Menu
Publications
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
Editor-in-Chief
Nikiforov
Vladimir O.
D.Sc., Prof.
Partners
doi: 10.17586/2226-1494-2019-19-6-1041-1048
ROBUST DYNAMICAL FEEDBACK DESIGN FOR BALLPOSITION CONTROL ON ROTARY PLATFORM
Read the full article
';
Article in Russian
For citation:
Abstract
For citation:
Konovalov D.E., Zimenko K.A., Margun A.A., Kremlev A.S., Dobriborsci D. Robust dynamical feedback design for ball position control on rotary platform. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2019, vol. 19, no. 6, pp. 1041–1048 (in Russian). doi: 10.17586/2226-1494-2019-19-6-1041-1048
Abstract
Subject of Research. The paper presents a method of dynamical control design for a robot with a parallel kinematic scheme. The stabilization problem of 2-Degree-of-Freedom Ball and Plate system is solved. It is assumed that the rotation angles of the platform are limited. Method. The proposed method is based on transforming the considered nonlinear system to the form of a homogeneous differential inclusion. Since the considered control object is described by a continuous and nonhomogeneous system of ordinary differential equations, the proposed method is based on the use of a homogeneous extension. The differential inclusion obtained by the homogeneous extension method is homogeneous with a negative degree, that provides the finite-time stability of the closed-loop system. Main Results. The dynamical feedback is robust and allows compensating non-Lipschitz disturbances of a certain class. Simulation results demonstrate the efficiency of the proposed approach. Despite the fact that the considered system and the obtained control law are nonlinear, the proposed dynamical feedback has a simple tuning procedure based on the solution of linear matrix inequalities. Practical Relevance. The proposed method is designed for robots with parallel kinematic scheme widely used, for example, in machine tools, flight simulators. The developed algorithm provides robust properties that are necessary in practice.
Keywords: tiltable plate, dynamical feedback control, homogeneous systems, differential inclusions, robustness
Acknowledgements. This work is performed in ITMO University and supported by the Russian Science Foundation under grant No. 17-19-01422.
References
Acknowledgements. This work is performed in ITMO University and supported by the Russian Science Foundation under grant No. 17-19-01422.
References
- Dobriborsch D., KolyubinS.A. Adaptive control of parallel kinematics robot manipulator. Journal of Instrument Engineering, 2017, vol. 60, no. 9, pp. 850–857. (in Russian). doi: 10.17586/0021-3454-2017-60-9-850-857
- Andrievskiy B.R., Arseniev D.G., Zegzhda S.A., Kazunin D.V., Kuznetsov N.V., Leonov G.A., Tovstik P.E., Tovstik T.P., Yushkov M.P. Dynamics of a Stewart platform. Vestnik St. Petersburg University: Mathematics, vol. 50, no. 3, pp. 298–309. doi: 10.3103/S1063454117030037
- Dobriborsci D., Kolyubin S., Margun A. Robust control system for parallel kinematics robotic manipulator. IFAC-PapersOnLine, 2018, vol. 51, no. 22, pp. 62–66. doi: 10.1016/j.ifacol.2018.11.519
- Ghobakhloo A., Eghtesad M., Azadi M. Adaptive-robust control of the Stewart-Gough platform as a six DOF parallel robot. Proc. 2006 World Automation Congress, WAC'06, 2006, pp. 4259906. doi: 10.1109/WAC.2006.375990
- Xing J., Peng L., Lv B. Vibration reduction of 6-dof hydraulic parallel robot based on robust control. Proc. 2008 International Conference on Computer and Electrical Engineering (ICCEE 2008), 2008, pp. 783–788. doi: 10.1109/ICCEE.2008.192
- Quanser Inc. 2 DOF Ball Balancer Instructor Version, 2013.
- Dobriborsci D., Margun A., Kolyubin S. Discrete Robust Controller for Ball and Plate System. Proc. 26th Mediterranean Conference on Control and Automation (MED 2018), 2018, pp. 655–660. doi: 10.1109/MED.2018.8442461
- Ho M.-T., Rizal Y., Chu L.-M. Visual servoing tracking control of a ball and plate system: design, implementation and experimental validation. International Journal of Advanced Robotic Systems, 2013, vol. 10, no. 7, pp. 287. doi: 10.5772/56525
- Polyakov A., Coron J.-M., Rosier L. On homogeneous finite-time control for linear evolution equation in hilbert space. IEEE Transactions on Automatic Control, 2018, vol. 63, no. 9, pp. 3143–3150. doi: 10.1109/TAC.2018.2797838
- Zimenko K., Polyakov A., Efimov D. On dynamical feedback control design for generalized homogeneous differential inclusions. Proc. 57th IEEE Conference on Decision and Control (CDC 2018), 2018, pp. 4785–4790. doi: 10.1109/CDC.2018.8619305
- Polyakov A., Efimov D., Fridman E., Perruquetti W. On homogeneous distributed parameter systems. IEEE Transactions on Automatic Control, 2016, vol. 61, no. 11, pp. 3657–3662. doi: 10.1109/TAC.2016.2525925
- Polyakov A., Coron J.-M., Rosier L. On finite-time stabilization of evolution equations: A homogeneous approach. Proc. 55th IEEE Conference on Decision and Control (CDC 2016), 2016, pp. 3143–3148. doi: 10.1109/CDC.2016.7798740
- Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, 1983, 282 p.
- Kawski M. Geometric Homogeneity and Stabilization. IFAC Proceedings Volumes, 1995, vol. 28, no. 14, pp. 147–152. doi: 10.1016/s1474-6670(17)46822-4
- Polyakov A. Sliding mode control design using canonical homogeneous norm. International Journal of Robust and Nonlinear Control, 2019, vol. 29, no. 3, pp. 682–701. doi: 10.1002/rnc.4058
- Bernuau E., Efimov D., Perruquetti W., Polyakov A. On an extension of homogeneity notion for differential inclusions. Proc. 12th European Control Conference (ECC 2013), 2013, pp. 2204–2209. doi: 10.23919/ECC.2013.6669525
- Zimenko K., Polyakov A., Efimov D., Perruquetti W. Generalized Feedback Homogenization and Stabilization of Linear MIMO Systems. Proc. 16th European Control Conference (ECC 2018), 2018, pp. 1987–1991. doi: 10.23919/ECC.2018.8550195
