Статті в журналах: "Linearization of the mathematical model"

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 linearized form of mechanical and mathematical equations that are required when designing controllers, active suspension and other driver assistance systems.

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2

Zhang, Bin, and Yung C. Shin. "A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems." Applied Sciences 11, no. 1 (December 23, 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 models can closely approximate the original unknown nonlinear system with a reduced number of linearizations. Based on T-S fuzzy models, optimal controllers are designed and implemented for a nonlinear two-link flexible joint robot, which demonstrates the possibility of implementing the well-established model-based optimal control method onto unknown nonlinear dynamic systems.

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3

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 (January 27, 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 proposed by incorporating these two estimators. The results are extended by the use of improved partial format dynamic linearization (iPFDL) and full format dynamic linearization (iFFDL). The theoretical results are shown using contraction mapping principle-based mathematical analysis, as well as simulations.

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4

Gavrus, Cristina, Nicolae-Valentin Ivan, and Gheorghe Oancea. "Machining Parameters Optimization Based on Objective Function Linearization." Mathematics 10, no. 5 (March 3, 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 mathematical programming. The optimization mathematical models are, however, nonlinear. Therefore, mathematical model linearization is required. The major and difficult problem is the linearization of the objective function. This represents the key element of the proposed optimization method. In this respect, the paper proposes an original mathematical procedure for calculating the part of the objective function that refers to the analytical integration of the tool life into the model. This calculus procedure was transposed into an original software tool. For demonstrating the validity of the method, a comparison is presented among the results obtained by certain optimization techniques. It results that the proposed method is simple and as good as those presented by the literature.

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5

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 performance of the control algorithm. From this stand point, on the basis of the dynamic model of the doubly fed induction generator considering magnetic saturation, the feedback linearizing control technique has been formulated. The mathematical model of the doubly fed induction generator, integrating the magnetic saturation has been formulated in the stator flux-oriented reference frame with rotor current and stator magnetizing current as state variables. Simulation studies demonstrate that the inclusion of magnetic saturation in the feedback linearization control of the doubly fed induction generator model increases its accuracy and results in a more efficient and reliable synthesis of the control algorithm.

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6

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 analyzing the parameters of the gas flow and physical processes of energy conversion directly inside the object and obtaining its static characteristics. A linearization method of static characteristics on the interval of input and output values is proposed which will expand the operating range without loss of linearization accuracy. A method of structural-parametric identification based on experimental logarithmic magnitude-frequency characteristics is proposed which will allow for the same set of experimental points to select the structure of the mathematical model of varying complexity depending on the specified accuracy. As a result of the work, the scheme for modeling the automatic control object was formed, consisting of the drive unit, sensor unit, and vortex energy separator, with the reflection of all the obtained operating modes. The methods used are the method of graphic linearization, Laplace transform, structural-parametric identification. The following results were obtained: a computer and linearized mathematical model of the small-sized vortex energy separator as an automatic control object reflecting its properties in the time and frequency domains was obtained. A comparative analysis of the reactions of the model and the real object to the same input action was carried out. Conclusions. The scientific novelty of the results obtained is as follows: 1) multiple graphic linearizations of one static characteristic to use the full range of the operation mode of vortex energy separator, which distinguishes it from the known;2) mathematical model structural-parametric identification for vortex energy separator with the help of known points of the Bode magnitude plots by using the interpolation polynomial and its derivatives graphs.

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7

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, a speed tracking controller is designed. The Simulink model of Svpwm is established. The control algorithm and the model of Svpwm are verified based on theMatlab7.6/Simulink & SimPowerSystems toolbox. The simulation results show that the controller designed has a very good control effect while the feedback linearization design is simple.

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8

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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9

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 inverse system method is deduced, and then close system controller is designed. Finally, the simulation system is set up with MATLAB software. The step response of system, the start up displacement curve of rotor and the performance of anti-disturbance of system are simulated. The simulation results have shown that the α-th order inverse system control strategy can realize accurate linearization for nonlinear mathematical model of the axial hybrid magnetic bearing, and the designed close control system has good dynamic and static performance.

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10

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 (May 25, 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 model is created for explicit MPC controller design. Moreover, the block diagram of the proposed method for PMSM system is presented. Finally, the simulation results are provided to demonstrate that the proposed explicit MPC controller based on multi-point linearization achieves better performance than that based on traditional single-point linearization, but requires the same online computation time because of the offline optimization of explicit MPC.

