Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On Relation Between Modal Controllability of Dynamic MIMO-system by Output and a Type of Matrices with Desirable Spectra

Author(s):

Nikolay Evgenievich Zubov

Dr. Sci. (Eng.), Professor
Professor of Dep. “Automatic Control Systems”, Dean of “Rocket and Space Techniques” faculty at Bauman MSTU
(Russia, 105005, Moscow, 2-nd Bauman Street, Building 5)

Nik.Zubov@gmail.com

Alexey Vladimirovich Lapin

Cand. Sci. (Eng.)
Senior Lecturer of Dep. “Automatic Control Systems” at Bauman MSTU
(Russia, 105005, Moscow, 2-nd Bauman Street, Building 5)

AlexeyPoeme@yandex.ru

Vladimir Nikolaevich Ryabchenko

Dr. Sci. (Eng.), Associate Professor
Senior Technologist of JSC “RDC at FGC of UES”
(Russia, 115201, Moscow, Kashirskoe highway, House 22, Building 3)
Professor of Dep. “Automatic Control Systems” at Bauman MSTU
(Russia, 105005, Moscow, 2-nd Bauman Street, House 5)

Ryabchenko.VN@yandex.ru

Abstract:

We consider a task of providing the modal controllability by output vector in linear dynamic systems at not completely measured vector of state applying decomposition method of control synthesis based on Van der Woude approach. It is typical that at meeting the condition «dimension of vector of control plus dimension of vector of observe is more than dimension of object of control» modal controllability of closed-loop system as a whole is provided not for all possible types of matrices with desirable spectrum which are assigned or calculated within decomposition of multi-dimension systems. It is shown that modal controllability by output is determined by whether a matrix with whatever desirable spectrum at zero level exists, which provides a solvability of linear matrix equation of relation between matrices of controllers by state and by output. We offer keeping the desirable spectra to set specified matrices in triangular form or to calculate them basing on equations formed in a certain way. At such approach modal controllability by output is provided regardless of ratios between the parameters of system and spectra at top levels of decomposition and calculation of matrices with desirable spectra is simplified at bottom levels. An example of applying the described approach is given at synthesis of controller by output for linear stationary automatic control system of 6th order containing 3 control inputs and 4 measured outputs. The results of mathematical simulation confirm the feasibility of application of suggested approaches.

Keywords

References:

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