scholarly journals Root-Locus Analysis of Delayed First and Second Order Systems

Enfoque UTE ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 69-76
Author(s):  
Moisés Ríos Flores ◽  
J.F. Marquez-Rubio ◽  
B. Del Muro-Cuellar ◽  
E. Aranda-Bricaire
Keyword(s):  
Linear System ◽  
Second Order ◽  
Computational Method ◽  
Root Locus ◽  
Delayed Systems ◽  
Finite Dimensional ◽  
Locus Method ◽  
Root Locus Analysis ◽  
Second Order Systems ◽  
Low Order

For finite dimensional linear system the root-locus method is well established however for the case of delayed systems the method has some problems due to the transcendental term involved. This work intends to illustrate the problems that arises when a root-locus diagram is performed as well as to develop a Matlab function that provides the root-locus diagram for delayed low order systems. In this way, some comments about the problems that should be tackled to obtain a generalization of the computational method for delayed systems with real m poles and n zeros

A Root Locus Method for Stability Analysis of Heat Conduction in Multilayer Composite Solids

2008 ◽  
Author(s):  
Bingen Yang ◽  
Hang Shi
Keyword(s):  
Heat Source ◽  
Characteristic Equation ◽  
Heat Generation ◽  
Stability Criterion ◽  
Internal Heat ◽  
Root Locus ◽  
Excessive Heat ◽  
Locus Method ◽  
Numerical Effort ◽  
Root Locus Analysis

Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a stability criterion is established for one-dimensional composite solids with internal heat generation at a rate proportional to their temperature. In the development, a spatial state formulation is used to derive a characteristic equation for system eigenvalues. A root locus analysis of the characteristic equation yields a stability criterion, by which an upper bound of heat source for thermal stability is obtained, and the gain of heat source is related to the number of unstable (positive) eigenvalues. The proposed stability test requires minimum numerical effort, does not require the information about system eigenvalues, and is applicable to various spatial distributions of heat source.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals ℋ∞ Control Tunning to Guarantee the Output Performance of LTI Second-Order Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4611-4616
Author(s):  
Ramón I. Verdés ◽  
Luis T. Aguilar ◽  
Yury Orlov
Keyword(s):  
Second Order ◽  
Output Performance ◽  
Second Order Systems

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

Second Order Two-Scale Method for Composite Plate with 3-D Periodic Configuration under Condition of Coupled Thermoelasticity

2014 ◽  
Vol 898 ◽  
pp. 7-10 ◽  
Author(s):  
Zi Qiang Wang ◽  
Jun Ying Cao
Keyword(s):  
Composite Plate ◽  
Second Order ◽  
Computational Method ◽  
Deformation Pattern ◽  
Effective Parameters ◽  
Coupled Thermoelasticity ◽  
Integral Projection ◽  
Cell Functions ◽  
Periodic Configuration ◽  
Micro Structures

In this paper, we give a second-order two-scale (SOTS) computational method for composite plate with 3-D periodic configuration under condition of coupled thermoelasticity by means of construction way. Based on the Reissner-Mindlin deformation pattern and integral projection operator of temperature, the homogenization solution is obtained. The SOTS's approximate solution is constructed by the cell functions and the homogenization solution. A set of numerical results are demonstrated for predicting the effective parameters, the displacement and temperature of composite plate. It shows that SOTS's method can capture the 3-D local behaviors caused by 3-D micro-structures well.

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