scholarly journals Application of Input–State of the System Transformation for Linearization of Selected Electrical Circuits

2016 ◽  
Vol 67 (3) ◽  
pp. 199-205 ◽  
Author(s):  
Andrzej Zawadzki ◽  
Sebastian Różowicz
Keyword(s):  
Nonlinear System ◽  
Feedback Loop ◽  
Numerical Solutions ◽  
Necessary Conditions ◽  
Electric Circuit ◽  
Input State ◽  
System Transformation ◽  
State Equations ◽  
Local Diffeomorphism ◽  
Linearized System

Abstract The paper presents a transformation of nonlinear electric circuit into linear one through changing coordinates (local diffeomorphism) with the use of closed feedback loop. The necessary conditions that must be fulfilled by nonlinear system to enable carrying out linearizing procedures are presented. Numerical solutions of state equations for the nonlinear system and equivalent linearized system are included.

scholarly journals Input-Output Transformation Using the Feedback of Nonlinear Electrical Circuits: Algorithms and Linearization Examples

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Sebastian Różowicz ◽  
Andrzej Zawadzki
Keyword(s):  
Nonlinear System ◽  
Feedback Loop ◽  
Electrical Circuit ◽  
Input Output ◽  
Local Diffeomorphism ◽  
Electrical Circuits ◽  
Circuit Input ◽  
Transformation Algorithms ◽  
Output Transformation ◽  
Closed Feedback Loop

This paper addresses the problem of nonlinear electrical circuit input-output linearization. The transformation algorithms for linearization of nonlinear system through changing coordinates (local diffeomorphism) with the use of closed feedback loop together with the conditions necessary for linearization are presented. The linearization stages and the results of numerical simulations are discussed.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

scholarly journals Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuying Shi ◽  
Qianshun Chang
Keyword(s):  
Nonlinear System ◽  
Total Variation ◽  
Multigrid Method ◽  
Algebraic Multigrid ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Linearized System ◽  
Outer Iteration ◽  
Anisotropic Total Variation ◽  
Deblurring And Denoising

A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.

scholarly journals Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model

2021 ◽  
Vol 11 (18) ◽  
pp. 8549
Author(s):  
Zulqurnain Sabir ◽  
Ag Asri Ag Ibrahim ◽  
Muhammad Asif Zahoor Raja ◽  
Kashif Nisar ◽  
Muhammad Umar ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Local Search ◽  
Objective Function ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Disease Model ◽  
Numerical Results ◽  
Active Set ◽  
System Equations ◽  
Global And Local

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

Analysis of methane production intensity during its displacement from a gas hydrate formation by carbon dioxide

2019 ◽  
Vol 14 (3) ◽  
pp. 149-156
Author(s):  
M.K. Khasanov ◽  
G.R. Rafikova
Keyword(s):  
Carbon Dioxide ◽  
Methane Hydrate ◽  
Numerical Solutions ◽  
Hydrate Formation ◽  
Absolute Permeability ◽  
Gas Mixture ◽  
State Equations ◽  
Substitution Process ◽  
Gas Hydrate Formation ◽  
Carbon Dioxide Hydrate

The theoretical model is considered in the one-dimensional approximations and numerical solutions are obtained for the process of replacing methane with carbon dioxide from a hydrate in a formation saturated with methane and its hydrate when carbon dioxide is injected into the formation. The process is considered under thermobaric conditions corresponding to the stability region of methane gas and carbon dioxide and the region of existence of CO2 in the form of a gaseous phase. The case is considered when the rate of carbon dioxide hydrate formation is limited by diffusion of carbon dioxide through the formed hydrate layer between the gas mixture stream and methane hydrate. It is accepted that the hydration substitution process occurs without the release of water from the hydrate. To describe the mathematical model, the main equations are the mass conservation equations for methane, carbon dioxide and their hydrates, Darcy’s law for filtration, Fick’s law for diffusive mixing of the gas mixture, state equations for the gas phase, Dalton’s law, energy equation, diffusion equation for transport CO2 through the hydration layer at the pore microchannel scale. The dynamics of the mass flow rates of the outgoing carbon dioxide and methane recovered has been investigated. The influence of the diffusion coefficient, the absolute permeability and the length of the formation on the intensity of the methane produced as a result of the gas substitution process is analyzed. Three main stages of the process were identified: displacement of free methane from the reservoir; extraction of free methane obtained as a result of the beginning of hydrate substitution in the formation; complete conversion of methane hydrate to carbon dioxide hydrate and complete extraction of methane from the formation. It is determined how the two main factors relate to each other in terms of the degree of influence on the replacement rate: heat and mass transfer in the reservoir and the kinetics of the replacement process.

