Search results for "Linear"
showing 10 items of 7165 documents
A nonlinear observer for rotor flux estimation considering magnetic saturation effects in induction motor drives
2015
This paper proposes a non-linear observer for In- duction Machine (IM) drives which takes into consideration the saturation effects. The non-linear observer is based on an original formulation of the dynamic model of the IM taking into consideration the magnetic saturation of the iron core. A Lyapunov based convergence analysis is proposed in order to suitably compute the observer gain guaranteeing the stability of the observer. The proposed non-linear observer has been tested in numerical simulation and experimentally on a suitably developed test set-up. Its behaviour has been compared to that obtained with a classic Full-Order Luenberger Observer (FOLO) in variable flux working conditions…
A Nonlinear Observer for Rotor Flux Estimation of Induction Motor Considering the Estimated Magnetization Characteristic
2017
This paper proposes a nonlinear observer for induction machine drives based on space-vector dynamic model of induction machine, expressed in state form, which presents the peculiarity of taking into consideration the magnetic saturation of the iron core. This observer is particularly suitable in order to obtain high accuracy in rotor flux estimation, in both amplitude and phase position, during working conditions characterized by varying flux, among which the most important are those during electrical losses minimization. A Lyapunov-based convergence analysis is proposed in order to suitably compute the numerical observer gain guaranteeing the convergence of the estimation error. The propos…
Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents
2021
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global at…
Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…
2018
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…
Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays
2010
This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using …
Linear flux observers for induction motors with quadratic Lyapunov certificates
2016
International audience; We propose a full order Linear Time-Varying (LTV) Luenberger observer for the rotor flux estimation of an induction motor. Introducing a suitable reduced-order Linear-Time-Invariant (LTI) system that is always observable and controllable, we show that any arbitrary LTI design and its quadratic Lyapunov certificates can be lifted to the higher-order original LTV dynamics obtaining the same certificates. As a result, we show that arbitrary global uniform exponential bounds can be imposed on the estimation error, regardless of the rotor speed. Then applying a suitable order reduction technique, we build a reduced observer providing the same guarantees. We also establish…
Control of uncertain highly nonlinear biological process based on Takagi–Sugeno fuzzy models
2015
This note deals with the control of uncertain highly nonlinear biological processes. Indeed, an adaptive fuzzy control (AFC) scheme is developed for the pre-treatment of wastewater represented by a Takagi-Sugeno (TS) fuzzy model. The proposed approach uses a fuzzy system to approximate the unknown substrate consumption rate in designing the adaptive controller, and then an observer is designed to estimate the concentration in substrate at the outlet bioreactor. The observer is employed to generate an error signal for the adaptive control law which permits to minimize the influence of the measurement noise on the estimation of the substrate concentration. An update of the fuzzy models parame…
Observer-based adaptive stabilization of a class of uncertain nonlinear systems
2014
In this paper, an adaptive output feedback stabilization method for a class of uncertain nonlinear systems is presented. Since this approach does not require any information about the bound of uncertainties, this information is not needed a priori and a mechanism for its estimation is exploited. The adaptation law is obtained using the Lyapunov direct method. Since all the states are not measurable, an observer is designed to estimate unmeasurable states for stabilization. Therefore, in the design procedure, first an observer is designed and then the control signal is constructed based on the estimated states and adaptation law with the σ-modification algorithm. The uniformly ultimately bou…
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
2015
The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a {hidden attractor} in the case of multistability as well as a classical {self-excited attractor}. The hidden attractor in this system can be localized by analytical-numerical methods based on the {continuation} and {perpetual points}. For numerical study of the attractors' dimension the concept of {finite-time Lyapunov dimension} is developed. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of {exact Lyapunov dimension} are discussed. A comparative survey on the computation of the finite-time Lyapunov expon…
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
2014
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance…