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Robustness of Controlled Lagrangian Method to the Structured Uncertainties | ||
| AUT Journal of Mechanical Engineering | ||
| مقاله 6، دوره 2، شماره 1، شهریور 2018، صفحه 61-72 اصل مقاله (1.9 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2017.12758.5431 | ||
| نویسندگان | ||
| M. Hemmasian Ettefagh* 1؛ M. Naraghi1؛ M. Mahzoon2 | ||
| 1Department of Mechanical Engineering, Amirkabir University of Technology (Tehran polytechnics), Tehran, Iran | ||
| 2School of Mechanical Engineering, Shiraz University, Shiraz, Iran | ||
| چکیده | ||
| Controlled Lagrangian method uses the inherent geometric structure of the energy of the mechanical systems to provide a stabilizing algorithm for underactuated mechanical systems. The presented method belongs to a larger family of nonlinear control algorithms, namely energy shaping methods in which the controller is designed by providing necessary modifications in the mechanical energy of the system. This paper presents a sensitivity analysis of Controlled Lagrangian method. It is shown that the method presents a suitable performance under the effect of structured (or parametric) uncertainties such as masses values, their positions and their influence on the inertia tensor. Then, the sequel investigates the robustness level of the designed controller in the presence of structured uncertainties. A detailed robustness proof of the scheme is established in this paper. Simulations are provided for a linear inverted pendulum cart system to validate analytical results of robustness to parametric uncertainties. Simulation results confirm that the designed controller for the inverted pendulum, which is unstable and underactuated, is well robust against parametric uncertainties as the analytical studies predicted. The method was also compared with the sliding mode approach, which showed a superior robustness against parametric uncertainties and a more practical control input value. | ||
| کلیدواژهها | ||
| Controlled Lagrangian؛ Sensitivity analysis؛ Robustness؛ Structured uncertainties؛ Underactuated systems | ||
| مراجع | ||
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[1] A.M. Bloch, N.E. Leonard, J.E. Marsden, Stabilization of mechanical systems using controlled Lagrangians, in: Decision and Control, 1997., Proceedings of the 36th IEEE Conference on, IEEE, 1997, pp. 2356-2361. [2] A.M. Bloch, N.E. Leonard, J.E. Marsden, Matching and stabilization by the method of controlled Lagrangians, in: Decision and Control, 1998. Proceedings of the 37th IEEE Conference on, IEEE, 1998, pp. 1446-1451.
[3] A.M. Bloch, N.E. Leonard, J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem, IEEE Transactions on automatic control, 45(12) (2000) 2253-2270
[4] A.M. Bloch, D.E. Chang, N.E. Leonard, J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping, IEEE Transactions on Automatic Control, 46(10) (2001) 1556-1571
[5] D. Auckly, L. Kapitanski, W. White, Control of nonlinear underactuated systems, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 53(3) (2000) 354-369.
[6] D. Auckly, L. Kapitanski, On the .-equations for matching control laws, SIAM Journal on control and optimization, 41(5) (2002) 1372-1388.
[7] F. Andreev, D. Auckly, S. Gosavi, L. Kapitanski, A. Kelkar, W. White, Matching, linear systems, and the ball and beam, Automatica, 38(12) (2002) 2147-2152.
[8] D.E. Chang, A.M. Bloch, N.E. Leonard, J.E. Marsden, C.A. Woolsey, The equivalence of controlled Lagrangian and controlled Hamiltonian systems, ESAIM: Control, Optimisation and Calculus of Variations, 8 (2002) 393-422.
[9] C. Woolsey, C.K. Reddy, A.M. Bloch, D.E. Chang, N.E. Leonard, J.E. Marsden, Controlled Lagrangian systems with gyroscopic forcing and dissipation, European Journal of Control, 10(5)(2004) 478-496.
[10] R. Ortega, M.W. Spong, Stabilization of underactuated mechanical systems via interconnection and damping assignment, IFAC Proceedings Volumes, 33(2) (2000) 69-74.
[11] R. Ortega, M.W. Spong, F. Gómez-Estern, G. Blankenstein, Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment, IEEE transactions on automatic control, 47(8) (2002) 1218-1233.
[12] R. Ortega, A. Van Der Schaft, B. Maschke, G. Escobar, Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, 38(4) (2002) 585-596.
[13] C.F. Aguilar.Iba.ez, O.O.G. Frias, A simple model matching for the stabilization of an inverted pendulum cart system, International Journal of Robust and Nonlinear Control, 18(6) (2008) 688-699.
[14] J.-J.E. Slotine, W. Li, Applied nonlinear control, Prentice hall Englewood Cliffs, NJ, 1991.
[15] J. José, E. Saletan, Classical dynamics: a contemporary approach, in, AAPT, 2000.
[16] J.E. Marsden, Lectures on mechanics, Cambridge University Press, 1992.
[17] A. Donaire, R. Mehra, R. Ortega, S. Satpute, J.G. Romero, F. Kazi, N.M. Singh, Shaping the energy of mechanical systems without solving partial differential equations, IEEE Transactions on Automatic Control, 61(4) (2016) 1051-1056.
[18] J.K. Holm, M.W. Spong, Kinetic energy shaping for gait regulation of underactuated bipeds, in: Control Applications, 2008. CCA 2008. IEEE International Conference on, IEEE, 2008, pp. 1232-1238.
[19] C. Belta, V. Kumar, Trajectory design for formations of robots by kinetic energy shaping, in: Robotics and Automation, 2002. Proceedings. ICRA'02. IEEE International Conference on, IEEE, 2002, pp. 2593-2598.
[20] N.K. Haddad, A. Chemori, S. Belghith, External disturbance rejection in IDA-PBC controller for underactuated mechanical systems: From theory to real time experiments, in: Control Applications (CCA), 2014 IEEE Conference on, IEEE, 2014, pp. 1747-1752.
[21] A. Donaire, J.G. Romero, R. Ortega, B. Siciliano, M. Crespo, Robust IDA.PBC for underactuated mechanical systems subject to matched disturbances, International Journal of Robust and Nonlinear Control, 27(6) (2017) 1000-1016.
[22] N.K. Haddad, A. Chemori, S. Belghith, Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments, International Journal of Control, (2017) 1-16.
[23] S. Riachy, Y. Orlov, T. Floquet, R. Santiesteban, J.P. Richard, Second.order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum, International Journal of Robust and Nonlinear Control, 18(4.5) (2008) 529-543. | ||
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