Einladung zum Vortrag im Kolloquium Technische Kybernetik

Robust nonlinear tracking control based on differential flatness

Dr. Veit Hagenmeyer

    Zeit: Dienstag · 12. 11. 2002 · 16:00 Uhr
    Ort: Hörsaal V 9. 31 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

In this talk, the concept of exact feedforward linearisation based on differential flatness is introduced. Instead of feedback linearising differentially flat systems, their structure is used to design nominal feedforward inputs which linearise the nonlinear system under the knowledge of the initial condition. Moreover it is proven that a unique solution exists in the cases, in which the initial condition considered for the nominal feedforward is not equal but close to the right initial condition.
The notion of exact feedforward linearisation based on differential flatness furthermore indicates the way, in which the aforementioned nominal feedforward should be combined with any kind of feedback to stabilise deviations from the desired trajectory. Stability of this control scheme can be demonstrated when using simple extended PID controls for the feedback part by considering a stability result from Kelemen. Thereby the two different tasks of designing the velocity of the desired trajectory and of choosing the controller coefficients have to be traded off carefully.
This is important with respect to the practicability of the proposed methodology: in the case of a given flat nonlinear system, for which there already exists a linear PID-like controller stabilising the system in the vicinity of an operation point, a nonlinear nominal feedforward based on flatness plus the existing PID-like controller can achieve very good tracking or set point changes.
In view of industrial applications the robustness analysis of the proposed methodology is introduced making use of results issued from interval analysis. A comparison of parametric robustness of exact feedforward linearisation based on differential flatness with exact feedback linearisation is presented.
Experimental results of the application of exact feedforward linearisation combined with an existing PID-controller to a magnetic levitation system show the performance of the proposed control strategy.

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