scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

A generalization of the Laplace transform

1967 ◽  
Vol 63 (1) ◽  
pp. 155-160 ◽  
Author(s):  
H. S. Dunn
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Finite Interval ◽  
Integral Transformation ◽  
System Response ◽  
Simple Scheme ◽  
Exponential Order ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Determine System

AbstractAn integral transformation is denned over a finite interval of the time domain. When the Laplace transform exists, the finite transform yields identical results. However, the finite transform is found to be considerably more general than the Laplace transform. It permits consideration of functions which are not of exponential order, leads to a simple scheme to determine system response, and is applicable to boundary-value problems.

Simple interpretation of time‐domain electromagnetic sounding using similarities between wave and diffusion propagation

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 763-774 ◽  
Author(s):  
Mier Gershenson
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Synthetic Data ◽  
Time Base ◽  
Time Interval ◽  
Exponential Time ◽  
The Laplace Transform ◽  
Image Function ◽  
The Time Domain ◽  
Conductive Media

By using similarities between EM sounding in dielectric and conductive media, it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between diffusive and nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power, while for the nondiffusive cases, similar equations occur with [Formula: see text]. Three alternative implementations are developed, and their use is demonstrated. The first implementation is based on substituting [Formula: see text] for the Laplace transform variable s using forward and inverse numerical Laplace transforms. The second implementation is based on expanding the diffusive time response on an exponential time base and replacing it with its image function in the wave case, namely, a sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The performance of the techniques on synthetic data is demonstrated. Besides the advantage of simple implementation of these techniques, other advantages and limitations of the method and each of the implementations are discussed. A case history is presented. The application of common techniques used in the processing of seismic and radar for processing and EM sounding in conductive media is discussed. The use of the Poynting vector as a means of determining distance and direction is demonstrated.

scholarly journals The Concentration of Digoxin Activity after Intravenous in Three Compartments Mathematical Model

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3653-3657
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Digoxin Concentration ◽  
Compartment Model ◽  
System Of Equations ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Concentration Time ◽  
The Laplace Transform ◽  
Three Compartment Model

Present paper is designed to compare the distribution of digoxin in three compartment model administered through an intravenous (i.v). These models under consideration is denoted by a system of non-linear ordinary differential equations. The Eigenvalue and the Laplace transform methods were used to solve the system of equations. Digoxin was administered to five subjects through Intravenous then, the serum digoxin concentrations were measured respectively over a period of 72 hours. The transfer coefficients were obtained from observed digoxin concentrations using method of residuals and the variation of digoxin concentration – time curves plotted using MATLAB.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

Time-Domain Input-Output Transient Performance Validation for Modular Control Systems: Method and Examples

2010 ◽  
Author(s):  
Deepak Sharma ◽  
D. M. Tilbury ◽  
Lucia Seno
Keyword(s):  
Control Systems ◽  
Time Domain ◽  
Convex Sets ◽  
Mimo Systems ◽  
Transient Performance ◽  
Input Output ◽  
Modular Control ◽  
Input And Output ◽  
The Time Domain ◽  
Performance Validation

This paper presents results that can be used to validate input-output transient performance for modular control systems. If bounds in the time-domain are specified for inputs of an LTI SISO system, the techniques in this paper can determine the minimum set containing all possible outputs. If both input and output bounds are given, they can determine whether these specifications are met. Network delay affecting the input of the system is also considered. Finally, this paper extends the techniques for MIMO systems. The results are derived using the theory of convex sets. Several examples are presented to illustrate the results and demonstrate their application.

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