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11

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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12

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 good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. Due to the complex nonlinear dynamics of the biological phenomena represented by S-systems, nonlinear intervention schemes are needed to cope with the complexity of the nonlinear S-system models. Here, we present an intervention technique based on feedback linearization for biological phenomena modeled by S-systems. This technique is based on perfect knowledge of the S-system model. The proposed intervention technique is applied to the glycolytic-glycogenolytic pathway, and simulation results presented demonstrate the effectiveness of the proposed technique.

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13

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 and deformations. Results. On the basis of the analysis, the main factors of the course of the biomass briquetting process in the closed matrix channel of the stamp press have been determined. The physical essence of obtaining briquettes from dispersed biomass is described. The developed graph-analytical model of biomass briquetting in the closed matrix of a stamp press is substantiated. The application of the method of linearization helps to simplify the mathematical model on the criterion of adequacy in relation to the real conditions of the process. Conclusions The developed graphic-analytical model of the process of briquetting of plant biomass in the closed matrix channel of the stamp press allows to find out in abstract form the physical essence of this complex phenomenon. According to the results of analytical modeling of the process of biomass compaction in the base with elastic properties it is established that the density of the briquette increases monotonically, asymptotically approaching the plastic state of the monolithic product. The application of the method of linearization of the nonlinear function F(y_1^((1) ) ) simplifies the analysis of the model on the length of the matrix channel in the interval (0; l_1 ), and the coefficient of linearization of the biomass resistance force is the basis of the mathematical model closed channel after each i-th blow. Keywords: briquette press, biomass, briquettes, shock method, stamp, closed channel, matrix, modeling, linearization.

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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 DG or a Microgrid.

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15

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 feedback linearization control rule was proposed, with feedback linearization control theory based on differential geometry, the coordinated transformation and nonlinear state feedback were obtained. The system was constructed with MATLAB/Simulink platform, the model and control strategy was adopted and the simulation result shows this method can realized optimal power control, which has maximum energy capture ability.

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16

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 (January 17, 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 the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.

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17

González Castillo, Iván, and Igor Loboda. "Analysis of nonlinear gas turbine models using influence coefficients." Ingeniería Investigación y Tecnología 22, no. 1 (January 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 software GasTurb 12, as an example. It was simulated a wide database with influence of fault parameters and condition operation, then it calculed the influence matrix ""H"" and ""G"" for prove the influence theirs on behavior of the models. The results show that if the model is sufficiently accuracy, it is possible to find an adequate interval where the linearization errors are not very large and it is just possible the linearization.

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18

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 (October 6, 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-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

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19

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 at each Newton iteration of each step of numerical integration can be used to obtain a linearized mathematical model, but the equilibrium equations, as a rule, contain several derivatives with respect to time. By introducing additional variables, it is possible to reduce the linearized mathematical model to the Cauchy normal form, while the Jacobi matrix structure remains essentially unchanged.The proposed solution is implemented in the mathematical core of the PRADIS Gen2 PA-8 software package, which made it possible to expand its functionality by an operator of modal analysis.The presented calculations of test schemes have shown the correctness of the method proposed.

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20

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 various types of damping devices affecting it

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21

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 (January 29, 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 (susceptible, Infected, Recovered, susceptible and Vaccine) is used for animal population and SI model (susceptible, Infected) is used for human population. The stability of model is analyzed at the critical points by linearization method. The free-disease unstable critical point and the stable endemic critical point are derived. The simulation shous that the number of infected animal and infected human population is not significantly different and indicates that the vaccination treatment could overcome the spread of anthrax succesfully.Keywords : Anthrax, Critical Point Endemic, Critical Point Non Disease, linearization method, Mathematical Models

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22

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 (December 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 more exponential functions and equilibrium values. Both methods give the same equilibrium values for both the relaxation and creep of wine gums and apple. The initial increasing rate of creep is higher by the Peleg linearization and lower by the Prony series. At relaxation the initial decreasing rate is lower by the Peleg linearization and higher by the Prony series.

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23

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 linearized. With MATLAB/Simulink platform, the model and control strategy was established and the simulation result shows this control system with feasible speed tracking performance, which can effectively implement maximum energy capture.

