scholarly journals Filtering Method Based on Symmetrical Second Order Systems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 813
Author(s):  
Cristian Toma
Keyword(s):  
Time Moment ◽  
Sampling Procedure ◽  
Second Order ◽  
Sampling Time ◽  
Half Period ◽  
Order System ◽  
Filtering Method ◽  
Oscillating Systems ◽  
Sampling Structure ◽  
Second Order Systems

This study presents a filtering and sampling structure based on symmetrical second order systems working on half-period. It is shown that undamped second order oscillating systems working on half-period could provide: (i) a large attenuation coefficient for an alternating signal (due to the filtering second order system), and (ii) a robust sampling procedure (the slope of the generated output being zero at the sampling time moment). Unlike previous studies on the same topics, these results are achieved without the use of an additional integrator.

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.

Two-sided form, differentiation and second-order observation in Escher’s artworks and Calvino’s stories

Kybernetes ◽  
2019 ◽  
Vol 48 (5) ◽  
pp. 1060-1077
Author(s):  
Laura Appignanesi
Keyword(s):  
Twentieth Century ◽  
Systems Theory ◽  
Second Order ◽  
Order System ◽  
Literary Works ◽  
Content Type ◽  
Theoretical Concepts ◽  
Art And Literature ◽  
Second Order Systems ◽  
Late Works

Purpose The purpose of this paper is to find a leading idea of the mid-twentieth century, demonstrating the pervasive nature of some concepts belonging to second-order systems theory. To achieve this objective, the paper looks at the art and literature of this era, to identify the principles developed by Luhmann in his late works. In particular, Escher’s drawings, Calvino’s stories and Luhmann’s concepts seem to express, in different ways, the same functioning mechanism of the complex social system. Design/methodology/approach With reference to theoretical approach and methodology, this paper carries out an interdisciplinary demonstration by alternative modes of logos and mythos. Some of the pillars of general systems theory are examined through the logical articulation of concepts developed by Spencer-Brown, von Foerster, and first of all through the late works of Luhmann, as well as through the analysis of Escher’s artworks and Calvino’s literary works. This paper interprets these artistic and literary works using cybernetic principles and systemic concepts, in particular, “two-sided forms,” “system–environment differentiation” and “second-order observation.” Findings In general, the main finding is the similarity of fascination with paradoxes and forms, with post-ontological reasoning, in twentieth century. The result of the cross-reading of Escher, Calvino and Luhmann reveals the presence of what Simmel called the “hidden king”: a philosophical paradigm of an era. In mid-1900s, this leading idea seems to express itself in the discoveries of biology and cybernetics, such as in Luhmann’s theory, art and literature. Escher’s drawings, Calvino’s stories and the concepts of Luhmann are projections of second-order system theory, in its constructivist value. Originality/value The originality of this paper lies mainly in the demonstration of theoretical concepts through the alternative modes of logos and mythos. These reflections can provide a new perspective to investigate social sciences from a cultural angle. This particular approach allows a deep awareness of the theory. The concrete value is to provide a better understanding to manage complexity.

Periodic Behavior of a Nonlinear Third Order Vibrating System

2002 ◽  
Author(s):  
Gholamreza Nakhaie Jazar ◽  
Mohammad H. Alimi ◽  
Mohammad Mahinfalah ◽  
Ali Khazaei
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Ad Hoc ◽  
Order Differential Equation ◽  
Second Order ◽  
Order System ◽  
Third Order ◽  
Modeling Process ◽  
Third Order Differential Equation ◽  
Second Order Systems

In modeling of dynamical systems, differential equations, either ordinary or partial, are a common outcome of the modeling process. The basic problem becomes the existence of solution of these deferential equations. In the early days of the solution of deferential equations at the beginning of the eighteenth century the methods for determining the existence of nontrivial solution were so limited and developed very much on an ad hoc basis. Most of the efforts on dynamical system are related to the second order systems, derived by applying Newton equation of motion to dynamical systems. But, behavior of some dynamical systems is governed by equations falling down in the general nonlinear third order differential equation x″′+f(t,x,x′,x″)=0, sometimes as a result of combination of a first and a second order system. It is shown in this paper that these equations could have nontrivial solutions, if x, x′, x″, and f(t,x,x′,x″) are bounded. Furthermore, it is shown that the third order differential equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. For this purpose, the concept of Green’s function and the Schauder’s fixed-point theorem has been used.

