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Journal articles on the topic 'Linearization of the mathematical model'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Miková, Lubica. "LINEARIZATION OF A NONLINEAR VEHICLE MODEL." TECHNICAL SCIENCES AND TECHNOLOGIES, no. 2(24) (2021): 33–37. http://dx.doi.org/10.25140/2411-5363-2021-2(24)-33-37.

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The purpose of this article is to create a mathematical model of a vehicle using dynamic equations of motion and simulation of perturbations acting on a vehicle. It is assumed that the tire in the car model behaves linearly. Because the vehicle model is nonlinear, the model will need to be linearized in order to find the transfer function between the angle of rotation of the front wheel and the lateral position of the vehicle. For this purpose, simple dynamic models of the car were created, which reflect its lateral and longitudinal dynamics. These types of models are usually used with a linea

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2

Zhang, Shuhua, and Ronghu Chi. "Model-free adaptive PID control for nonlinear discrete-time systems." Transactions of the Institute of Measurement and Control 42, no. 10 (2020): 1797–807. http://dx.doi.org/10.1177/0142331219896649.

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This work explores a model-free adaptive PID (MFA-PID) control for nonlinear discrete-time systems with rigorous mathematical analysis under a data-driven framework. An improved compact form dynamic linearization (iCFDL) is proposed to transfer the original nonlinear system into an affined linear data model including a nonlinear residual term. Both a time-difference estimator and a gradient parameter estimator are designed to estimate the nonlinear residual uncertainties and the unknown parameters in the iCFDL model. Subsequently, a novel improved CFDL based MFA-PID (iCFDL-MFA-PID) control is

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3

Zhang, Bin, and Yung C. Shin. "A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems." Applied Sciences 11, no. 1 (2020): 62. http://dx.doi.org/10.3390/app11010062.

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A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy

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Jose, Julia Tholath, and Adhir Baran Chattopadhyay. "Mathematical Formulation of Feedback Linearizing Control of Doubly Fed Induction Generator Including Magnetic Saturation Effects." Mathematical Problems in Engineering 2020 (February 1, 2020): 1–10. http://dx.doi.org/10.1155/2020/3012406.

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This paper proposes a control methodology based on feedback linearization for a doubly fed induction generator (DFIG) incorporating the magnetic saturation. The feedback linearization algebraically converts a nonlinear system model into a linear model, allowing the use of linear control techniques. Feedback linearization control depends on the model of the system and is therefore sensitive to parameter variations. The doubly fed induction generator (DFIG) operating under the magnetic saturation conditions results in the nonlinear variation of magnetizing inductance, which affects the performan

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Wang, He Hua, Xiao He Liu, Ming Jie Ma, and Cheng Yang. "Feedback Linearization Control of Pmssm Based on Svpwm." Advanced Materials Research 591-593 (November 2012): 1655–58. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1655.

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In this paper, according to the AC permanent magnet synchronous servo motor of the laboratory, using appropriate method to deal with servo motor makes its physical model be established. The nonlinear dynamic mathematical model of permanent magnet synchronous servo motor is established on the basis of the physical model. Based on nonlinear dynamic mathematical model of the permanent magnet synchronous servo motor, and through the coordinate transformation and state feedback, the input-output linearization is realized and the system decoupling is achieved. According to the system's linear model,

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Liu, Xuan, Xiang Shi, Zhe Xu, and Ka Tian. "Mathematical Modelling for Wheeled Inverted Pendulum." Applied Mechanics and Materials 543-547 (March 2014): 1365–68. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1365.

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To control wheeled inverted pendulum is a good way to test all kinds of theories of control, On the basis of Newtonian mechanics and dynamic characteristics, the dynamical equation of DC motor, cart and pendulum is studied. Then the approximate linear model of wheeled inverted pendulum is concluded, which is based on the way of linearization of small Angle.

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Gavrus, Cristina, Nicolae-Valentin Ivan, and Gheorghe Oancea. "Machining Parameters Optimization Based on Objective Function Linearization." Mathematics 10, no. 5 (2022): 803. http://dx.doi.org/10.3390/math10050803.

