Abstract
Nested saturation control design techniques are usually applied to derive a control law for a two-wheeled vehicle with an inverted pendulum. In presence of external disturbances, this control law may result in a catastrophic problem of finite escape time in the controlled system. This paper proposes control solutions to overcome the above problem. First, a disturbance observer is designed to estimate the external disturbances exponentially. Several coordinate transformations and partial-feedback linearization techniques are then derived to transform the vehicle’s dynamics into an upper-triangular form. Next, nested p-times differentiable saturation and backstepping techniques are combined to design a control law for the transformed system. Attractive features of our proposed control design include a large domain of attraction and simplicity of tuning control gains and the controller implementation. Numerical simulations illustrate the results.
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Do, K.D., Pan, J.: Control of Ships and Underwater Vehicles: Design for Underactuated and Nonlinear Marine Systems. Springer (2009)
Lozano, R., Fantoni, I., Block, D.: Stabilization of the invened pendulum around its homoclinic orbit. Syst. Control Lett. 31, 851–862 (1995)
Chung, C., Hauser, J.: Nonlinear control of a swinging pendulum. Automatica 31, 851–862 (1995)
Astrom, K., Furuta, K.: Swinging up a pendulum by energy control. In: IFAC 96 Preprints 13th World Congress of IFAC, pp. 37–42 (1996)
Mazenc, E., Praly, L.: Adding integrators, saturated controls and stabilization for feedforward systems. IEEE Trans. Automat. Contr. 41(11), 1559–1577 (1996)
Wei, Q., Dayawansa, W., Levine, W.: Nonlinear controller for an inverted pendulum having restricted travel. Automatica 31, 841–850 (1995)
Teel, A.: A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Trans. Automat. Contr. 41(9), 1256–1270 (1996)
Olfati-Saber, R.: Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. PhD. thesis, Massachusetts Institute of Technology (2001)
Zhao, J., Spong, M.: Hybrid control for global stabilization of the cart-pendulum system. Automatica 37(12), 1941–1951 (2001)
Khalil, H.: Nonlinear Systems. Prentice Hall, Englewood Cliffs, NJ (2002)
Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Olfati-Saber, R., Megretski, A.: Controller design for a class of underactuted nonlinear systems. In: Proceedings of the 37th Conference on Decision and Control, pp. 4182–4187 (1998)
Waldron, K.J., Kinzel, G.L.: Kinematics Dynamics and Design of Machinery. Wiley, New York (2004)
Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Automat. Contr. 51, 401–420 (2006)
Do, K.D.: Output-feedback formation tracking control of unicycle-type mobile robots with limited sensing ranges. Robot. Auton. Syst. 57, 34–47 (2009)
Do, K.D.: Bounded controllers for formation stabilization of mobile agents with limited sensing ranges. IEEE Trans. Automat. Contr. 52(3), 569–576 (2007)
Widder, D.V.: Advanced Calculus, 2nd edn. Dover, New York (1989)
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Do, K.D., Seet, G. Motion Control of a Two-Wheeled Mobile Vehicle with an Inverted Pendulum. J Intell Robot Syst 60, 577–605 (2010). https://doi.org/10.1007/s10846-010-9432-9
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DOI: https://doi.org/10.1007/s10846-010-9432-9