Jean Levine's Analysis and Control of Nonlinear Systems: A Flatness-based PDF

By Jean Levine

ISBN-10: 3642008380

ISBN-13: 9783642008382

This is the 1st booklet on a scorching subject within the box of keep watch over of nonlinear structures. It levels from mathematical approach thought to sensible commercial keep watch over purposes and addresses primary questions in structures and regulate: the best way to plan the movement of a procedure and song the corresponding trajectory in presence of perturbations. It emphasizes on structural elements and particularly on a category of structures referred to as differentially flat.

Part 1 discusses the mathematical conception and half 2 outlines purposes of this technique within the fields of electrical drives (DC automobiles and linear synchronous motors), magnetic bearings, automobile equipments, cranes, and automated flight keep an eye on systems.

The writer bargains web-based video clips illustrating a few dynamical elements and case reviews in simulation (Scilab and Matlab).

Show description

Read or Download Analysis and Control of Nonlinear Systems: A Flatness-based Approach PDF

Similar differential geometry books

Download e-book for iPad: An Introduction To Differential Geometry With Use Of Tensor by Luther Pfahler Eisenhart

A few of the earliest books, relatively these relationship again to the 1900s and sooner than, at the moment are super scarce and more and more pricey. we're republishing those vintage works in cheap, prime quality, sleek variants, utilizing the unique textual content and paintings.

Download e-book for kindle: Parabolic Geometries I (Mathematical Surveys and Monographs) by Andreas Cap and Jan Slovak

Parabolic geometries surround a truly diversified category of geometric constructions, together with such vital examples as conformal, projective, and virtually quaternionic constructions, hypersurface kind CR-structures and diverse varieties of commonly used distributions. The attribute characteristic of parabolic geometries is an similar description through a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie staff by means of a parabolic subgroup).

Variational principles for second-order differential by Joseph Grifone, Zoltan Muzsnay PDF

During this booklet the writer has attempted to use "a little mind's eye and pondering" to modelling dynamical phenomena from a classical atomic and molecular viewpoint. Nonlinearity is emphasised, as are phenomena that are elusive from the continuum mechanics viewpoint. FORTRAN programmes are supplied within the appendices An advent to formal integrability conception of partial differential structures; Frolicher-Nijenhuis thought of derivations; differential algebraic formalism of connections; precious stipulations for variational sprays; obstructions to the integrability of the Euler-Lagrange process; the type of in the neighborhood variational sprays on two-dimensional manifolds; Euler-Lagrange platforms within the isotropic case

Extra info for Analysis and Control of Nonlinear Systems: A Flatness-based Approach

Sample text

2 that an instationary vector field on a manifold X may be seen as a stationary one on the augmented manifold X × R. However, we’ll see that many properties of stationary vector fields do not extend to time-varying ones. In particular, an arbitrary change of coordinates would change (x, t) in (z, s) = ϕ(x, t), s playing the role of a new clock, the sign of s˙ being arbitrary. Therefore, if the sign of s˙ changes along an integral curve, we may lose the possibility of capturing the asymptotic properties of the system (when t → ±∞) in the transformed coordinates.

We immediately deduce that L[ϕ∗ f1 ,ϕ∗ f2 ] h(ϕ(x)) = L[f1 ,f2 ] h(ϕ(x)), which proves the Proposition. The bracket[f, g] has the following geometric interpretation: let us denote def by Xt (x) = exp tf (x), by analogy with the solution of a linear differential equation, the point of the integral curve of f at time t passing through the point x at time 0. This notation allows to precise which vector field is considered when several vector fields may be integrated. Thus, the point of the integral curve of g at time t passing through x at time 0 is noted exp tg(x).

P ) such that ξ ∈ ϕ(V ). The solution y is thus immediately deduced from z by y = z ◦ ϕ. In the case where D is not involutive and if D has constant rank r, we follow the same lines with D in place of D. 18). The supplementary equations generated by the vector fields of D that are not in D are often called compatibility conditions. It results that D cannot be straightened out without simultaneously straightening out D, which implies that z(ξ) = z(ξ) for all ξ = (ξr+1 , . . , ξp ) such that ξ ∈ ϕ(V ).

Download PDF sample

Analysis and Control of Nonlinear Systems: A Flatness-based Approach by Jean Levine


by Donald
4.0

Rated 4.38 of 5 – based on 50 votes