DOI:https://doi.org/10.15407/kvt201.03.033
Cybernetics and Computer Engineering, 2020, 3(201)
ZHITECKII L.S.1, PhD (Engineering),
Acting Head of the Intelligent Automatic Systems Department
e-mail: leonid_zhiteckii@i.ua
AZARSKOV V.N.2, DSc. (Engineering), Professor,
Head of the Aerospace Control Systems Department,
e-mail: azarskov@nau.edu.ua
SUSHCHENKO O.A.2, DSc. (Engineering), Professor,
Professor of the Aerospace Control Systems Department,
e-mail: sushoa@ukr.net
YANOVSKY F.J.2, DSc. (Engineering), Professor,
Head of the Department of Electronics, Robotics,
Monitoring and IoT Technologies
e-mail: yanovsky@nau.edu.ua
SOLOVCHUK K.Yu.3,
Senior Lecturer at the Higher and Applied Mathematics Department
e-mail: solovchuk_ok@ukr.net
1 International Research and Training Center for Information Technologies
and Systems of the NAS of Ukraine
and MES of Ukraine, Kyiv, Ukraine,
40, Acad. Glushkov av., Kyiv, 03187, Ukraine
2 National Aviation University, Kyiv, Ukraine.
1, Lubomyra Husara av., Kyiv, 03680, Ukraine
3 National University «Yuri Kondratyuk Poltava Polytechnic»
24, Pershotravnevyj av., Poltava, 36011, Ukraine
CONTROL OF A NONSQUARE MULTIVARIABLE SYSTEM USING PSEUDOINVERSE MODEL-BASED STATIC OUTPUT FEEDBACK
Introduction. The paper deals with nonzero set-point regulating the first-order linear discrete-time multivariable system. The case where the number of outputs exceeds the number of control inputs is considered. It is assumed that arbitrary but bounded unmeasurable disturbances are present. The assumption that the elements of the matricies arising in the system equation are unknown. However, their bounds are assumed to be known a priori. From practical point of view, it is important to design a simple controller similar to reduced-order or static output feedback (SOF) controllers. A difficulty associated with this problem is in establishing the existence of SOF control to be able to cope with a given system. The three different problems concerning the optimality, ultimate boundedness and robustness features are stated and solved.
The purpose of the paper is to answer the question: is there the SOF control based on the pseudoinverse concept to stabilize some first-order multivariable system with nonsquare gain matrix?
Methods. The methods based on the theory of matricies are utilized.
Results. The pseudoinverse model-based control leading to static output feedback is proposed to reject unmeasured disturbances. The optimality and robustness properties of such controller are established. Numerical examples and simulation results are presented to support theoretical study.
Conclusion. The paper shed some light on the existence of the pseudoinverse static output feedback controllers which can either be optimal (in the absence of any uncertainty) or be robust stable against parameter uncertainties dealing with the linear multivariable first-order discrete-time system in a hard case when its gain matrix is nonsquare (in contrast to the known results).
Keywords: discrete time, feedback control methods, pseudoinversion, multivariable control systems, robustness.
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Received 10.03.2020