Article

Article title RESEARCH OF THE INFLUENCE OF ISOLATED POLES ON THE CONTROLLABILITY AND OBSERVABILITY OF MULTIVARIABLE PLANTS
Authors K.V. Kolokolova
Section SECTION I. AUTOMATION AND CONTROL
Month, Year 05, 2016 @en
Index UDC 681.5.075
DOI
Abstract The purpose of this paper is to establish the connection between the properties of controlla-bility, observability and completeness of multivariable plants with the presence of isolated poles. The aim of the paper is to study the effect of isolating zeros and isolated poles on the opportunity to give the system the desired properties. The definition of zero in the case of one-variable and multivariable plant is given. The classification of the zeros of the multivariable plant is given and the concept of isolating zeros is introduced. The definition of isolating zeros using the Rosenbrock matrix is shown. There is justified the connection between the properties of multivariable plant and the presence of isolated poles. The influence of the isolating zeros on properties of the com-pleteness and stability of multivariable control systems is shown. There is given a numerical ex-ample of the synthesis of multivariable automatic control system to control a two-variable plant, the transfer matrix of which contains isolating zeros. It is shown that the presence of the isolating zeros causes the property of the incompleteness of the plant. To prove this statement the matrix of controllability and observability of the control object and the matrix Rosenbrock are given. For the synthesis of multivariable control system there is convenient to use the method of dynamic decomposition of multivariable plant for a number of one-variable ones. This method allows to synthesize multivariable control for the transfer matrix of the plant. The paper presents the key synthesis steps, in particular calculation of diagonalizing matrix and building of the desired trans-fer functions of the channels of the closed multivariable system. If in the process of synthesis an incomplete unstable part of the multivariable plant caused by the isolating zeros is not considered so as it’s shown calculated closed-loop system transfer matrix resulting synthesis seems to be sta-ble. But actually real closed-loop system will be unstable. Thereby isolating (decoupling by Rosenbrock) zeros have a significant impact on the properties of closed-loop multivariable control systems. This makes it necessary to calculate the isolating zeros and research the multivariable plants poles character during the synthesis by the method of dynamic decomposition.

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Keywords Multivariable plant, multivariable control system, isolated poles, decoupling zeros, the method of dynamic decomposition
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