Search results for "linearization"
showing 10 items of 115 documents
Pseudo-force method for a stochastic analysis of nonlinear systems
1996
Nonlinear systems, driven by external white noise input processes and handled by means of pseudo-force theory, are transformed through simple coordinate transformation to quasi-linear systems. By means of Itô stochastic differential calculus for parametric processes, a finite hierarchy for the moment equations of these systems can be exactly obtained. Applications of this procedure to the first-order differential equation with cubic nonlinearity and to the Duffing oscillator show the versatility of the proposed method. The accuracy of the proposed procedure improves by making use of the classical equivalent linearization technique.
Symmetric identities in graded algebras
1997
Let P k be the symmetric polynomial of degree k i.e., the full linearization of the polynomial x k . Let G be a cancellation semigroup with 1 and R a G-graded ring with finite support of order n. We prove that if R 1 satisfies $ P_k \equiv 0 $ then R satisfies $ P_{kn} \equiv 0 $ .
Linearization of holomorphic mappings on fully nuclear spaces with a basis
1994
In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].
Input-Output Feedback Linearization Control of a Linear Induction Motor Taking Into Consideration Its Dynamic End-Effects and Iron Losses
2020
This article proposes a new input-output feedback linearization control (FLC) technique of linear induction motors (LIMs), taking into consideration both the dynamic end-effects and the iron losses. Starting from a previously conceived dynamic model, including the dynamic end-effects and the iron losses, all the theoretical framework of the FLC has been developed. The proposed FLC improves a previous version of FLC in accounting also the iron losses, which in LIMs with fixed-secondary sheet play a pivotal role more than in rotating induction motors (RIMs). The proposed FLC has been experimentally tested on a suitably developed test setup, and experimental comparisons between the proposed FL…
Input-Output Feedback Linearization Control of Linear Induction Motors Including the dynamic End-Effects
2014
This paper proposes the theoretical framework and the consequent application of the input-output feedback linearization (FL) control technique to linear induction motors (LIM). LIM, additionally to RIM, presents other strong non-linearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. The proposed approach has been validated experimentally on a suitably developed test set-up. Furt…
Experimental validation of a direct pre-design formula for TLCD
2014
The passive control of vibrations has received in recent years a great deal of attention from researchers. Several types of devices have been proposed in order to reduce the dynamic responses of different kinds of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) has proved to be very effective in reducing vibration of structures. However, since the equations governing the TLCD controlled systems response is nonlinear, the calibration of TLCD parameters is time consuming and not convenient to perform in a pre-design phase. In this context, it has recently been introduced by the authors a formula that allows to choose the optimal parameters of TLCD in a direct and fast wa…
A pedagogical flight simulator for longitudinal airplane flight
2009
This article presents a bi-dimensional model of flight and describes the implementation of a flight simulator able to describe the different phases of longitudinal flight of a real airplane. After identifying the relevant physical variables, the equations of motion are written and solved using a numerical integration method. Using computer simulations, flight paths and time evolution of the kinematics variables are analyzed for a complete flight of a light commercial airplane. The simulations take into account and reproduce the basic actions of a pilot to control the flight. The main maneuvers involved in pilotage are also predicted and explained in terms of model parameter variations induc…
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
2003
This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of…
Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially o…
2014
In the near future, millions of load curves measuring the electricity consumption of French households in small time grids (probably half hours) will be available. All these collected load curves represent a huge amount of information which could be exploited using survey sampling techniques. In particular, the total consumption of a specific cus- tomer group (for example all the customers of an electricity supplier) could be estimated using unequal probability random sampling methods. Unfortunately, data collection may undergo technical problems resulting in missing values. In this paper we study a new estimation method for the mean curve in the presence of missing values which consists in…
Functional Principal Components Analysis with Survey Data
2008
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. FPCA relies on estimations of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and convergent. Under mild assumptions, asymptotic variances are derived for the FPCA’ estimators and convergent estimators of them are proposed. Our approach is illustrated with a simulation study and we…