{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T13:26:54Z","timestamp":1723037214046},"reference-count":15,"publisher":"The Russian Academy of Sciences","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ARC"],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:p>This paper continues previous studies on designing stabilizing control laws for a mechanical system consisting of a wheel and a pendulum suspended on its axis. The control objective is to simultaneously stabilize the vertical position of the pendulum and a given position of the wheel. The difficulty of this problem is that the same control is used to achieve two targets, i.e., stabilize the pendulum angle and the wheel rotation angle. Previously, the output feedback linearization method was applied to this problem. The sum of the pendulum angle and the wheel rotation angle was taken as the output. For the closed loop system to be not only asymptotically stable in the output but also to have asymptotically stable zero dynamics, a dissipative term was added to the output-stabilizing control law. Below, a two-parameter modification of this law is described. Along with the dissipative term, we introduce a positive factor. The more general parameterization allows stabilizing this system in the cases where the control law proposed previously appeared ineffective. The properties of the new control law are investigated, and the attraction domain is estimated. The estimation procedure is reduced to checking the feasibility of linear matrix inequalities.<\/jats:p>","DOI":"10.31857\/s0005117924040043","type":"journal-article","created":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T09:22:35Z","timestamp":1718788955000},"page":"396-411","source":"Crossref","is-referenced-by-count":0,"title":["An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel"],"prefix":"10.31857","volume":"85","author":[{"name":"Moscow Institute of Physics and Technology, Dolgoprudny, Russia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. B.","family":"Rapoport","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. A.","family":"Generalov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Topcon Technology Finland, Espoo, Finland","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B. A.","family":"Barulin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. D.","family":"Gorbachev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"17106","reference":[{"key":"ref0","doi-asserted-by":"publisher","unstructured":"1. Rapoport, L.B. and Generalov, A.A., Control of an Inverted Pendulum on a Wheel, Autom. Remote Control, 2022, vol. 83, pp. 1151-1171.","DOI":"10.1134\/S000511792208001X"},{"key":"ref1","doi-asserted-by":"publisher","unstructured":"2. Martynenko, Y.G. and Formal'skii, A.M., Controlled Pendulum on a Movable Base, Mech. Solids, 2013, vol. 48, pp. 6-18.","DOI":"10.3103\/S0025654413010020"},{"key":"ref2","doi-asserted-by":"publisher","unstructured":"3. Formalskii, A.M., Stabilisation and Motion Control of Unstable Objects, De Gruyter, 2015.","DOI":"10.1515\/9783110375893"},{"key":"ref3","unstructured":"4. Khalil, H., Nonlinear Systems, 3rd ed., Pearson, 2001."},{"key":"ref4","unstructured":"5. Utkin, V.I., Guldner, J., and Shi, J., Sliding Mode Control in Electro-mechanical Systems, CRC Press, 2009."},{"key":"ref5","unstructured":"6. Ha, J.-S. and Lee, J.-J., Position Control of Mobile Two Wheeled Inverted Pendulum Robot by Sliding Mode Control, Proceedings of 12th International Conference on Control, Automation and Systems, 2012, pp. 715-719."},{"key":"ref6","doi-asserted-by":"publisher","unstructured":"7. Li, Z., Yang, C., and Fan, L., Advanced Control of Wheeled Inverted Pendulum Systems, Springer, 2013.","DOI":"10.1007\/978-1-4471-2963-9"},{"key":"ref7","doi-asserted-by":"publisher","unstructured":"8. Pesterev, A.V. and Morozov, Y.V., Stabilization of a Cart with Inverted Pendulum, Autom. Remote Control, 2022, vol. 83, no. 1, pp. 78-91.","DOI":"10.1134\/S0005117922010064"},{"key":"ref8","doi-asserted-by":"publisher","unstructured":"9. Teel, A.R., A Nonlinear Small Gain Theorem for the Analysis of Control Systems with Saturation, IEEE Trans. Autom. Contr., 1996, vol. 41, no. 9, pp. 1256-1270.","DOI":"10.1109\/9.536496"},{"key":"ref9","doi-asserted-by":"publisher","unstructured":"10. Reshmin, S.A., and Chernous'ko, F.L., A Time-Optimal Control Synthesis for a Nonlinear Pendulum, J. Comput. Syst. Sci. Int., 2007, vol. 46, pp. 9-18.","DOI":"10.1134\/S1064230707010030"},{"key":"ref10","doi-asserted-by":"publisher","unstructured":"11. Srinivasan, B., Huguenin, P., and Bonvin, D., Global Stabilization of an Inverted Pendulum. Control Strategy and Experimental Verification, Automatica, 2009, vol. 45, pp. 265-269.","DOI":"10.1016\/j.automatica.2008.07.004"},{"key":"ref11","unstructured":"12. Tkachev, S.B., Stabilization of Non-minimal Phase Affine Systems with Linearization of the Part of Variables, Science & Education, 2011, no. 11, pp. 1-29."},{"key":"ref12","unstructured":"13. https:\/\/wxMaxima-developers.github.io\/wxmaxima\/."},{"key":"ref13","unstructured":"14. Voronov, A.A., Teoriya avtomaticheskogo upravleniya. Ch. I (Automatic Control Theory. Part I), Moscow: Vysshaya Shkola, 1986."},{"key":"ref14","unstructured":"15. https:\/\/www.scilab.org\/."}],"container-title":["Automation and Remote Control"],"original-title":[],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T09:38:20Z","timestamp":1718789900000},"score":1,"resource":{"primary":{"URL":"http:\/\/ait.mtas.ru\/en\/archive\/volume85issue4\/ARC04-2024%20004Rapoport.pdf"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,4]]}},"URL":"https:\/\/doi.org\/10.31857\/s0005117924040043","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"type":"print","value":"0005-1179"},{"type":"electronic","value":"1608-3032"}],"subject":[],"published":{"date-parts":[[2024,4]]}}}