doi: 10.17586/2226-1494-2016-16-5-928-935

# IDENTIFICATION METHOD FOR PENDULUM SYSTEM MOMENT OF INERTIA WITH VISCOUS DAMPING

A. S. Alyshev, V. G. Melnikov, G. I. Melnikov

Article in Russian

For citation: Alyshev A.S., Melnikov V.G., Melnikov G.I. Identification method for pendulum system moment of inertia with viscous damping. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 5, pp. 928–935. doi: 10.17586/2226-1494-2016-16-5-928-935

Abstract

The paper proposes a method for identification of axial moment of inertia of the mechanical system called reaction wheel pendulum with a viscous friction in the bearings of the suspension. The method is based on the reversible symmetric motions. Pendulum system motion includes a free measured motion and reverse symmetrical motion at the same angular interval. The pendulum includes a rod with a low-power DC motor with a flywheel attached to the end of the rod. The angle of rotation and velocity of the rod and the flywheel are measured by encoders. The paper introduces a new method,presents a design formula,a mathematical model of the pendulum system and a robust motor control law for it. The method is based on energy algorithm and control residing in electric motor operational changes by means of a flywheel. The mechanical system moves symmetrically that is provided by nonuniform controlled flywheel rotation. As a result, the influence of dissipative factors on identification results is eliminated. Dynamic modeling is carried out for the pendulum system and proves high accuracy of the method. The research results can be used for identification of complex mechanical systems under the action of resistance, dissipative and other forces.

Keywords: moment of inertia identification, energy method, reversible-symmetric motions, reference model, reaction wheel pendulum

Acknowledgements. This work was supported by the RFBR Grant 16-08-00997.

