79,154 research outputs found
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Non-linear estimation is easy
Non-linear state estimation and some related topics, like parametric
estimation, fault diagnosis, and perturbation attenuation, are tackled here via
a new methodology in numerical differentiation. The corresponding basic system
theoretic definitions and properties are presented within the framework of
differential algebra, which permits to handle system variables and their
derivatives of any order. Several academic examples and their computer
simulations, with on-line estimations, are illustrating our viewpoint
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
On the computation of -flat outputs for differential-delay systems
We introduce a new definition of -flatness for linear differential delay
systems with time-varying coefficients. We characterize - and -0-flat
outputs and provide an algorithm to efficiently compute such outputs. We
present an academic example of motion planning to discuss the pertinence of the
approach.Comment: Minor corrections to fit with the journal versio
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