Modelling an Inertia Wheel Pendulum Benchmark

In this paper, modelling and parameter identification of an inertia wheel pendulum benchmark is considered. This is an underactuated mechanical system useful for teaching and research. Attention is focused on deriving a simple but accurate model capable of reproducing large amplitude oscillations. Due to the particular design of the prototype, the friction forces on the actuated joint are noticeable. A simple friction model including dead-zone effects and viscous terms is proposed, and a compensation method for the dead zone is derived. The accuracy of the compensation strategy and the predictive quality of the derived model are analysed by comparing numerical simulations with experimental data.

[1]  Jorge L. Moiola,et al.  Controlling an Inverted Pendulum with Bounded Controls , 2002 .

[2]  Lennart Ljung,et al.  Tools for semiphysical modelling , 1995 .

[3]  B. Armstrong-Hélouvry.  Stick slip and control in low-speed motion , 1993, IEEE Trans. Autom. Control..

[4]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[5]  Romeo Ortega,et al.  Stabilization of nonlinear systems via forwarding mod {LgV} , 2001, IEEE Trans. Autom. Control..

[6]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[7]  Ronald M. Hirschorn,et al.  Control of nonlinear systems with friction , 1999, IEEE Trans. Control. Syst. Technol..

[8]  Karl Johan Åström,et al.  Friction generated limit cycles , 1996, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro.

[9]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[10]  Daniel W. Berns,et al.  Bifurcation Control in Feedback Systems , 2003 .

[11]  Peter I. Corke,et al.  Nonlinear control of the Reaction Wheel Pendulum , 2001, Autom..

[12]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[13]  A. Krall.  Applied Analysis , 1986 .

[14]  Maarten Steinbuch,et al.  Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model , 2003, Autom..

[15]  R. Ortega,et al.  Stabilization of nonlinear systems via forwarding mod {L/sub g/V} , 2001 .

[16]  R. Olfati-Saber.  Global stabilization of a flat underactuated system: the inertia wheel pendulum , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[17]  Jorge L. Moiola,et al.  An Experimental Application of the Anticontrol of Hopf bifurcations , 2001, Int. J. Bifurc. Chaos.