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24

Teskeredzic, Armin, and Rejhana Blazevic. "Transient Radiator Room Heating—Mathematical Model and Solution Algorithm." Buildings 8, no. 11 (November 18, 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 simple, accurate, and stabile solution algorithm. Verification of the developed methodology is demonstrated on three carefully selected test cases for which an analytical solution can be found. The obtained results show that even for the small temperature differences between inner walls and room air, the corresponding heat flux can be larger than the transmission heat flux through outer walls or windows. The benefits of the current approach are stressed, while the plans for the further development and application of the methodology are highlighted at the end.

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Ge, P., and M. Jouaneh. "Modeling of the Backlash Hysteresis Nonlinearity." Journal of Mechanical Design 120, no. 3 (September 1, 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 that used in the modeling. The results show that our model-based linearization scheme although running in an open loop fashion, provides a simpler way to perform tracking control for structures with backlash hysteresis nonlinearity.

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26

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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27

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

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28

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 (August 17, 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 approach proposed in the literature for the same problem. The results showed the efficiency of the proposed method.

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29

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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30

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 (January 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 hierarchical logit model resolves the overlapping problem through the similarity index while still accounting for both congestion and stochastic effects in the mathematical programming formulation.

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31

Stefanello, Michel Baptistella, Gervásio Annes Degrazia, Silvana Maldaner, Celene Buriol, Lilian Moor, Jonas Carvalho, Luca Mortarini, and Umberto Rizza. "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 situations in which the meandering phenomenon plays a decisive role.

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32

Nazarov, Serdar, Muhammetberdi Rakhimov, and Gurbanyaz Khekimov. "Linearization of the Navier-Stokes equations." E3S Web of Conferences 216 (2020): 01060. http://dx.doi.org/10.1051/e3sconf/202021601060.

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This paper studies mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier-Stokes equation for a plane fluid flow are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

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33

Simonov, V. M. "Combinatorial linearization of data processing algoritmic complexes. Theory and Heuristics." Informatization and communication 1 (January 2021): 97–104. http://dx.doi.org/10.34219/2078-8320-2021-12-1-97-104.

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theoretical redundancy of the proof theorem about data processing algorithmic complexes’s combinatorial linearization [ 1 ] opens additional heuristic possibilities for decision of this problem. The correlation between theory and heuristics is illustrated in article on concrete examples. It had been shown, that heuristic transformations of DPAC’s mathematical models are able not only correspond to theoretical recommendations, but also break them, realizing, nevertheless, the purpose of combinatorial linearization itself. As a hole, the heuristic approach widenes possibilities of DPAC’s combinatorial linearization, that is essential for applications.

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34

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 (November 28, 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. The current controller decouples the d–q axis current from the flux linkage information of the motor and outputs a control voltage. When the motor speed reaches above the base speed, the field-forward and straight-axis current components are newly distributed to achieve field weakening control, which can realize the smooth transition between the constant torque region and weak magnetic region. Simulation and experimental results show the feasibility and viability of the strategy.

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35

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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36

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 into canonical controllable form and realized physically.

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37

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 model, the paper verify the stability of the system when the external applied load mutate. The result shows that the control strategy of the composite is effective and timely when tacking the maximum power.

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38

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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39

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 (December 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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40

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 (April 1, 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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41

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 (March 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 obtained from mathematical model simulation. The NN model is trained using the Levenberg-Marquardt optimization algorithm. The proposed controller is compared with a constant-gain PID controller (based on the Ziegler-Nichols tuning method) during suspension travel setpoint tracking in the presence of deterministic road disturbance. Simulation results demonstrate the superior performance of the proposed direct adaptive NNFBL controller over the generic PID controller in rejecting the deterministic road disturbance. This superior performance is achieved at a much lower control cost within the stipulated constraints.

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42

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 improve the stability and the dynamic response of the system.

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43

Grana, Dario. "Bayesian linearized rock-physics inversion." GEOPHYSICS 81, no. 6 (November 2016): D625—D641. http://dx.doi.org/10.1190/geo2016-0161.1.