CHAOTIC PHENOMENA IN AN ORDER 1 DPCM TRANSMISSION SYSTEM

1995 ◽  
Vol 05 (04) ◽  
pp. 1033-1070 ◽  
Author(s):  
C. UHL ◽  
D. FOURNIER-PRUNARET
Keyword(s):  
Stability Condition ◽  
Output Signal ◽  
Feedback Loop ◽  
Transmission System ◽  
Linear Filter ◽  
Bifurcation Structure ◽  
State Equations ◽  
Chaotic Phenomena ◽  
Nonlinear Quantization ◽  
The Stability

The existence of chaotic phenomena in DPCM transmission systems of order 1 is studied. The coupling at the encoder between the nonlinear quantization and the prediction makes the encoder recursive even if the prediction is transversal; The encoder has a feedback loop which is a recursive linear filter. For an order 1 transversal predictor, the bifurcation structure of the encoder state equations is determined. It is proven that the encoder output signal may be chaotic even if the stability condition of the linear filter is satisfied. Parameters giving rise to chaotic phenomena can be determined in order to avoid dysfunctioning of the system.

Pressure Behavior During Polymer Flow in Petroleum Reservoirs

1982 ◽  
Vol 104 (2) ◽  
pp. 149-156 ◽  
Author(s):  
Chi U. Ikoku ◽  
H. J. Ramey
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
State Equations ◽  
Partial Differential ◽  
Dimensionless Radius ◽  
Dimensionless Pressure

This paper presents solutions of the nonlinear partial differential equation using the Douglas-Jones predictor-corrector method for the numerical solution of nonlinear partial differential equations. The results are presented in tabular form and as semilogarithmic and log-log type-curve graphs. Graphs of dimensionless pressure versus dimensionless radius also are presented. Compared to results from analytical solutions of the linear partial differential equation, the graphs have the same shape. The error introduced by the linearizing approximation is small for many values of the flow behavior index, n, and decreases as n tends to unity. Dimensionless pressure is a linear function of dimensionless radius to the power (1–n), near the well, as predicted by the steady-state equations. Also radius of investigation equation derived analytically agrees with results from numerical solutions.

scholarly journals High Sensitive, Linear and Thermostable Pressure Sensor Utilizing Bipolar Junction Transistor for 5 kPa

2021 ◽  
Author(s):  
Mikhail Basov
Keyword(s):  
Pressure Sensor ◽  
Feedback Loop ◽  
Electric Circuit ◽  
Electrical Circuit ◽  
Sensor Chip ◽  
Burst Pressure ◽  
Negative Feedback Loop ◽  
Chip Area ◽  
Bipolar Junction Transistor ◽  
Junction Transistor

Research of pressure sensor chip utilizing novel electrical circuit with bipolar-junction transistor-based (BJT) piezosensitive differential amplifier with negative feedback loop (PDA-NFL) for 5 kPa differential range was done. The significant advantages of developed chip PDA-NFL in the comparative analysis of advanced pressure sensor analogs, which are using the Wheatstone piezoresistive bridge, are clearly shown. The experimental results prove that pressure sensor chip PDA-NFL with 4.0x4.0 mm<sup>2</sup> chip area has sensitivity S = 11.2 ± 1.8 mV/V/kPa with nonlinearity of 2K<sub>NLback</sub> = 0.11 ± 0.09 %/FS (pressure is applied from the back chip side) and 2K<sub>NLtop</sub> = 0.18 ± 0.09 %/FS (pressure is applied from the top chip side). All temperature characteristics have low errors, because the precision elements balance of PDA-NFL electric circuit was used. Additionally, the burst pressure is 80 times higher than the working range.

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