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Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods are comparable and it is difficult to establish which method is the best. For machining parameters optimization, this paper proposes a novel, simple and efficient method, without additional costs related to new software packages. This approach is based on linear mat

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8

Xian, Yang Jin, Li Zhi Peng, and Chen Chao. "Study of a Four Rotor Aircraft Modeling." Applied Mechanics and Materials 494-495 (February 2014): 293–96. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.293.

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In order to design the four rotor aircraft attitude control system, take the hover state or low speed flight state as a benchmark, firstly, divide the aircraft model into linear motion model and the angular motion model and model it separately, the nonlinear mathematical model of aircraft can be obtained. And then use the small disturbance linearization principle to linear mathematical model for a simplified model. After substituting into the previous experimental data, the mathematical model which controller design needs is got.

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9

Guo, Qian, Tianhong Pan, Jinfeng Liu, and Shan Chen. "Explicit model predictive control of permanent magnet synchronous motors based on multi-point linearization." Transactions of the Institute of Measurement and Control 43, no. 12 (2021): 2872–81. http://dx.doi.org/10.1177/01423312211015120.

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Permanent magnet synchronous motors (PMSMs) have been broadly applied in servo-drive applications. It is necessary to improve the performance of PMSM. An explicit controller designed for PMSM based on multi-point linearization is proposed to reduce the linearized model error caused by different running status of PMSM. The mathematical model of PMSM system in the synchronous rotating frame and the problem formulation are introduced at first. Then, the preliminaries about explicit model predictive control (MPC) algorithm are presented in this article. Based on this, the multi-point linearization

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Zeng, Run Zhang, та Huang Qiu Zhu. "Mathematical Model and Control of Axial Hybrid Magnetic Bearings Based on α-th Order Inverse System Theory". Applied Mechanics and Materials 529 (червень 2014): 539–43. http://dx.doi.org/10.4028/www.scientific.net/amm.529.539.

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A linearization control research based on α-th order inverse system method has been developed for an axial hybrid magnetic bearing, which is a nonlinear system. The configuration of the axial hybrid magnetic bearing is briefly introduced, the working principle of the hybrid magnetic bearing is analyzed, and then the suction equations are set up. Based on expounding of α-th order inverse system method, and aiming at dynamics model of the axial hybrid magnetic bearing, the feasibility of linearization control is discussed in detail, the linearization control arithmetic based on α-th order invers

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11

Kulik, Anatoliy, Sergey Pasichnik, and Dmytro Sokol. "MODELING OF PHYSICAL PROCESSES OF ENERGY CONVERSION IN SMALL-SIZED VORTEX ENERGY SEPARATORS." Aerospace technic and technology, no. 1 (February 26, 2021): 20–30. http://dx.doi.org/10.32620/aktt.2021.1.03.

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The object of study in the article is the vortex effect of temperature separation in a rotating gas flow, which is realized in small-sized vortex energy separators. The subject matter is the models that describe the physical processes of energy conversion in small-sized vortex energy separators as objects of automatic control. The goal is to obtain models of a vortex energy separator reflecting its static and dynamic properties as an automatic control object. The tasks to be solved are: to develop a three-dimensional computer model of a small-sized vortex energy separator which will allow anal

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Yeremenko, O. I., and S. V. Subota. "Analytical modeling of the biomass briquetting process in a closed channel." Mehanization and electrification of agricultural, no. 13(112) (2021): 126–34. http://dx.doi.org/10.37204/0131-2189-2021-13-13.

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Annotation Purpose. Increasing the efficiency of biomass briquetting by developing, at the first stage, a graphic-analytical model of a shock-mechanical press with a closed matrix channel. Methods. Graphic-analytical modeling of impact pressing of biomass into briquettes in a closed channel of the matrix; linearization, according to which a non-linear function is replaced by a linear function; mathematical modeling, assumes the dependence of the degree of compaction of biomass on the magnitude of the shock load (impulse) and reveals the nonlinear nature of the resistance of biomass to shocks a

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13

Serbes, Sefer Arda, Tahsin Engin, Muaz Kemerli, Egemen Kayrakoğlu, and Ahmet Aydın. "The Fluid Behavior of a Non-Orifice TLCD under Harmonic Excitation: From Experiments to Analytical Solution." Buildings 14, no. 9 (2024): 2782. http://dx.doi.org/10.3390/buildings14092782.

