access icon free Output-feedback stabilisation control for a class of under-actuated mechanical systems

© The Institution of Engineering and Technology
Received 16/12/2011, Accepted 21/02/2013, Revised 20/02/2013, Published

Output-feedback control of general underactuated mechanical systems is currently considered a major open problem. This study is focused on the output-feedback stabilisation control problems for a special class of underactuated mechanical systems, which appear in robotics and aerospace applications. For the synthesis of controller, first, the considered underactuated mechanical system is explicitly transformed into two cascade connected subsystems, and then an auxiliary filter-based virtual stabilisation controller is developed to locally asymptotically stabilise the first subsystem. Further, the designed virtual controller is again involved into the second subsystem using backstepping procedure to construct the actual control law, in which a series of auxiliary time-varying first-order low-pass filters are also implemented to avoid using the derivative of the system non-linear functions. Moreover, in the second step, finite-time observer technique is utilised to precisely reconstruct the immeasurable states to achieve the finite-time stabilisation control in the sense of output feedback. Lyapunov analysis shows the local asymptotic stability of the closed-loop system through the cascade system stability criteria. Simulation results are presented by using two benchmark non-linear underactuated mechanical systems to demonstrate the feasibility and the effectiveness of the proposed controller.

Inspec keywords: closed loop systems; low-pass filters; Lyapunov methods; feedback; mechanical variables control; control nonlinearities; time-varying filters; control system synthesis; nonlinear control systems; asymptotic stability; cascade systems; stability criteria

Other keywords: Lyapunov analysis; cascade connected subsystems; virtual controller design; local asymptotic stability; finite-time stabilisation control; closed loop system; auxiliary filter-based virtual stabilisation controller; auxiliary time-varying first-order low-pass filters; backstepping procedure; benchmark nonlinear underactuated mechanical systems; immeasurable state reconstruction; finite-time observer technique; output-feedback stabilisation control law; cascade system stability criteria; controller synthesis; system nonlinear functions

Subjects: Mechanical variables control; Signal processing theory; Nonlinear control systems; Stability in control theory; Control system analysis and synthesis methods

