254 research outputs found
A Structurally Flat Triangular Form Based on the Extended Chained Form
In this paper, we present a structurally flat triangular form which is based
on the extended chained form. We provide a complete geometric characterization
of the proposed triangular form in terms of necessary and sufficient conditions
for an affine input system with two inputs to be static feedback equivalent to
this triangular form. This yields a sufficient condition for an affine input
system to be flat.Comment: arXiv admin note: substantial text overlap with arXiv:2002.0120
A triangular canonical form for a class of 0-flat nonlinear systems
International audienceThis article proposes a triangular canonical form for a class of 0-flat nonlinear systems. Necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0-flat canonical form, which enables us to compute the flat output as well
A Flat System Possessing no (x,u)-Flat Output
In general, flat outputs of a nonlinear system may depend on the system's
state and input as well as on an arbitrary number of time derivatives of the
latter. If a flat output which also depends on time derivatives of the input is
known, one may pose the question whether there also exists a flat output which
is independent of these time derivatives, i.e., an (x,u)-flat output. Until
now, the question whether every flat system also possesses an (x,u)-flat output
has been open. In this contribution, this conjecture is disproved by means of a
counterexample. We present a two-input system which is differentially flat with
a flat output depending on the state, the input and first-order time
derivatives of the input, but which does not possess any (x,u)-flat output. The
proof relies on the fact that every (x,u)-flat two-input system can be exactly
linearized after an at most dim(x)-fold prolongation of one of its (new) inputs
after a suitable input transformation has been applied
Flat singularities of chained systems, illustrated with an aircraft model
We consider flat differential control systems for which there exist flat
outputs that are part of the state variables and study them using Jacobi bound.
We introduce a notion of saddle Jacobi bound for an ordinary differential
system for equations in variables. Systems with saddle Jacobi number
generalize various notions of chained and diagonal systems and form the widest
class of systems admitting subsets of state variables as flat output, for which
flat parametrization may be computed without differentiating the initial
equations. We investigate apparent and intrinsic flat singularities of such
systems. As an illustration, we consider the case of a simplified aircraft
model, providing new flat outputs and showing that it is flat at all points
except possibly in stalling conditions. Finally, we present numerical
simulations showing that a feedback using those flat outputs is robust to
perturbations and can also compensate model errors, when using a more realistic
aerodynamic model.Comment: 36 pages, 8 figure
Regelungstheorie
The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering
Control Theory: On the Way to New Application Fields
Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control
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