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Tuned liquid column damper (TLCD) is a well-known liquid damper designed to absorb the vibration of structures used in many applications, such as high-story buildings, wind turbines, and offshore platforms, requiring an accurate mathematical determination of the liquid level to model the TLCD structure system motion. The mathematical model of a TLCD is a nonlinear ordinary differential equation, unlike the structure, due to the term containing a viscous damping coefficient, and cannot be solved analytically. In this study, the fluid behavior of a TLCD without an orifice, directly connected to

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14

Khadem Abbasi, Alireza, and Mohd Wazir Mustafa. "Mathematical Model and Stability Analysis of Inverter-Based Distributed Generator." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/195038.

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This paper presents a mathematical (small-signal) model of an electronically interfaced distributed generator (DG) by considering the effect of voltage and frequency variations of the prime source. Dynamic equations are found by linearization about an operating point. In this study, the dynamic of DC part of the interface is included in the model. The stability analysis shows with proper selection of system parameters; the system is stable during steady-state and dynamic situations, and oscillatory modes are well damped. The proposed model is useful to study stability analysis of a standalone

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15

Mohos, Ferenc Á., and Eszter Vozáry. "Evaluation of relaxation and creep curve by application of peleg linearization and prony series." Progress in Agricultural Engineering Sciences 14, no. 1 (2018): 61–75. http://dx.doi.org/10.1556/446.14.2018.1.3.

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In practice, there is a demand for quick characterization of rheological properties of food materials. The exact model calculation requires complex and long-term mathematical process. In this work, a simple, quick linearization method – the Peleg linearization – is discussed and is compared with the Prony series method. In the Peleg linearization only two constants are used, one of them gives the initial rate of relaxation or creep and the second one gives the equilibrium value of relaxing force or of creeping strain. The Prony series approach the relaxation and creep with the sum of two or mo

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16

Volosatov, A. A., and M. V. Ryabinin. "CORRECTION OF THE DYNAMIC CHARACTERISTICS OF THE PRESSURE REGULATOR OF APGN USING ALGEBRAIC STABILITY CRITERIA." Spravochnik. Inzhenernyi zhurnal, no. 335 (February 2025): 42–49. https://doi.org/10.14489/hb.2025.02.pp.042-049.

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The article presents a mathematical model of the system consisting of an axial piston pump, indirectacting pressure regulator and load. The transient process at change of load in the system is constructed. Linearization of the mathematical model of the system is carried out. The method of improving the quality of pressure regulator regulation based on algebraic stability criteria is described. The results of using the proposed method of regulator parameters correction are given.

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17

Trudonoshin, V. A., V. A. Ovchinnikov, and V. G. Fedoruk. "Modal Analysis Problem Solution for a Mathematical Model Formed by the Extended Nodal Method." Mathematics and Mathematical Modeling, no. 2 (May 30, 2021): 33. http://dx.doi.org/10.24108/mathm.0221.0000257.

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The article proposes an option for transforming a mathematical model of the object, formed by the extended nodal method in the time-domain solution for modal analysis. Since finding the eigenvalues and eigenvectors for systems of ordinary equations given in the Cauchy normal form is possible, calculations are presented that allow us to obtain a system of equations in the Cauchy normal form from a mathematical model in a differential-algebraic form through linearization. The extended nodal method contains derivatives of state variables in the vector of unknown, and the Jacobi matrix obtained

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18

Geng, Yue Feng, and Wu Wang. "Application of Feedback Linearization Control for Optimal Power Tracking with Energy in Wind Power Generation System." Advanced Materials Research 648 (January 2013): 293–96. http://dx.doi.org/10.4028/www.scientific.net/amr.648.293.

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Fluctuation, intermittence and uncertain are the characteristics of wind energy which cause wind energy output power fluctuation and influence the grid stability and power quality, it is hard to be controlled exactly by traditional controllers. The feedback linearization control was applied to wind power generation system (WPGS), which was to reduce the cost of wind energy conversion system and improve its performance. The WPGS model was constructed with mathematical models of aerodynamics subsystem, drive train subsystem and permanent magnetic synchronous generator (PMSG) subsystem. The feedb

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19

Ge, P., and M. Jouaneh. "Modeling of the Backlash Hysteresis Nonlinearity." Journal of Mechanical Design 120, no. 3 (1998): 408–13. http://dx.doi.org/10.1115/1.2829167.