A Reduced Second-Order Approach for Linear Viscoelastic Oscillators

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Sondipon Adhikari
Keyword(s):  
Past History ◽  
Kernel Functions ◽  
Second Order ◽  
Order System ◽  
Closed Form Expression ◽  
Internal Variables ◽  
Dynamical Response ◽  
Convolution Integrals ◽  
History Of ◽  
Second Order Systems

This paper proposes a new approach for the reduction in the model-order of linear multiple-degree-of-freedom viscoelastic systems via equivalent second-order systems. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. Here, an approximate reduced second-order approach is proposed for this type of problems. The proposed approximation utilizes the idea of generalized proportional damping and expressions of approximate eigenvalues of the system. A closed-form expression of the equivalent second-order system has been derived. The new expression is obtained by elementary operations involving the mass, stiffness, and the kernel function matrix only. This enables one to approximately calculate the dynamical response of complex viscoelastic systems using the standard tools for conventional second-order systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

scholarly journals Extracting second-order system matrices from state space system

2006 ◽  
Vol 220 (8) ◽  
pp. 1147-1149 ◽  
Author(s):  
P R Houlston
Keyword(s):  
Technical Note ◽  
Second Order ◽  
Order System ◽  
System Modelling ◽  
Direct Control ◽  
Space System ◽  
First Order ◽  
The Reformation ◽  
State Space System ◽  
Second Order Systems

This technical note concerns the reformation of a second-order system from an arbitrary first-order system. At present, the majority of control literature is concerned with controlling systems within the first-order linearization of a system. The author is part of a growing community looking to expand the direct control of second-order systems and the benefits associated in doing so. However, there are potential stages of system modelling that may result in it being necessary to form the first-order form of the system, such as model reduction. This may have the effect of destroying the second-order notion of the system. The purpose of this note is to regain the structure of the second-order system and thus enable the benefits of direct second-order control to be realized. Although the problem itself has been previously resolved, the author proposes the virtue of a simpler method.

scholarly journals Second-Order Systems With Singular Mass Matrix and an Extension of Guyan Reduction

1995 ◽  
Author(s):  
Sanjay P. Bhat ◽  
Dennis S. Bernstein
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mass Matrix ◽  
Regular System ◽  
Second Order ◽  
Order System ◽  
Coupled Subsystems ◽  
Singular Mass Matrix ◽  
Guyan Reduction ◽  
Second Order Systems

Abstract The set of consistent initial conditions for a second-order system with singular mass matrix is obtained. In general, such a system can be decomposed (i.e., partitioned) into three coupled subsystems of which the first is algebraic, the second is a regular system of first-order differential equations, and the third is a regular system of second-order differential equations. Under specialized conditions, these subsystems are decoupled. This result provides an extension of Guyan reduction to include viscous damping.

Approximate Decoupling of Weakly Nonclassically Damped Linear Second-Order Systems Under Harmonic Excitations

1993 ◽  
Vol 115 (1) ◽  
pp. 214-218 ◽  
Author(s):  
S. M. Shahruz ◽  
A. K. Packard
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Approximation Error ◽  
Second Order ◽  
Order System ◽  
Damping Matrix ◽  
Approximation Errors ◽  
Harmonic Excitations ◽  
Second Order Systems ◽  
Damped Systems

A simple and commonly used approximate technique of solving the normalized equations of motion of a nonclassically damped linear second-order system is to decouple the system equations by neglecting the off-diagonal elements of the normalized damping matrix, and then solve the decoupled equations. This approximate technique can result in a solution with large errors, even when the off-diagonal elements of the normalized damping matrix are small. Large approximation errors can arise in lightly damped systems under harmonic excitations when some of the undamped natural frequencies of the system are close to the excitation frequency. In this paper, a rigorous analysis of the approximation error in lightly damped systems is given. Easy-to-check conditions under which neglecting the off-diagonal elements of the normalized damping matrix can result in large approximation errors are presented.

