• V. A. Zozulya State University of Trade and Economics, Kyiv, Ukraine, Ukraine
  • S. І. Osadchy Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine, Ukraine
  • S. N. Nedilko Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine, Ukraine



Identification, transfer function matrix, spectral density, quality functional, Stewart platform


Context. At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion.

Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification.

Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals.

Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models.

Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences.

Author Biographies

V. A. Zozulya, State University of Trade and Economics, Kyiv, Ukraine

PhD, Associate Professor of the Department of Digital Economy and System Analysis

S. І. Osadchy, Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine

Dr. Sc., Professor, of the Department of Aircraft Construction, Aircraft Engines and Airworthiness Maintenance

S. N. Nedilko, Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine

 Dr. Sc., Professor, Acting Director of the Dr. Sc., Professor, Acting Director


Azarskov V. N., Blokhin L. N., Zhitetsky L.S.; eds.: L. N. Blokhin Methodology of designing optimal systems of stochastic stabilisation: Monograph. Kyiv, Book publishing house NAU, 2006, 440 p. ISBN 966-598-325-3.

Kondratenko Y. P., Kuntsevich V. M., Chikrii A. A., Gubarev V. F. Advanced Control Systems: Theory and Applications. River Publishers Series in Automation, Control and Robotics, 2021, 300 p.

Merlet J.-P. Parallel Robots. Springer, 2nd edition, 2006, 394 p.

Gubarev V. F. Modeling and identification of complex systems. Kyiv, Naukova Dumka, 2019, 248 p.

Levchuk I. L., Manko H. I., Tryshkin V. Ya., Korsun V. I. Theory and practice of identification of controled objects: Monograph. Dnipro, SHEI USUCT, 2019, 203 p. ISBN 978617-7478-46-0

Lutska N. M., Ladaniuk A. P. Optimal and robust control systems for technological objects: monograph. Kyiv, LiraK Publishing House, 2015, 288 p.

Taghirad H. D. Parallel Robots. Mechanics and Control. Taylor & Francis Group, CRC Press., 2013, 533 p.

Blokhin L. M., Burichenko M. Y., Bilak N. V. et al.Statistical dynamics of control systems. Kyiv, NAU, 2014, 300 p.

Osadchy S., Zozulya V., Timoshenko A. Advances in Intelligent Robotics and Collaborative Automation – Robots, Book. – River Publishers, 2015. – Chapter 2: The Dynamic Characteristics of the Manipulator with Parallel Kinematic Structure Based on Experimental Data, pp. 27–48

Afrooz Ebadat. Experiment Design for Closed-loop System Identification with Applications in Model Predictive Control and Occupancy Estimation: thesis ... doctor of philosophy / Afrooz Ebadat. Royal Institute of Technology (KTH). Stockholm, Sweden, 2017, 231 p. ISSN 1653-5146. ISBN 978-91-7729-464-1.

Osadchyi S. I., Vikhrova L. H. Structural identification in the problem of linearisation of the model of dynamics of longitudinal gliding of the transom of a supercavitating object, Bulletin of the National Technical University “Kharkiv Polytechnic Institute”. Collection of scientific papers. Thematic issue: Computing and modelling: NTU “KhPI”, 2011, № 36, pp. 128–134.

Jianhong W., Ramirez-Mendoza R. A. The practical analysis for closed-loop system identification. Cogent Engineering, 2020. DOI:10.1080/23311916.2020.1796895

Osadchyi S. І., Zozulia V. A., Kalich V. M. et al. The frequency method for optimal identification of close-loop system elements, Radio Electronics, Computer Science, Control, 2023, No. 4, pp. 193–205. DOI 10.15588/1607-32742023-4-18

Melnichenko M. M., Osadchy S. I., Zozulya V. A. Identification of the signals in position control circuits of a hexapod platform, Conference: Methods and Systems of Navigation and Motion Control (MSNMC 2016): proceedings. Kyiv: IEEE, КNАU, 2016, pp. 51–57

Korn G., Korn T. Handbook of Mathematics (for scientists and engineers). Moscow, Nauka, 1977, 831 p.

Aliev F. A., Bordyug V. A., Larin V. B. Factorisation of polynomial matrices with respect to imaginary axis and unit circle, Avtomatika, 1989, No. 4, pp. 51–58.

Davis M.C. Factoring the spectral matrix, IEEE Trans. Automat. Cointr., 1963, AC-8, N 4, pp. 296–305.

Kucera Vladimir. The H2 control problem: a general transfer-function solution, International Journal of Control, 2007, Vol. 80, №5, pp. 800–815 DOI:10.1080/00207170701203590.

Development of a physical model of a lathe based on a parallel structure mechanism with a control system for the displacement drives of the working body: Report on Research Work (NDDKR) Kirovohrad National Technical University. Kirovohrad, 2011, 176 p. No. DR 0109U00210. registration No. 0211U005056

Tunik A. A., Rydlo K., Savchenko O. V. et al. Practical Experience of Intellectual UAV Attitude Stabilization System Computer-Aided Design, Electronics and Control Systems, 2015, No. 1(43), pp. 17–25.

Patankar P., Kulkarni S. MATLAB and Simulink In-Depth. BPB Publications, 2022, 602 p.

Osadchy S. I., Zozulya V. A., Rudiuk G. I. The Dynamics of 3-dimensional micro-mechanic sensor of angle motions of a robot-hexapod, Conference: Intelligent Data Acquisition and Advanced Computing Systems (IDAACS’2015): proceedings. Warsaw, IEEE, 2015, Vol. 2, pp. 908–912 https:/

Osadchy S. I., Zozulya V. A.Optimal Filtering of Hexapod Acceleration Data Obtained Under Action of Electromagnetic Interference, Conference: Methods and Systems of Navigation and Motion Control (MSNMC 2014): proceedings. Kyiv, IEEE, КNАU, 2014, pp. 21–23. https:/




How to Cite

Zozulya, V. A., Osadchy S. І., & Nedilko, S. N. (2024). STEWART PLATFORM DYNAMICS MODEL IDENTIFICATION . Radio Electronics, Computer Science, Control, (1), 242.



Control in technical systems