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In this paper, the backlash hysteresis nonlinearity is examined, and a mathematical model based on the particular behavior of the backlash is developed. A geometrical interpretation of this model using switching operators is provided to facilitate an understanding of it. Simulation of output prediction of the backlash mechanism using an arbitrary input signal is performed to verify the correctness of the developed model. A linearization scheme based on the model is also developed to compensate for the backlash nonlinearity. The scheme was applied for tracking an arbitrary signal similar to tha

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20

Guechi, El-Hadi, Samir Bouzoualegh, Youcef Zennir, and Sašo Blažič. "MPC Control and LQ Optimal Control of A Two-Link Robot Arm: A Comparative Study." Machines 6, no. 3 (2018): 37. http://dx.doi.org/10.3390/machines6030037.

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This study examined the control of a planar two-link robot arm. The control approach design was based on the dynamic model of the robot. The mathematical model of the system was nonlinear, and thus a feedback linearization control was first proposed to obtain a linear system for which a model predictive control (MPC) was developed. The MPC control parameters were obtained analytically by minimizing a cost function. In addition, a simulation study was done comparing the proposed MPC control approach, the linear quadratic (LQ) control based on the same feedback linearization, and a control appro

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21

Zhu, Linhe, Gui Guan, and Zhengdi Zhang. "Mathematical analysis of information propagation model in complex networks." International Journal of Modern Physics B 34, no. 26 (2020): 2050240. http://dx.doi.org/10.1142/s0217979220502409.

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In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-s

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22

Stefanello, Michel Baptistella, Gervásio Annes Degrazia, Silvana Maldaner, et al. "DESENVOLVIMENTO DE UM MODELO MATEMÁTICO PARA DESCREVER A DISPERSÃO DE CONTAMINANTES EM SITUAÇÕES DE MEANDRO DO VENTO HORIZONTAL." Ciência e Natura 38 (July 20, 2016): 326. http://dx.doi.org/10.5902/2179460x20248.

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In this work it’s derived a mathematical model to describe the meandering contaminants dispersion in the planetary boundary layer. The model employs a heuristic functional form for the velocity autocorrelation function which describes the negatives lobes observed in meandering data. Furthermore, the model is derived from the linearization of the Langevin equation. The mathematical equations, that represent the longitudinal and lateral wind components describe the bi-dimensional pattern of the meandering flow and can be utilized to calculate the contaminant concentrations occurring in situation

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23

Zhou, Kai, Min Ai, Dongyang Sun, Ningzhi Jin, and Xiaogang Wu. "Field Weakening Operation Control Strategies of PMSM Based on Feedback Linearization." Energies 12, no. 23 (2019): 4526. http://dx.doi.org/10.3390/en12234526.

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Based on current research into the mathematical model of the permanent magnet synchronous motor (PMSM) and the feedback linearization theory, a control strategy established upon feedback linearization is proposed. The Lie differential operation is performed on the output variable to obtain the state feedback of the nonlinear system, and the dynamic characteristics of the original system are transformed into linear dynamic characteristics. A current controller based on the input–output feedback linearization algorithm is designed to realize the input–output linearization control of the PMSM. Th

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Bakhramov, Umarkhoja. "Development of a Mathematical Model of Stochastic Flow Distribution in Pipeline Engineering Networks." E3S Web of Conferences 477 (2024): 00063. http://dx.doi.org/10.1051/e3sconf/202447700063.

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The article discusses the developed methods for accounting for stochastic water consumption, as well as mathematical models for accounting for stochastic water consumption in water supply and distribution systems. Due to the fact that pipeline engineering networks are non-linear, we will first determine the conditions for their linearization, and then we will show the solution of the problem for the resulting linearized network. The objective of this work is to connect the parameters of the stochastic process of water consumption from the network.

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Zi, Nie, and Chen Ming. "Stability and Control Analysis on a Small-Scale Coaxial Helicopter with Bell-Hiller Stabilizer Bar." Applied Mechanics and Materials 340 (July 2013): 862–66. http://dx.doi.org/10.4028/www.scientific.net/amm.340.862.