Structure Preserving Transformations and Isospectral Flows for Second Order Systems

2003 ◽  
Author(s):  
Michael I. Friswell ◽  
Seamus D. Garvey ◽  
Uwe Prells
Keyword(s):  
State Space ◽  
State Vector ◽  
Second Order ◽  
The State ◽  
Order System ◽  
Coordinate Transformations ◽  
Structure Preserving ◽  
Characteristic Behaviour ◽  
Second Order Systems ◽  
Parameter Values

When the dynamics of any general second order system are cast in a state-space format, the initial choice of the state-vector usually comprises one partition representing system displacements and another representing system velocities. Coordinate transformations can be defined which result in more general definitions of the state-vector. This paper discusses the general case of coordinate transformations of state-space representations for second order systems. It identifies one extremely important subset of such coordinate transformations — namely the set of structure-preserving transformations for second order systems — and it highlights the importance of these. It shows that one particular structure-preserving transformation results in a new system characterised by real diagonal matrices and presents a forceful case that this structure-preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems — in preference to the eigenvalue-eigenvector solutions conventionally accepted. The regular λ-matrix λ2M + λD + K with M,D,K ∈ Rn×n defines a second-order system. A one-parameter trajectory of such a system {M(t),D(t),K(t)} is an isospectral flow (or more correctly an equivalence flow) if the eigenvalues and the dimensions of the associated eigenspaces are the same for all parameter values t ∈ R. This paper presents the general form for real isospectral flows of real-valued second order systems.

scholarly journals Detection of Short-Step Pulses Using Practical Test-Functions and Resonance Aspects

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Alexandru Toma ◽  
Cristian Morarescu
Keyword(s):  
Second Order ◽  
Order System ◽  
Time Interval ◽  
Limited Time ◽  
Large Step ◽  
Working Frequency ◽  
Second Order Systems ◽  
Intelligent Methods ◽  
Physical Quantities ◽  
Limited Time Interval

An important aspect in modeling dynamic phenomena consists in measuring with higher accuracy some physical quantities corresponding to the dynamic system. Yet for measurements performed on limited time interval at high working frequency, certain intelligent methods should be added. The high working frequency requires that the measurement and data processing time interval should be greater than the time interval when the step input is received, so as to allow an accurate measurement. This paper will show that an intelligent processing method based on oscillating second-order systems working on limited time interval can differentiate between large step inputs (which are active on the whole limited time interval) and short step inputs (which are active on a time interval shorter than the limited working period). Some resonance aspects (appearing when the input frequency is close to the working frequency of the oscillating second-order system) will be also presented.

Computer Assisted Displays Enabling Internalization and Reduction of Operator Workload in Higher Order Systems, or, Pushing the Barrier of Human Control beyond Second Order Systems

1980 ◽  
Vol 24 (1) ◽  
pp. 59-62 ◽  
Author(s):  
Ray Eberts ◽  
Walter Schneider
Keyword(s):  
Control Systems ◽  
Higher Order ◽  
Second Order ◽  
Order System ◽  
Computer Assisted ◽  
Engineering Practice ◽  
Human Control ◽  
Control Functions ◽  
Second Order Systems ◽  
Operator Workload

It has long been known that the control of high order systems (second order and above) is much more difficult than controlling lower order systems. In order to make the higher order system more controllable, research and engineering practice have emphasized removing the operator from the direct control of the vehicle, reducing the order of control of the system (by quickening), and designing displays that predict the path of the vehicle. These methods have been developed to try to compensate for the inability of operators to master higher order control functions. We are proposing a novel type of display indicator which allows subjects to spatially control and conceptualize higher order control systems.

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