References

    1. 1)
      • 22. Dierks, T., Jagannathan, S.: ‘Output feedback control of a quadrotor UAV using neural networks’, IEEE Trans. Neural Netw., 2010, 21, (1), pp. 50–66 (doi: 10.1109/TNN.2009.2034145).
    2. 2)
      • 1. Sun, N., Fang, Y.C.: ‘New energy analytical results for the regulation of underactuated overhead cranes: an end-effector motion-based approach’, IEEE Trans. Ind. Electron., 2012, 59, (12), pp. 4723–4734 (doi: 10.1109/TIE.2012.2183837).
    3. 3)
      • 18. Jiang, Z.P., Kanellakopoulos, I.: ‘Global output-feedback tracking for a benchmark nonlinear system’, IEEE Trans. Autom. Control., 2000, 45, (5), pp. 1023–1027 (doi: 10.1109/9.855577).
    4. 4)
      • 24. Sontag, E.D.: ‘Further facts about input to state stabilization’, IEEE Trans. Autom. Control, 1990, 35, (4), pp. 473–476 (doi: 10.1109/9.52307).
    5. 5)
      • 2. Xin, X., Yamasaki, T.: ‘Energy-based swing-up control for a remotely driven acrobot: theoretical and experimental results’, IEEE Trans. Control Syst. Technol., 2012, 20, (4), pp. 1048–1056 (doi: 10.1109/TCST.2011.2159220).
    6. 6)
      • 23. Olfati-Saber, R.: ‘Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles’ (Massachusetts Institute of Technology, Massachusetts, USA, 2000).
    7. 7)
      • 20. Liu, G.Y., Nesic, D., Mareels, I.: ‘Non-linear stable inversion-based output tracking control for a spherical inverted pendulum’, Int. J. Control, 2008, 81, (1), pp. 116–133 (doi: 10.1080/00207170701383798).
    8. 8)
      • 27. Perruquetti, W., Floquet, T., Moulay, E.: ‘Finite-time observers: application to secure communication’, IEEE Trans. Autom. Control, 2008, 53, (1), pp. 356–360 (doi: 10.1109/TAC.2007.914264).
    9. 9)
      • 16. Chang, Y.-H., Chan, W.-S., Chang, C.-W., et al: ‘Adaptive fuzzy dynamic surface control for ball and beam system’, Int. J. Fuzzy Syst., 2011, 13, (1), pp. 1–7.
    10. 10)
      • 13. Chen, Y.F., Huang, A.C.: ‘Controller design for a class of underactuated mechanical systems’, IET Control Theory Appl., 2012, 6, (1), pp. 103–110 (doi: 10.1049/iet-cta.2010.0667).
    11. 11)
      • 8. Sankaranarayanan, V., Mahindrakar, A.D.: ‘Control of a class of underactuated mechanical systems using sliding modes’, IEEE Trans. Robot., 2009, 25, (2), pp. 459–467 (doi: 10.1109/TRO.2008.2012338).
    12. 12)
      • 17. Roy, B., Asada, H.H.: ‘Nonlinear feedback control of a gravity-assisted underactuated manipulator with application to aircraft assembly’, IEEE Trans. Robot., 2009, 25, (5), pp. 1125–1133 (doi: 10.1109/TRO.2009.2025067).
    13. 13)
      • 25. Loria, A., Nijmeijer, H.: ‘Bounded output feedback tracking control of fully actuated Euler–Lagrange systems’, Syst. Control Lett., 1998, 33, (3), pp. 151–161 (doi: 10.1016/S0167-6911(97)80170-3).
    14. 14)
      • 11. Meza-Sanchez, I.M., Aguilar, L.T., Shiriaev, A., et al: ‘Periodic motion planning and nonlinear H-infinity tracking control of a 3-DOF underactuated helicopter’, Int. J. Syst. Sci., 2011, 42, (5), pp. 829–838 (doi: 10.1080/00207721.2010.517874).
    15. 15)
      • 28. Yip, P.P., Hedrick, J.K.: ‘Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems’, Int. J. Control, 1998, 71, (5), pp. 959–979 (doi: 10.1080/002071798221650).
    16. 16)
      • 3. Li, M.Q., Huo, W.: ‘Controller design for mechanical systems with underactuation degree one based on controlled Lagrangians method’, Int. J. Control., 2009, 82, (9), pp. 1747–1761 (doi: 10.1080/00207170902748724).
    17. 17)
      • 14. Liu, Z., Yu, R., Zhu, Q.: ‘Asymptotic backstepping stabilization of an underactuated surface vessel (vol 14, pg 1150, 2006)’, IEEE Trans. Control Syst. Technol., 2012, 20, (1), pp. 286–288 (doi: 10.1109/TCST.2011.2107574).
    18. 18)
      • 12. Fang, Y.C., Ma, B.J., Wang, P.C., et al: ‘A motion planning-based adaptive control method for an underactuated crane system’, IEEE Trans. Control Syst. Technol., 2012, 20, (1), pp. 241–248.
    19. 19)
      • 10. Yu, R., Zhu, Q., Xia, G., et al: ‘Sliding mode tracking control of an underactuated surface vessel’, IET Control Theory Appl., 2012, 6, (3), pp. 461–466 (doi: 10.1049/iet-cta.2011.0176).
    20. 20)
      • 26. Khalil, H.K.: ‘Nonlinear Systems’ (Englewood Cliffs, Prentice-Hall, NJ, 2002, 3rd edn.).
    21. 21)
      • 15. Hwang, C.-L., Wu, H.-M., Shih, C.-L.: ‘Fuzzy sliding-mode underactuated control for autonomous dynamic balance of an electrical bicycle’, IEEE Trans. Control Syst. Technol., 2009, 17, (3), pp. 658–670 (doi: 10.1109/TCST.2008.2004349).
    22. 22)
      • 7. Xu, R., Ozguener, U.: ‘Sliding mode control of a class of underactuated systems’, Automatica, 2008, 44, (1), pp. 233–241 (doi: 10.1016/j.automatica.2007.05.014).
    23. 23)
      • 9. Muske, K.R., Ashrafiuon, H., Nersesov, S., et al: ‘Optimal sliding mode cascade control for stabilization of underactuated nonlinear systems’, J. Dyn. Syst. Meas. Control-Trans. ASME, 2012, 134, (2), pp. 1–11 (doi: 10.1115/1.4005367).
    24. 24)
      • 21. Li, Z.J., Yang, Y.P., Li, J.X.: ‘Adaptive motion/force control of mobile under-actuated manipulators with dynamics uncertainties by dynamic coupling and output feedback’, IEEE Trans. Control Syst. Technol., 2010, 18, (5), pp. 1068–1079 (doi: 10.1109/TCST.2009.2033573).
    25. 25)
      • 4. Ortega, R., Spong, M.W., Gomez-Estern, F., et al: ‘Stabilization of a class of undercactuated mechanical systems via interconnection and damping assignment’, IEEE Trans. Autom. Control., 2002, 47, (8), pp. 1218–1233 (doi: 10.1109/TAC.2002.800770).
    26. 26)
      • 19. Karagiannis, D., Jiang, Z.P., Ortega, R., et al: ‘Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems’, Automatica, 2005, 41, (9), pp. 1609–1615 (doi: 10.1016/j.automatica.2005.04.013).
    27. 27)
      • 6. Reyhanoglu, M., van der Schaft, A., McClamroch, N.H., et al: ‘Dynamics and control of a class of underactuated mechanical systems’, IEEE Trans. Autom. Control., 1999, 44, (9), pp. 1663–1671 (doi: 10.1109/9.788533).
    28. 28)
      • 29. Spong, M.W., Corke, P., Lozano, R.: ‘Nonlinear control of the reaction wheel pendulum’, Automatica, 2001, 37, (11), pp. 1845–1851 (doi: 10.1016/S0005-1098(01)00145-5).
    29. 29)
      • 5. Acosta, J.A., Ortega, R., Astolfi, A., et al: ‘Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one’, IEEE Trans. Autom. Control., 2005, 50, (12), pp. 1936–1955 (doi: 10.1109/TAC.2005.860292).
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