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In the paper, we present a linearized mathematical model of a small scale coaxial helicopter with Bell-Hiller stabilizer bar, which is extracted from numerical linearization of a non-linear mathematical model with small perturbation theory. Stability and control derivatives calculated by numerical method are compared and analyzed for stability and control analysis on coaxial helicopters equipped with different type stabilizer bar. The study indicates that the coaxial helicopter with stabilizer bar fixed on the upper rotors has better capability on stability and control.

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Fnaiech, Mohamed Amine, Hazem Nounou, Mohamed Nounou, and Aniruddha Datta. "Intervention in Biological Phenomena via Feedback Linearization." Advances in Bioinformatics 2012 (November 6, 2012): 1–9. http://dx.doi.org/10.1155/2012/534810.

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The problems of modeling and intervention of biological phenomena have captured the interest of many researchers in the past few decades. The aim of the therapeutic intervention strategies is to move an undesirable state of a diseased network towards a more desirable one. Such an objective can be achieved by the application of drugs to act on some genes/metabolites that experience the undesirable behavior. For the purpose of design and analysis of intervention strategies, mathematical models that can capture the complex dynamics of the biological systems are needed. S-systems, which offer a go

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Chen, Anthony, Panatda Kasikitwiwat, and Zhaowang Ji. "Solving the Overlapping Problem in Route Choice with Paired Combinatorial Logit Model." Transportation Research Record: Journal of the Transportation Research Board 1857, no. 1 (2003): 65–73. http://dx.doi.org/10.3141/1857-08.

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Recently, there has been renewed interest in improving the logit-based route choice model because of the importance of the route choice model in intelligent transportation systems applications, particularly the applications of advanced traveler information systems. The paired combinatorial logit (PCL) model and its equivalent mathematical programming formulation for the route choice problem have been studied. An algorithm based on the partial linearization method is presented for solving the PCL stochastic user equilibrium problem. Detailed examples are provided to explain how this hierarchica

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28

Boyko, I., M. Petryk, M. Shynkaryk, and O. Petryk. "NONLINEAR MODEL OF THE THREE-COMPONENTS COMPETITIVE ADSORPTION USING LANGMUIR EQUILIBRIUM." Bukovinian Mathematical Journal 9, no. 1 (2021): 64–78. http://dx.doi.org/10.31861/bmj2021.01.06.

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A basis for the mathematical modeling of non-isothermal gas competitive adsorption in a porous solid using Langmuir equilibrium is given. High-performance analytical solutions of considered adsorption models based on the Heaviside operating method and Landau’s decom- position and linearization approach of Langmuir equilibrium by expanding into a convergent series in the temperature phase transition point are proposed. Numerical experiments results based on high-speed computations on multicore computers are presented.

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29

Cheng, Ruo Fa, and Li Hu Chen. "Maximum Wind Power Tracking Control Based on PID and Feedback Linearization." Advanced Materials Research 1055 (November 2014): 358–62. http://dx.doi.org/10.4028/www.scientific.net/amr.1055.358.

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Based on the mathematical model of permanent magnet synchronous generator, the paper discussed the effect of the simplifying torque coefficient equation on direct-drive permanent magnet synchronous wind power generator. On the basis of feedback linearization principle, designed a PID and feedback linearization compound controller in this paper, and validated under varying wind speed, power coefficient remains at a constant value, which reached the maximum wind power capture purposes. Using MATLAB/simulink tool to build direct-drive permanent magnet synchronous wind power system simulation mode

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30

Megawati, R. Ratianingsih, and Hajar. "Analisis Kestabilan Penyebaran Penyakit Antraks Pada Populasi Hewan Dengan Pemberian Vaksinasi: Studi Kasus Untuk Infeksi Pada Populasi Manusia." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 16, no. 2 (2020): 172–84. http://dx.doi.org/10.22487/2540766x.2019.v16.i2.14989.

