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Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 4, pp. 219—231
DOI: 10.17587/mau.19.219-231

Synthesis Robust H_¥ -Regulator of the Low Order by using of Linear Matrix Inequalities and Projective Lemmas

V. I. Krasnoshchechenko, kviip@yandex.ru, Kaluga Branch of the Bauman Moscow State Technical University, Kaluga, 248600, Russian Federation

Corresponding author: Krasnoshchechenko Vladimir I., Ph. D., Senior Lecturer, Kaluga Branch of the Bauman Moscow State Technical University, Kaluga, 248600, Russian Federation, e-mail: kviip@yandex.ru

Accepted on November 24, 2017

In this article the direct method of synthesis of a robust regulator of the low order is considered. For synthesis robust Н?-regulator of the low order for plant with polytopic uncertainty are using bounded real lemma for linear matrix inequalities and two procedures of projection: 1) the projective lemma for linear matrix inequalities and 2) projection of nonnegative matrixes to reduced space also nonnegative matrixes. At the first stage of design the weakened problem with a convex linear matrix inequality is solved. For performance of not convex rank condition a procedure of orthogonal projection of singular value decomposition of a matrix and by rejection zero singular values is used. The order reduction a regulator is carried out by rejection small singular values. The submitted algorithm of synthesis of the reduced regulator is considered on an example of synthesis of robust regulator for plant with polytopic uncertainty. The plant is a satellite connected by a flexible boom with the sensor package (two-mass system). It is necessary to control angular position of the sensor package on which there is a star sensor and the sensor of angular position of the package, and the actuator control by angular position of the satellite. In view of no rigid connections inconsistency of movements of the actuator and the sensor of angular position of the sensor package takes place, i.e. there is a noncollocated system. Synthesis of a robust regulator for the weak damping plant of the fourth order with polytopic uncertainty is in detail considered. It is shown, that the order of a regulator it is possible to lower with initial the fourth to the second at insignificant deterioration of performance. specifications.
Keywords: robust, linear matrix inequalities, a projective lemma, polytopic uncertainty, two-mass system, a regulator of the low order

For citation:
Krasnoshchechenko V. I. Synthesis Robust H_¥-Regulator of the Low Order by using of Linear Matrix Inequalities and Projective Lemmas, Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 4, pp. 219—231.

DOI: 10.17587/mau.19.219-231

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