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The estimation of rock and fluid properties from seismic attributes is an inverse problem. Rock-physics modeling provides physical relations to link elastic and petrophysical variables. Most of these models are nonlinear; therefore, the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties. We have developed a new approach based on the linearization of the rock-physics forward model using first-order Taylor series approximations. The mathematical method adopted for the inversion is the Bayesian approach previously applied successfully to amplitude variation with offset linearized inversion. We developed the analytical formulation of the linearized rock-physics relations for three different models: empirical, granular media, and inclusion models, and we derived the formulation of the Bayesian rock-physics inversion under Gaussian assumptions for the prior distribution of the model. The application of the inversion to real data sets delivers accurate results. The main advantage of this method is the small computational cost due to the analytical solution given by the linearization and the Bayesian Gaussian approach.

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44

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 the problem of creating PU on PSE with the required quality indicators at the design stage, when it is necessary to take into account the properties of compressed gas. For this, an original methodology for the development of nonlinear DMMs for various typical variants of the midrange is proposed, the basis of which is a number of provisions of the theory of gas dynamics. Without invoking this theory, it is impossible to ta into account the properties of compressed gas (compressibility of the working medium, dependence on temperature and gas flow rate in the shell, the nature of the gas expansion processes), and, therefore, to reliably describe the state of unsteady gas processes inside the shell and develop a DMM of the PU, to a sufficient taking into account the mentioned properties. Since the topic of this review is intended mainly for engineers who develop SPD (theoreticians and practitioners), the review also contains materials on the linearization of the found nonlinear DMMs. As a result of linearization, nonlinear DMMs are transformed into transfer functions for displacement of the output coordinate and effort. The correctness of the linearization carried out is confirmed by the results of experiments. The review briefly discusses several options for pneumatic supply systems for SPD. Here, of particular interest for a specialist is the material on imparting invariance properties to SPDs to air intake from the atmosphere nd discharge of exhaust air into the atmosphere, which significantly expands the scope of SPDs and reduce their cost.

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45

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 routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.

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46

Zheng, Yingsong, and Henning Struchtrup. "A linearization of Mieussens's discrete velocity model for kinetic equations." European Journal of Mechanics - B/Fluids 26, no. 2 (March 2007): 182–92. http://dx.doi.org/10.1016/j.euromechflu.2006.08.003.

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47

Babak, Oleg V. "Method for Linearization of Deterministic Nonlinear Mathematical Models of Control Objects." Journal of Automation and Information Sciences 29, no. 1 (1997): 16–22. http://dx.doi.org/10.1615/jautomatinfscien.v29.i1.20.

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48

Ciușdel, C. F., S. Coman, Cr Boldișor, T. Kessler, A. Muradyan, A. Kovachev, H. Lehrach, C. Wierling, and L. M. Itu. "Effect of Linearization in a WNT Signaling Model." Computational and Mathematical Methods in Medicine 2019 (June 10, 2019): 1–9. http://dx.doi.org/10.1155/2019/8461820.

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A nonlinear model consisting of a system of coupled ordinary differential equations (ODE), describing a biological process linked with cancer development, is linearized using Taylor series and tested against different magnitudes of input perturbations, in order to investigate the extent to which the linearization is accurate. The canonical wingless/integrated (WNT) signaling pathway is considered. The linearization procedure is described, and special considerations for linearization validity are analyzed. The analytical properties of nonlinear and linearized systems are studied, including aspects such as existence of steady state and initial value sensitivity. Linearization is a useful tool for speeding up drug response computations or for providing analytical answers to problems such as required drug concentrations. A Monte Carlo-based error testing workflow is employed to study the errors introduced by the linearization for different input conditions and parameter vectors. The deviations between the nonlinear and the linearized system were found to increase in a polynomial fashion w.r.t. the magnitude of tested perturbations. The linearized system closely followed the original one for perturbations of magnitude within 10% of the base input vector which yielded the state-space fixed point used for the linearization.

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49

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 that are chosen for the comparison are step changes in the reference speed and torque of the motor drive. Here the IM is mathematically modeled in different reference frames for input output linearization (IOL) control, field oriented control (FOC), and direct torque control method (DTC) which are designed using hardware equivalent mathematical equations. The most important contributions in this paper are mathematical simulation structure of IM model in rotor flux frame using current and speed that were developed and implemented in MATLAB-Simulink. The operation and performance of the different vector control methods are verified by simulation using MATLAB/SIMULINK and experimental results.

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50

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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