WA2 Some LMI Problems in Control (invited)

Organized by: Garcia G., LAAS-CNRS, France Bernussou J., LAAS-CNRS, France

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Output-reference tracking problem for discrete-time systems with input saturations and constant references

Authors:

Tarbouriech S., LAAS-CNRS, France

Queinnec I., LAAS-CNRS, France

Pittet C. - LAAS-CNRS, France

ABSTRACT

Nonlinear state feedback controllers are exhibited for locally stabilizing linear discrete-time systems with both saturating actuators and additive disturbances when the output must track a certain reference level. The objective is then to bring the steady-state error due to disturbances to zero by using a saturated controller and a dead-zone function. Thus, we want to determine both a stabilizing controller and a region of the state space over which the stability of the resulting closed-loop system is ensured, when the controls are allowed to saturate.

wa2-1

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A Multi-Objective Control Algorithm: application to a launcher with bending modes

Authors:

Clement B., Ecole Superieure d' Electricite, France

Duc G., Ecole Superieure d' Electricite, France

ABSTRACT

A multi-objective control synthesis algorithm is first presented: it allows to avoid conservatism using different Lyapunov functions by combining the Youla parameterization, an observer-based structure and congruence transformations to obtain an LMI formulation. The efficiency of this approach is then tested by considering the problem of robustly stabilizing an aerospace launcher during the atmospheric flight.

Key Words. Robust control, LMI optimization, Youla parameterization, Aerospace.

wa2-2

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Guaranteed cost and positive real uncertainty

Authors:

Bernussou J., LAAS-CNRS, France

Garcia G., LAAS-CNRS, France

Geromel J., LAC-DT, School of Electrical Eng., UNICAMP, Brazil

ABSTRACT

This paper presents a kind of overview of the quadratic guaranteed cost problem in face of positive real uncertainty. Continuous as well as discrete time systems are discussed to point out the main discrepancies and difficulties arising when considering the different stability conditions associated with the positive real and strongly positive real conditions. The state feedback control problem is only addressed.

wa2-3

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Observers interpolation for state reconstruction of Linear Parameter Varying (LPV) systems: A LMI approach

Authors:

Bara I., CRAN-INPL-ENSEM, France

Daafouz J., CRAN-INPL-ENSEM, France

Kratz F., CRAN-INPL-ENSEM, France

Ragot J., CRAN-INPL-ENSEM, France

ABSTRACT

This paper invistigates a state observation design problem for dis- crete time linear parameter varying (LPV) systems. The main contribution of this paper consists in providing an interpolation scheme to build the LPV observer. We show that an appropriate choice of the interpolation functions allow to use available quadratic stability conditions to design an LPV observer.

Key Words. LPV systems, LPV Observers, Interpolation, Quadratic stability.

wa2-4

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Synthesis of a non-integer control loop using performance contours

Authors:

Pommier V., Universite Bordeaux I, France

Oustaloup A., Universite Bordeaux I, France

Lanusse P., Universite Bordeaux I, France

ABSTRACT

The article proposes a method to design a controller ensuring dynamic behavior of a closed-loop control. Dynamic performance is, in the time domain, the first overshoot of the step response, and the damping ratio and the natural frequency of its dominant oscillatory mode. Dynamic performance is quantified, in the frequency domain, by two contours called “performance contours” and the open-loop gain crossover frequency. The first contour is the Nichols chart magnitude contour which can be considered as an iso-overshoot contour. The second contour, whose construction and analytic expression are given in this article, is a new contour defined in the Nichols plane and parameterized by the damping ratio. The proposed method uses complex non-integer (or fractional) differentiation to compute a transfer function whose open-loop Nichols locus tangents both performance contours, thus ensuring stability margins (or stability degree).

Key words: Dynamic behavior, Stability margins, Overshoot, Damping ratio, Fractional differo-integration

wa2-5

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