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Robust Pole Clustering of Parametric Uncertain Systems Using Interval Methods


Ratschan,  Stefan
Programming Logics, MPI for Informatics, Max Planck Society;

Vehi,  Josep
Max Planck Society;

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Ratschan, S., & Vehi, J. (2004). Robust Pole Clustering of Parametric Uncertain Systems Using Interval Methods. In Robust control design 2003: (ROCOND 2003); a proceedings volume from the 4th IFAC symposium (pp. 323-328). Oxford: Publ. for the International Federation of Automatic Control by Elsevier.

In this paper a new methodology to solve the pole clustering problem for parametric uncertain systems is introduced: The problem of clustering the closed loop poles into prescribed D-regions in the complex plane is stated as a quantified constraint problem that represents bounded uncertain parameters by intervals; and an engineering-oriented approach based on interval methods is developed to solve this quantified constraint problem. The result is a new, robust, reliable and design oriented method to deal with parametric uncertain systems. The methodology presented in this paper allows to find a good controller that places the closed loop poles in the desired location in the complex plane. In case there is no solution, the method allows also to "tune" the problem, either enlarging the pole locations or reducing the uncertainty domain. The approach presented in this paper can be used either for linear or non-linear systems and for any kind of parametric bounded uncertainty. Several simple examples illustrate the uses, limits and scope of the methodology.