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ABSTRACTAnthrax is an infectious disease that caused by the Bacillus anthracis bacteria. The disease attacks animals such as cows in acute and preacute stage. Anthrax is a zoonotic disease that can be transmitted to humans through three types of media that are skin, digestive and respiratory tracts. To overcome the high death risk, treatment and vaccination of the period 6 – 12 months are conducted. The aims of this study is developing a mathematical model of anthrax spread in animal populations with vaccination treatment. The model is also consider human populations, such that the SIRSV model

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González Castillo, Iván, and Igor Loboda. "Analysis of nonlinear gas turbine models using influence coefficients." Ingeniería Investigación y Tecnología 22, no. 1 (2021): 1–17. http://dx.doi.org/10.22201/fi.25940732e.2021.22.1.008.

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The limited availability of gas turbine data, especially faults data and the high costs and risks of using test benches to obtain it,causes that rarely have enough data for form a fault classification. These circumstances have created the need to develop models that can provide simulated data. The quality of the data generated depends on the complexity of the thermodynamic model and the mathematical solution. A method to evaluate the accuracy of the models and their linearization capacity is presented. The method is applied to the models of a turbo shaft and a turbo fan of the commercial softw

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Permatasari, Anindita Henindya, and Robertus Heri Soelistyo Utomo. "MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION." Journal of Fundamental Mathematics and Applications (JFMA) 6, no. 1 (2023): 80–89. http://dx.doi.org/10.14710/jfma.v5i2.15723.

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Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov funct

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Pedro, Jimoh, and Olurotimi Dahunsi. "Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system." International Journal of Applied Mathematics and Computer Science 21, no. 1 (2011): 137–47. http://dx.doi.org/10.2478/v10006-011-0010-5.

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Neural network based feedback linearization control of a servo-hydraulic vehicle suspension systemThis paper presents the design of a neural network based feedback linearization (NNFBL) controller for a two degree-of-freedom (DOF), quarter-car, servo-hydraulic vehicle suspension system. The main objective of the direct adaptive NNFBL controller is to improve the system's ride comfort and handling quality. A feedforward, multi-layer perceptron (MLP) neural network (NN) model that is well suited for control by discrete input-output linearization (NNIOL) is developed using input-output data sets

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Asghari, Mohammad, Amir M. Fathollahi-Fard, S. M. J. Mirzapour Al-e-hashem, and Maxim A. Dulebenets. "Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey." Mathematics 10, no. 2 (2022): 283. http://dx.doi.org/10.3390/math10020283.

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To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease th

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Teskeredzic, Armin, and Rejhana Blazevic. "Transient Radiator Room Heating—Mathematical Model and Solution Algorithm." Buildings 8, no. 11 (2018): 163. http://dx.doi.org/10.3390/buildings8110163.

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A mathematical model and robust numerical solution algorithm for radiator heating of an arbitrary room is presented in this paper. Three separate and coupled transient thermal energy equations are solved. A modified transient heat conduction equation is used for solving the heat transfer at multi-layer outer walls and room assembly. Heat exchange between the inner walls and the observed room are represented with their own transport equation and the transient thermal energy equation is solved for radiators as well. Explicit coupling of equations and linearization of source terms result in a sim

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Sun, Yan, and Maoxiang Lang. "Modeling the Multicommodity Multimodal Routing Problem with Schedule-Based Services and Carbon Dioxide Emission Costs." Mathematical Problems in Engineering 2015 (2015): 1–21. http://dx.doi.org/10.1155/2015/406218.

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We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1) multicommodity flow routing; (2) a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services; (3) carbon dioxide emissions consideration; and (4) a generalized costs optimum oriented to customer demands. The specific planning of freight routin

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Luo, Cui Hua, Hai Feng Qi, and Cai Wen Ma. "Linearization of Coupled Pointing and Tracking Dynamical Equations." Advanced Materials Research 971-973 (June 2014): 1637–42. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1637.

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Cooperative pointing and tracking is one important characteristic of deep space inter-satellite laser communication, so that the dynamic mathematical model is complicated nonlinearity and coupling. The contribution of this paper is to substitute the time-domain error transfer function of state equations and to linearize the state space for the sake of physical realization easily in terms of previous authors’ work. The method applied is state feedback and coordinate transformation in nonlinear field, the calculated result is demonstrated that differential equations modeled can be transferred in

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Sutulo, Serge, and C. Guedes Soares. "AN ALGORITHM FOR CONSISTENT LINEARIZATION OF SHIP MANOEUVRING MATHEMATICAL MODELS." IFAC Proceedings Volumes 40, no. 17 (2007): 243–48. http://dx.doi.org/10.3182/20070919-3-hr-3904.00043.

