U value at night. The prediction outcomes underscored the substantial energy-saving advantages conferred by the proposed system across diverse building types. The projected payback periods in subtropical and tropical regions were estimated to be around 2–4 years.

Uncovering specific mechanisms across cell types in dynamical models.

Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements.

Control synthesis via Impedance-Matching in panchromatic conditions: a generalised framework for moored systems

This study focuses on addressing the challenge of integrating the tangled mathematical model of the mooring system into an effective control synthesis. The presented synthesis framework utilises the impedance-matching technique to achieve the desired controller performance by adapting the control parameters to align with the dynamic characteristics of the moored wave energy device. By leveraging this technique, the simulation framework provides a means to effectively incorporate the intricate mooring dynamics into the control synthesis process. Furthermore, this paper aims to delve into the concept of defining a representative control action by examining the input-exciting force of the feedback-controlled system. Through a straightforward case study, the authors demonstrate the significant impact of the mooring on the system dynamics and underscore the applicability of the proposed simulation framework. Moreover, the paper verifies the importance of considering the controlled system’s exciting input when addressing control synthesis, particularly in panchromatic conditions.