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Concept# Time-variant system

Résumé

A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently to the same input at different times. The opposite is true for time invariant systems (TIV).
Overview
There are many well developed techniques for dealing with the response of linear time invariant systems, such as Laplace and Fourier transforms. However, these techniques are not strictly valid for time-varying systems. A system undergoing slow time variation in comparison to its time constants can usually be considered to be time invariant: they are close to time invariant on a small scale. An example of this is the aging and wear of electronic components, which happens on a scale of years, and thus does not result in any behaviour qualitatively different

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Théorie du contrôle

En mathématiques et en sciences de l'ingénieur, la théorie du contrôle a comme objet l'étude du comportement de systèmes dynamiques paramétrés en fonction des trajectoires de leurs paramètres.

System analysis

System analysis in the field of electrical engineering characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio

Réponse impulsionnelle

vignette|300px|right|Réponses impulsionnelles d'un système audio simple (de haut en bas) : impulsion originale à l'entrée, réponse après amplification des hautes fréquences et réponse après amplificat

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Victor Constantin, Pascal Fua, Sina Honari, Helge Jochen Rhodin, Mathieu Salzmann

In this paper we propose an unsupervised feature extraction method to capture temporal information on monocular videos, where we detect and encode subject of interest in each frame and leverage contrastive self-supervised (CSS) learning to extract rich latent vectors. Instead of simply treating the latent features of nearby frames as positive pairs and those of temporally-distant ones as negative pairs as in other CSS approaches, we explicitly disentangle each latent vector into a time-variant component and a time-invariant one. We then show that applying contrastive loss only to the time-variant features and encouraging a gradual transition on them between nearby and away frames while also reconstructing the input, extract rich temporal features, well-suited for human pose estimation. Our approach reduces error by about 50% compared to the standard CSS strategies, outperforms other unsupervised single-view methods and matches the performance of multi-view techniques. When 2D pose is available, our approach can extract even richer latent features and improve the 3D pose estimation accuracy, outperforming other state-of-the-art weakly supervised methods.

2022Among the various logical components of a phasor measurement unit (PMU), the synchrophasor estimation (SE) algorithm definitely represents the core one. Its choice is driven by two main factors: its accuracy in steady state and dynamic conditions as well as its computational complexity. Most of the SE algorithms proposed in the literature are based on the direct implementation of the Discrete Fourier Transform (DFT). This is due to the relatively low computational complexity of such technique and to the inherent DFT capability to isolate and identify the main tone of a discrete sinusoidal signal and to reject closeby harmonics. Nevertheless, these qualities come with non-negligible drawbacks and limitations that typically characterize the DFT: mainly they refer to the fact that the DFT theory assumes a periodic signal with time-invariant parameters, at least along the observation window. The latter, from one side should be as short as possible to be closer to the above-mentioned quasi-steady-state hypothesis also during power system transient; on the other hand, longer windows are needed when interested in rejecting and isolating harmonic and inter-harmonic signals that are quite frequent in power systems. In this respect, this chapter first analyses the DFT with a particular focus on the origin of the well-known aliasing and spectral leakage effects. Then it formulates and validates in a simulation environment a novel SE algorithm, hereafter referred as iterative-Interpolated DFT (i-IpDFT), which considerably improves the accuracies of classical DFT- and IpDFT-based techniques and is capable of keeping the same static and dynamic performances independently of the adopted window length that can be reduced down to two cycles of signal at the nominal frequency of the power system. This chapter is organized as follows: Section 3.2 introduces the nomenclature and some basic concepts in the field of synchrophasors. Section 3.3 presents the theoretical background of the DFT, with a specific focus on the detrimental effects of aliasing and spectral leakage. Next, Section 3.4 discusses advantages and drawbacks of DFT-based SE algorithms and derives the analytical formulation of the i-IpDFT method. Finally, Section 3.5, after illustrating the procedure presented in Reference 1 to assess the performances of a PMU, analyses the performances of the i-IpDFT algorithm using two of the testing conditions presented in Reference 1 and compares them with those of the classical IpDFT technique.

Karim Achouri, Christophe Caloz

We aim at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in recent developments of the field. We provide a general definition of nonreciprocity and classify nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV), or nonlinear natures. The theory of nonreciprocal systems is established on the foundation formed by the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking, and related OnsagerCasimir relations. Special attention is given to LTI systems, the most-common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energyconservation considerations. An overview of the fundamental characteristics and applications of LTI, LTV, and nonlinear nonreciprocal systems is given with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.

Cours associés (8)

Introduction to the basic techniques of image processing. Introduction to the development of image-processing software and to prototyping in JAVA. Application to real-world examples in industrial vision and biomedical imaging.

Identification of discrete-time linear models using experimental data is studied. The correlation method and spectral analysis are used to identify nonparametric models and the subspace and prediction error methods to estimate the plant and noise model parameters. Hands-on labs are included.

The course covers control theory and design for linear time-invariant systems : (i) Mathematical descriptions of systems (ii) Multivariables realizations; (iii) Stability ; (iv) Controllability and Observability; (v) Minimal realizations and coprime fractions; (vi) Pole placement and model matching.

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