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Van Gorder, Robert A. "A Linearization Approach for Rational Nonlinear Models in Mathematical Physics." Communications in Theoretical Physics 57, no. 4 (2012): 530–40. http://dx.doi.org/10.1088/0253-6102/57/4/03.

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Mary Celin Sharmila, D., T. Praveen, and L. Rajendran. "Mathematical Modeling and Analysis of Nonlinear Enzyme Catalyzed Reaction Processes." Journal of Theoretical Chemistry 2013 (December 24, 2013): 1–7. http://dx.doi.org/10.1155/2013/931091.

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A mathematical model for the nonlinear enzymatic reaction process is discussed. An approximate analytical expression of concentrations of substrate, enzyme, and free enzyme-product is obtained using homotopy perturbation method (HPM). The main objective is to propose an analytical solution, which does not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to analyze the effect of different parameters. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.

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Bouzoualegh, Samir, El-Hadi Guechi, and Ridha Kelaiaia. "Model Predictive Control of a Differential-Drive Mobile Robot." Acta Universitatis Sapientiae Electrical and Mechanical Engineering 10, no. 1 (2018): 20–41. http://dx.doi.org/10.2478/auseme-2018-0002.

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Abstract This paper presents a model predictive control (MPC) for a differential-drive mobile robot (DDMR) based on the dynamic model. The robot’s mathematical model is nonlinear, which is why an input–output linearization technique is used, and, based on the obtained linear model, an MPC was developed. The predictive control law gains were acquired by minimizing a quadratic criterion. In addition, to enable better tuning of the obtained predictive controller gains, torques and settling time graphs were used. To show the efficiency of the proposed approach, some simulation results are provided

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Gawade, T. R., S. Mukherjee, and D. Mohan. "Six-degree-of-freedom three-wheeled-vehicle model validation." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 219, no. 4 (2005): 487–98. http://dx.doi.org/10.1243/095440705x11194.

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A spatial six-degree-of-freedom mathematical model of a three-wheeled vehicle used in Asian countries is developed. The governing equations are derived and integrated explicitly without linearization to yield a large displacement model that can be used for parametric studies. The model includes suspension model, tyre compliance, lateral force due to cornering stiffness, and rolling resistance at the tyre. The model is validated against vertical accelerations measured when passing over a road bump. The lateral steady state response is validated through a steady state circular test procedure.

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Wu, Wang. "Application of Direct Feedback Linearization Control for Permanent Magnet Synchronous Generator Based Wind Energy Conversion System." Applied Mechanics and Materials 313-314 (March 2013): 571–76. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.571.

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Direct feedback linearization control was applied to permanent magnet synchronous generator (PMSG) wind energy conversion system (WECS), which was to reduce the cost of wind energy conversion system and improve its performance. The PMSG-based wind energy conversion system was constructed with mathematical models of aerodynamics subsystem, drive train subsystem and simplified electromagnetic subsystem. With feedback linearization control theory based on differential geometry, the coordinated transformation and nonlinear state feedback were obtained and PMSG wind energy conversion system was lin

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Kulik, Anatoliy, Konstantin Dergachov, and Sergey Pasichnik. "THE MODELS OF A HOLDING-BALANCE TWO-WHEELED EXPERIMENTAL SAMPLE PLANAR MOTION." International Scientific Technical Journal "Problems of Control and Informatics 67, no. 4 (2022): 18–34. http://dx.doi.org/10.34229/2786-6505-2022-4-2.

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The subject is the process of holding-balance two-wheeled experimental sample (HTES) planar motion models formation. The goal is to develop an approach to the formation of flat motion models of the HTES as an automatic controlled object. The problems: to form a physical model of a holding-balance two-wheeled experimental sample; to develop a nonlinear mathematical description of the forward and angular HTES motion on the plane using the Lagrangian formalism; to make a description of the controlled object in the frequency domain using Laplace transforms; to obtain a linearized mathematical desc

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Khramov, B. A., and A. V. Gusev. "Investigation of dynamic characteristics of three-linear flow regulator." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 1 (March 30, 2019): 91–97. http://dx.doi.org/10.38013/2542-0542-2019-1-91-97.