References

1. Jamisola R.S., Dadios E.P. Identifying moments of inertia parameters for rigid-body manipulators. Proc. 13th Int. Conf. on Mechatronics Technology. Cebu City, Philippines, 2009.
2. Almeida R.A.B., Urgueira A.P.V., Maia N.M.M. Identification of rigid body properties from vibration measurements. Journal of Sound and Vibration, 2007, vol. 299, no. 4-5, pp. 884–899. doi: 10.1016/j.jsv.2006.07.043
3. Pandit S.M., Hu Z., Yao Y. Experimental technique for accurate determination of rigid body characteristics. Proc. 10th Int. Modal Analysis Conference, IMAC, pp. 307–311.
4. Aranovskiy S.V., Aleksandrova S.A., Lovlin S.U. Identification method for the electromechanical system with the variable friction torque. Information and Control Systems, 2012, no. 1, pp. 8–11.
5. Almeida R.A.B., Urgueira A.P.V., Maia N.M.M. Evaluation of the performance of three different methods used in the identification of rigid body properties. Shock and Vibration, 2008, vol. 15, no. 3–4, pp. 467–479.
6. Hou Z.-C., Lu Y.-N., Lao Y.-X., Liu D. A new trifilar pendulum approach to identify all inertia parameters of a rigid body or assembly. Mechanism and Machine Theory, 2009, vol. 44, no. 6, p. 1270–1280. doi: 10.1016/j.mechmachtheory.2008.07.004
7. Barreto J., Munoz L. Inertia parameter identification using a Stewart platform. Proc. 41st Int. Symposium on Robotics. Munich, Germany, 2010, vol. 2, pp. 765–772.
8. Malekjafarian A., Ashory M.R., Khatibi M.M., Saberlatibari M. Rigid body stiffness matrix for identification of inertia properties from output-only data. European Journal of Mechanics, A/Solids, 2016, vol. 59, pp. 85–94. doi: 10.1016/j.euromechsol.2016.03.009
9. Bobtsov A.A., Kolyubin S.A., Pyrkin A.A. Stabilization of reaction wheel pendulum on movable support with on-line identification of unknown parameters. Proc. 4th Int. Conf. Physics and Control. Catania, Italy, 2009.
10. Gobbi M., Mastinu G., Previati G. A method for measuring the inertia properties of rigid bodies. Mechanical Systems and Signal Processing, 2011, vol. 25, no. 1, pp. 305–318. doi: 10.1016/j.ymssp.2010.09.004
11. Garcia-Alarcon O., Puga-Guzman S., Moreno-Valenzuela J. On parameter identiﬁcation of the Furuta pendulum. Procedia Engineering, 2012, vol. 35, pp. 1–8. doi: 10.1016/j.proeng.2012.04.167
12. Melnikov V.G. An energy method for parametrical identification of object inertia tensors. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 1, pp. 59–63. (In Russian)
13. Mel'nikov V.G., Kravchuk R.Yu., Mel'nikov G.I., Shakhoval S.N. Inertia tensor identification on reverse-symmetric motions in a finite angular range. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 1, pp. 153–154. (In Russian)
14. Melnikov V.G. Inertia tensor matrixes and centres of weights identification on rever- sively symmetric precession motions. Vestnik of the St. Petersburg University: Mathematics, 2010, no. 3, pp. 97–104. (In Russian)
15. Melnikov G.I., Dudarenko N.A., Melnikov V.G., Alyshev A.S. Parametric identification of inertial parameters. Applied Mathematical Sciences, 2015, vol. 9, no. 136, pp. 6757–6765. doi: 10.12988/ams.2015.59584
16. Melnikov V.G. A new method for inertia tensor and center of gravity identification. Nonlinear Analysis, Theory, Methods and Applications, 2005, vol. 63, no. 5-7, pp. e1377–e1382. doi: 10.1016/j.na.2005.02.001
17. Melnikov V.G. Inertia tensors and centres of masses identification at semiprogram precession motions. Proc. IEEE Int. Conf. on Control Applications. Dubrovnik, Croatia, 2012, pp. 494–497. doi: 10.1109/CCA.2012.6402471
18. Dudarenko N.A., Melnikov V.G., Melnikov G.I. A method for inertia tensors and centres of masses identification on symmetric precessions. International Congress on Ultra Modern Telecommunications and Control Systems and Workshops. St. Petersburg, Russia, 2015, vol. 1, pp. 596–601. doi: 10.1109/ICUMT.2014.7002168
19. Block D.J., Astrom K.J., Spong M.W. The Reaction Wheel Pendulum. San Rafael, Morgan & Claypool Publ., 2007.
20. Kolyubin S.A., Pyrkin A.A. Adaptive hybrid control of Schmidt pendulum on unsteady base with friction compensation. Proc. XIII Conf. on Navigation and Motion Control. St. Petersburg, Russia, 2011. (In Russian)
21. Andrievskii B.R. Stabilization of the inverted pendulum with inertial flywheel as an engine. In: Upravlenie v Fiziko-Tekhnicheskikh Sistemakh [Control in Physical and Technical Systems]. Ed. A.L. Fradkov. St. Petersburg, Nauka Publ., 2004, pp. 52–71.
22. Ivanov S.E. Definition of the steady state vibration isolation systems with two degrees of freedom. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 4, pp. 44–46. (In Russian)
23. Kosyakov E.A., Tikhonov A.A. On resonances generated by torque of Lorentz forces in the satellite vibrations. Proc. III Int.Conf. on Stability and Control Processes. St. Petersburg, 2015, pp. 129–130. (In Russian)
24. Nikiforov V.O. Adaptivnoe i Robastnoe Upravlenie s Kompensatsiei Vozmushchenii [Adaptive and Robust Control with Perturbations Compensation]. St. Petersburg, Nauka Publ., 2003, 282 p.
25. Tsykunov A.M. Robust Control of nonlinear plant by output. Control Science, 2010, no. 5, pp. 15–21. (In Russian)
26. Furtat I.B., Tupichin E.A. Simplified backstepping algorithm for control of nonlinear systems. Journal of Instrument Engineering, 2015, vol. 58, no. 3, pp. 173–178. doi: 10.17586/0021-3454-2015-58-3-173-178
27. Tsykunov A.M. Robastnoe Upravlenie s Kompensatsiei Vozmushchenii [Robust Control with Perturbations Compensation]. Moscow, Fizmatlit Publ., 2012, 300 p.