STEWART PLATFORM MULTIDIMENSIONAL TRACKING CONTROL SYSTEM SYNTHESIS
DOI:
https://doi.org/10.15588/1607-3274-2024-3-20Keywords:
synthesis, transfer function matrix, tracking control system, quality functional, Stewart platformAbstract
Context. Creating guaranteed competitive motion control systems for complex multidimensional moving objects, including unstable ones, that operate under random controlled and uncontrolled disturbing factors, with minimal design costs, is one of the main requirements for achieving success in this class devices market. Additionally, to meet modern demands for the accuracy of motion control processes along a specified or programmed trajectory, it is essential to synthesize an optimal control system based on experimental data obtained under conditions closely approximating the real operating mode of the test object.
Objective. The research presented in this article aims to synthesize an optimal tracking control system for the Stewart platform’s working surface motion, taking into account its multidimensional dynamic model.
Method. The article employs a method of a multidimensional tracking control system structural transformation into an equivalent stabilization system for the motion of a multidimensional control object. It also utilizes an algorithm for synthesizing optimal stabilization systems for dynamic objects, whether stable or not, under stationary random external disturbances. The justified algorithm for synthesizing optimal stochastic stabilization systems is constructed using operations such as addition and multiplication of polynomial and fractional-rational matrices, Wiener factorization, Wiener separation of fractional-rational matrices, and the calculation of dispersion integrals.
Results. As a result of the conducted research, the problem of defining the concept of analytical design for a Stewart platform’s optimal motion control system has been formalized. The results include the derived transformation equations from the tracking control system to the equivalent stabilization system of the Stewart platform’s working surface motion. Furthermore, the structure and parameters of the main controller transfer function matrix for of this control system have been determined.
Conclusions. The justified use of the analytical design concept for the Stewart platform’s working surface optimal motion control system formalizes and significantly simplifies the solution to the problem of synthesizing complex dynamic systems, applying the developed technology presented in [1]. The obtained structure and parameters of the Stewart platform’s working surface motion control system main controller, which is divided into three components W1, W2, and W3, improve the tracking quality of the program signal vector, account for the cross-connections within the Stewart platform, and increase the accuracy of executing the specified trajectory by increasing the degrees of freedom in choosing the controller structure
References
Osadchiy S. I., Zozulya V. A. Combined method for the synthesis of optimal stabilization systems of multidimensional moving objects under stationary random impacts, Automation and Information Sciences, 2013, Vol. 45, Issue 6, pp. 25–35 DOI: 10.1615/JAutomatInfScien.v45.i6.30
Hamid D. Taghirad Parallel Robots. Mechanics and Control. CRC Press; 1 edition, by Taylor & Francis Group, 2013, 533 p. DOI: 10.1201/b16096
Zozulya V. A., Osadchyi S. І., Nedilko S. N. Stewart platform dynamics model identification, Radio Electronics, Computer Science, Control, 2024, № 4, pp. 242–255. DOI: 10.15588/1607-32742024-1-22
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. DOI: 10.1007/978-3-030-21927-7
Merlet J.-P. Parallel Robots. Springer, 2nd edition, 2006, 394 p. DOI: 10.1007/1-4020-4133-0
Azarskov V. N., Blokhin L. N., Zhitetsky L. S.; eds.: Blokhin L. N. Methodology of designing optimal systems of stochastic stabilisation: Monograph. K., Book publishing house NAU, 2006, 440 p. ISBN 966-598-325-3.
Trentelman H., Stoorvogel A., Hautus M., Dewell L. Control Theory for Linear Systems. London, UK, Springer, 2002, 389 p. DOI: 10.1115/1.1497472
Aliev F. А., Larin V. B., Naumenko К. I. et al. Optimization of Linear Invariant in Time Control Systems. Kyiv, Naukova Dumka, 1978, 208 p.
Naumenko K. I. Observation and Control of Dynamic Systems’ Motion. Kyiv, Naukova Dumka, 1984, 208 p.
Kucera Vladimir. The H2 control problem: a general transferfunction solution, International Journal of Control, 2007, Vol. 80, № 5, pp. 800–815 DOI: 10.1080/00207170701203590.
Vidyasagar M. Control System Synthesis: A Coprime Factorization Approach. Part I. Morgan & Claypool Publishers, 2011, 184 p. DOI: 10.1007/978-3-031-01828-2
Davis M. C. Factoring the spectral matrix, IEEE Trans. Automat. Cointr., 1963, AC-8, N 4, pp. 296–305.
Horn R. A., Johnson C. R. Matrix Analysis. Cambridge University Press (2nd ed.), 2012, 643 p. DOI: 10.1017/CBO9781139020411
Kvakernaak H., Sivan R. Linear optimal control systems. New York, John Wiley & Son Inc., 1972, 575 p.
Osadchyi S., Zozulia V. Synthesis of Optimal Multivariable Robust Systems of Stochastic Stabilization of Moving Objects, International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD 2019), proceedings. Kyiv, IEEE, NАU, 2019, pp. 106–111 DOI: 10.1109/APUAVD47061.2019.8943861
Osadchy S. I., Zozulya V. A., Rudiuk G. I. The Dynamics of 3dimensional micro-mechanic sensor of angle motions of a robothexapod, Intelligent Data Acquisition and Advanced Computing Systems (IDAACS’2015): proceedings. Warsaw, IEEE, 2015, Vol. 2, pp. 908–912 DOI: 10.1109/IDAACS.2015.7341435.
Vidyasagar M. Normalized coprime factorization for non strictly proper systems, Transactions on Automatic Control: proceedings, IEEE, AC-33, 1988, pp. 300–301 DOI: 10.1109/9.408
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 V. A. Zozulya, S. І. Osadchy
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