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The study focuses on the dynamic model of the three-linear spool flow regulator for various solutions of the spool geometry, and for two variants of mathematical description of hydraulic damping devices. The paper describes the process of small deflection linearization of the obtained mathematical models. As a result of Laplace transformation of the mathematical models, we obtained a block diagram of the spool flow regulator operation. By using Nyquist criterion, we analyzed the spool flow regulator stability. As a result, we draw conclusions on the spool flow regulator stability, and on the v

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Mark, Arul Prasanna, Rajasekaran Vairamani, and Gerald Christopher Raj Irudayaraj. "Mathematical Modeling and Analysis of Different Vector Controlled CSI Fed 3-Phase Induction Motor Drive." Journal of Applied Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/623982.

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The main objective of this paper is to build a simple mathematical competent model that describes the circuits and interconnections of a 3-phase squirrel cage induction motor used for industrial applications. This paper presents the detailed analysis of theoretical concepts used in mathematical modeling, simulation’ and hardware implementation. The objective of this work is to compare the dynamic performances of the vector control methods for CSI fed IM drives. Based on the results, dynamic performances of the proposed drives are individually analysed using the sensitivity tests. The tests tha

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Yılmaz, Kadir, and Münevver Turanlı. "A Multi-disciplinary Investigation of Linearization Deviations in Different Regression Models." Asian Journal of Probability and Statistics 22, no. 3 (2023): 15–19. http://dx.doi.org/10.9734/ajpas/2023/v22i3484.

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Aim: This study's objective is to examine linearization deviations in various regression models using a multidisciplinary approach. Methods: Curve estimate models' accuracy for each type of data was tested using social, financial, and medical data sets. Results: Although the power of a given model reduces with non-normal distributions, linearization in the social sciences is more efficient and has less variation from regression points in parametric equations. However, single-center distributions in the social sciences typically lead to nonparametric distributions. When compared to

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Li, Gang, Bao Ren Li, and Jing Min Du. "Nonlinear Model-Based Control for Vacuum Altitude Simulator." Applied Mechanics and Materials 470 (December 2013): 663–67. http://dx.doi.org/10.4028/www.scientific.net/amm.470.663.

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Vacuum altitude simulator (VAS) is the key component of the hardware in the loop simulation (HILS) of the aircraft control system. Due to the compressibility of the air and the nonlinearity of the exhaust capacity of the vacuum pump, it is difficult to get a good performance with normal linear controller. In this paper, the nonlinear mathematical model of the system is established. A feedback linearization controller is developed based on the model. To handle the uncertain nonlinear dynamics, the integral control is introduced. Experiments indicate that the proposed controller can effectively

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Jin, Yu Qiang, Jun Wei Lei, and Di Liu. "Modeling and PID Control of Single-Stage Inverted Pendulum System." Applied Mechanics and Materials 644-650 (September 2014): 142–45. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.142.

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The dynamic model is obtained based on researching the structure of single inverted pendulum system in this paper. Mathematical model of inverted pendulum that is close to the working point is deduced by linearization. A PID control algorithm is put forward by analyzing the factor of influencing inverted pendulum stability. The effectiveness of proposed algorithm is verified by simulation. This algorithm has the features of high control precision and good stability.

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Chernus, Pavel P., A. K. Arbiev, Petr P. Chernus, P. A. Loshitskiy, and V. T. Sharovatov. "POWER SHELL ELEMENTS: DYNAMIC MATHEMATICAL MODELS, POWER SYSTEMS (OVERVIEW)." Spravochnik. Inzhenernyi zhurnal, no. 291 (June 2021): 31–39. http://dx.doi.org/10.14489/hb.2021.06.pp.031-039.

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This article is a review devoted to the theory and practice of the application of power shell elements (PSE) in pneumatic drives (PD). She makes acquaint the reader with the main provisions of the theory of PD, performed on the PSE. The review briefly presents materials on the development of dynamic mathematical models (DMM) of power units (PU) of shell PDs (SPD), based on the use of static characteristics of SPD, an assessment of the advantages and disadvantages of PU based on traditional pneumatic cylinders (PC) and PSE is given. The main attention in the review is paid to the solution of th

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