• Y. V. Kulanina Zaporizhzhia National Technical University
  • D. S. Yarymbash Zaporizhzhia National Technical University
  • М. І. Kotsur Zaporizhzhia National Technical University
  • S. T. Yarymbash Zaporizhzhia National Technical University



model, linearity, control, observer, robustness.


Context. A sufficient number of ways to implement vector control algorithms are very complex and in most cases tend to mismatch the vector of the resulting parameters of the control object. Therefore, there is a need to simplify complex non-linear vector control systems and apply linear dynamic models of a non-linear object with vector control for them. Currently, for a complex vector control system, there are no sufficiently accurate equivalent simple models. Development of reliable simple dynamic models will allow to design a vector control system with maximum use of linear methods of synthesis and analysis.
Objective. The goal of the paper is development of linear dynamic model of a non-linear object with vector control, which
reproduces its dynamics accurately enough for practice.
Method. The following methods were used to solve the problems posed: the state space method for describing the operation of
control systems; filtering theory, in particular, observers for estimation state vectors, uncertainties, and parameter identification;
modal control methods for the synthesis of observers and regulators; numerical simulation method to illustrate the performance of
synthesized control systems; vector control of a nonlinear object.
Results. For the investigated robust vector control system of the object with a substantial non-linearity of properties and
characteristics, simple linear equivalent mathematical models were compiled, rather accurately reproducing the operation of the
original system in all modes of operation. Simplification of mathematical models is achieved by considering the dynamics of the
entire system in a synchronous basis, robust methods for controlling parameters, and by neglecting really small errors in the work of regulators and observers. The synthesized models, as well as the original nonlinear system, have the property of robustness due to the use of combined control.
Conclusions. The simplicity and linearity of the equivalent system allows us to synthesize the control laws of the original
nonlinear system by well-developed linear methods with significantly less time spent on modeling. Numerical simulation of the
dynamics of the original nonlinear and equivalent linear systems showed a good agreement between transient and stationary

Author Biographies

Y. V. Kulanina, Zaporizhzhia National Technical University

PhD, Senior lecturer of the Electrical Machines Department

D. S. Yarymbash, Zaporizhzhia National Technical University

Dr. Sc., Associate Professor, Head of the Electrical Machines Department

М. І. Kotsur, Zaporizhzhia National Technical University

PhD, Associate Professor, Electrical and Electronic Apparatuses Department

S. T. Yarymbash, Zaporizhzhia National Technical University

PhD, Associate Professor, Electrical Machines Department


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How to Cite

Kulanina, Y. V., Yarymbash, D. S., Kotsur М. І., & Yarymbash, S. T. (2019). LINEARIZATION OF OBJECT MODEL WITH VECTOR CONTROL. Radio Electronics, Computer Science, Control, (2), 189–201.



Control in technical systems