Natural Observer Design for Singularly Perturbed Vector Second-Order Systems

2004 ◽  
Vol 127 (4) ◽  
pp. 648-655 ◽  
Author(s):  
Michael A. Demetriou ◽  
Nikolaos Kazantzis
Keyword(s):  
Singular Perturbation ◽  
System Dynamics ◽  
Slow Component ◽  
Estimation Error ◽  
Second Order ◽  
Observer Design ◽  
Order System ◽  
Observation Error ◽  
State Variables ◽  
Second Order Systems

Our aim in the present research study is to develop a systematic natural observer design framework for vector second-order systems in the presence of time-scale multiplicity. Specifically, vector second-order mechanical systems are considered along with fast sensor dynamics, and the primary objective is to obtain accurate estimates of the unmeasurable slow system state variables that are generated by an appropriately designed model-based observer. Within a singular perturbation framework, the proposed observer is designed on the basis of the system dynamics that evolves on the slow manifold, and the dynamic behavior of the estimation error that induces is analyzed and mathematically characterized in the presence of the unmodeled fast sensor dynamics. It is shown, that the observation error generated by neglecting the (unmodeled) fast sensor dynamics is of order O(ε), where ε is the singular perturbation parameter and a measure of the relative speed/time constant of the fast (sensor) and the slow component (vector second-order system) of the overall instrumented system dynamics. Finally, the performance of the proposed method and the convergence properties of the natural observer designed are evaluated in an illustrative example of a two-degree of freedom mechanical system.

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.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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.

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.

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 System identification applied to a single area electric power system under frequency response

2021 ◽  
Vol 22 (3) ◽  
pp. 1236
Author(s):  
José Angel Barrios ◽  
F. Sanchez ◽  
Francisco Gonzalez-Longatt ◽  
Gianfranco Claudio
Keyword(s):  
Transfer Function ◽  
Power System ◽  
Electric Power ◽  
Simulation Analysis ◽  
Estimation Error ◽  
Hydraulic Turbine ◽  
Electric Power System ◽  
Order System ◽  
Generalized Poisson ◽  
Second Order Systems

This research paper proposes a methodology to apply identification methods to find a simplified model of three different governors in a single area electric power system (SAEPS). A SAEPS with different governors-turbine is presented: a hydraulic turbine, a steam turbine and a steam reheat turbine. In this same investigation, an analytic reduction has been performed, a fifth order system was found analytically, thus a transfer function equivalent to the three different governor-turbine elements was obtained, this equivalent transfer function models the complete behavior of the three devices. Two systems identification (SI) algorithms have been proposed to apply them to this generic subspace state-space (N4SID) and generalized poisson moment functionals (GPMF) electrical system, these presented similar results. The results of the performance and simulation analysis exhibit that using the SI technique, fifth, fourth and third-order systems were obtained that graphically show a very small estimation error compared to the original signal, this fact could be check simulating the simplified models using the same input-output data. The results are presented in a table that shows a comparison of the model respond the fifth, fourth, third and second-order systems.

Performance Study of a Bat Searching Algorithm From System Dynamics Perspective

2019 ◽  
Author(s):  
Haopeng Zhang ◽  
Nathan Schutte
Keyword(s):  
System Dynamics ◽  
Optimization Problems ◽  
Second Order ◽  
Point Of View ◽  
Great Success ◽  
Performance Study ◽  
Step Size ◽  
Discrete Time Systems ◽  
Second Order Systems ◽  
Time Systems

Abstract In this paper, the performance of a bat searching algorithm is studied from system dynamics point of view. Bat searching algorithm (BA) is a recently developed swarm intelligence based optimization algorithm which has shown great success when solving complicated optimization problems. Each bat in the BA has two main states: velocity and position. The position represents the solution of the optimization problems while the velocity represents the searching direction and step size during each iteration. Due to the nature of the update equations, the dynamics of the bats are formulated as a group of second-order discrete-time systems. In this paper, the performance of the algorithm is analyzed based on the nature of the responses in the second-order systems. The over-damped response, under-damped responses are studied and the parameters requirements are derived. Moreover, unstable scenarios of the bats are also considered when examining the performance of the algorithm. Numerical evaluations are conducted to test different choices of the parameters in the BA.

Sign in / Sign up

Export Citation Format

Share Document