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

By Jean Levine

ISBN-10: 3642008380

ISBN-13: 9783642008382

This is the 1st ebook on a sizzling subject within the box of keep watch over of nonlinear structures. It levels from mathematical procedure conception to sensible business regulate purposes and addresses primary questions in structures and regulate: how you can plan the movement of a process and song the corresponding trajectory in presence of perturbations. It emphasizes on structural points and specifically on a category of structures known 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, car equipments, cranes, and automated flight regulate systems.

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

Show description

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

Best differential geometry books

Morse Theory for Hamiltonian Systems

This learn observe explores lifestyles and multiplicity questions for periodic strategies of first order, non-convex Hamiltonian platforms. It introduces a brand new Morse (index) thought that's more straightforward to take advantage of, much less technical, and extra versatile than latest theories and contours strategies and effects that, previously, have seemed merely in scattered journals.

Harmonic maps

Specific services and q-series are presently very energetic components of analysis which overlap with many different components of arithmetic, reminiscent of illustration concept, classical and quantum teams, affine Lie algebras, quantity concept, harmonic research, and mathematical physics. This booklet offers the cutting-edge of the topic and its purposes

Additional resources for Analysis and Control of Nonlinear Systems: A Flatness-based Approach

Example text

Fp )T ∼ fi (x) i=1 ∂ ∂xi 22 2 Introduction to Differential Geometry the sign ∼ meaning “identified with”. In the sequel, we systematically make p ∂ the abuse of notation f = (f1 , . . , fp )T = i=1 fi (x) ∂x . i Note that it results from this definition (exercise) that the Lie derivative formula is not affected by changes of coordinates3 : Lf h(x) = Lϕ∗ f (h ◦ ϕ−1 )(y). 7. In an open set U of R2 with coordinates (x, t), we consider v the vector field f (t, x) = where v is an arbitrary real number, and the 1 function h(t, x) = x−vt from U to R.

Dxjr ∈ Λk+r (X). ,jr An obvious consequence of the skew-symmetry is that every form of degree higher than p on a p-dimensional manifold vanishes identically. 24) where ω is a 1-form defined, as before, by ω = i ωi dxi . The previous formula shows that if h is a C ∞ function from X to R and if ω ∈ Λ1 (X), the (usual) product hω belongs to Λ1 (X) and the exterior derivative of this product satisfies d(hω) = dh ∧ ω + hdω. 25) for all ω, θ ∈ Λ1 (X), since then dω ∧ θ and ω ∧ dθ are 3-forms. This results from the fact that ω ∧ θ = j ωj dxj ∧ ( k θk dxk ) = j,k ωj θk dxj ∧ dxk .

Gk (x)) = k for all x ∈ V . Let us introduce the distribution D given by D(x) = span {g1 (x), . . , gk (x)} for all x ∈ V . 18), since L[gi ,gj ] y = Lgi (Lgj y) − Lgj (Lgi y) = 0 − 0 = 0, we have Lg y = 0 for every g ∈ D. Conversely, since g1 , . . , gk are linearly independent, one can find regular vector fields gk+1 , . . , gr such that g1 , . . , gr form a basis of D(x) at every point of V and Lg y = 0 for every g ∈ D implies that Lgi y = 0 for i = 1, . . 18). By Frobenius Theorem, a necessary and sufficient condition for D to be straightened out in V is that D is involutive.

Download PDF sample

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

by Michael

Rated 4.90 of 5 – based on 34 votes