CONTROLLABILITY OF A DYNAMICAL SYSTEM WITH A GYROSCOPIC STRUCTURE UNDER THE ACTION OF DISSIPA-TIVE FORCES AND FORCES OF RADIAL CORRECTION WITH A CERTAIN NONLINEAR EXTERNAL DISTURBANCES OF MIXED TYPE

  • V. V. Leontieva Zaporizhzhia National University
  • N. О. Kondratieva Zaporizhzhia National University
Keywords: dynamical system, gyroscopic system, external disturbances, state variable model, controllability of the system, controllability matrix

Abstract

In the study of objects of different physical nature there is often a need for improvement their dynamic properties, adjusting the parameters of mathematical models describing the movement of the studied objects, stabilization of unstable objects, that is, when there is a need for changing the studied objects in such a way that their characteristics satisfy certain requirements. In the major cases indicated changes could be achieved by the application the certain types of control to the studied objects, become possible under the conditions when the objects are characterized by the property of complete or partial controllability, that is essential for building workable control systems and consists in establishing the fundamental possibility of transferring an control object from one state to another using information about its state variables.

From the point of view of obtaining further scientifically based results in the field of control theory one of the most popular objects is the gyroscopic system. This work is devoted to the study of the controllability problem of a dynamical system with a gyroscopic structure under the influence of dissipative and radial correction forces with a certain nonlinear external disturbances of mixed type described with the refined mathematical model, that is presented in the form of linearizing differential equations with a nonlinear right-hand side and, depending from the certain physical limitations of the object, has two different forms of presentation – with the existing possibility (impossibility) of union of disturbing forces acting on the system. For each of obtained models are constructed the models in state variables, according to which an analysis of the system’s controllability is carried out. As a result of the analysis the conditions for complete controllability are satisfied for the studied system. Moreover, it was determined that the results of the analysis of the controllability of the studied system are affected only by the results of the study of one of the obtained controllability matrices compiled for the case of the existing possibility of combining disturbing forces. The use of another form of representation of model turned out to be less popular due to the complication of the corresponding controllability matrix along with the coincidence of the results obtained for the second model.

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Published
2020-03-03
How to Cite
Leontieva, V. V., & KondratievaN. О. (2020). CONTROLLABILITY OF A DYNAMICAL SYSTEM WITH A GYROSCOPIC STRUCTURE UNDER THE ACTION OF DISSIPA-TIVE FORCES AND FORCES OF RADIAL CORRECTION WITH A CERTAIN NONLINEAR EXTERNAL DISTURBANCES OF MIXED TYPE. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences, (2), 90-100. Retrieved from http://journalsofznu.zp.ua/index.php/phys-math/article/view/259