Discrete-time H∞ control of a triple inverted pendulum with single control input

A design of a robust computer control system for balancing and improving the steady-state performance of a triple inverted pendulum-cart system is considered. The controller is based on discrete-time H/sub /spl infin// theory and is implemented via a robust reduced order dynamic observer. An integrator is used to eliminate the effects of small constant sensor offsets and rail inclinations. Disturbance attenuation and relative stability characteristics are studied via frequency response analysis. Simulation and experimental results are reported.

[1]  H. Unbehauen,et al.  Discrete computer control of a triple-inverted pendulum , 1990 .

[2]  S. C. Sinha,et al.  Control of General Dynamic Systems With Periodically Varying Parameters Via Liapunov-Floquet Transformation , 1994 .

[3]  Frederick W. Fairman,et al.  A State-Space Approach to Discrete-Time , 1992 .

[4]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  Katsuhisa Furuta,et al.  Control of unstable mechanical system Control of pendulum , 1976 .

[6]  G.A. Medrano-Cerda,et al.  Biped robot locomotion in the sagittal I plane , 1997 .

[7]  C.W. Anderson,et al.  Learning to control an inverted pendulum using neural networks , 1989, IEEE Control Systems Magazine.

[8]  N. Ono,et al.  Attitude control of a triple inverted pendulum , 1984 .

[9]  G. Medrano-Cerda,et al.  Balancing and Attitude Control of Double and Triple Inverted Pendulums , 1995 .

[10]  Kazuhiro Kosuge,et al.  Digital control of a double inverted pendulum on an inclined rail , 1980 .

[11]  M. A. Peters,et al.  Minimum Entropy Control for Time-Varying Systems , 1997 .

[12]  John O'Reilly,et al.  Observers for Linear Systems , 1983 .

[13]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[14]  Michael Green,et al.  H8 controller synthesis by J-lossless coprime factorization , 1992 .

[15]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[16]  K. Glover,et al.  State-space approach to discrete-time H∞ control , 1991 .

[17]  G.-W. van der Linden,et al.  H/sub infinity / control of an experimental inverted pendulum with dry friction , 1992, [Proceedings 1992] The First IEEE Conference on Control Applications.

[18]  G. A. Medrano-Cerda,et al.  Robust stabilization of a triple inverted pendulum-cart , 1997 .

[19]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[20]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[21]  G.-W. van der Linden,et al.  H/sub ∞/ control of an experimental inverted pendulum with dry friction , 1993, IEEE Control Systems.

[22]  K. G. Eltohamy,et al.  Nonlinear optimal control of a triple link inverted pendulum with single control input , 1998 .

[23]  P. Larcombe.  On the control of a two-dimensional multi-link inverted pendulum: the form of the dynamic equations from choice of co-ordinate system , 1992 .