TWO RELAY CONTROLLER FOR REAL TIME TRAJECTORY GENERATION AND ITS APPLICATION TO INVERTED ORBITAL STABILIZATION OF INERTIA WHEEL PENDULUM VIA QUASI-CONTINUOUS HOSM

A quasi-continuous high-order sliding mode (QC-HOSM) control is developedto solvethe trackingcontrolproblemfor an inertiawheelpendulum. A first step towards the solution of the tracking control problem in underactuated systems is to find the set of reference trajectories. A reference model based on the two relay controller idea is then developed for generating a set of desired periodic trajectories for the pendulum centered at its upright position. The two relay controller produces oscillations at the scalar output of the reference underactuated system where the desired amplitude and frequency are reached by choosing its gains. The HOSM will be capable of making the pendulum move, tracking the prescribed reference signals determined by the trajectory generator. Performance issues of the controller constructed are illustrated in an experimental study.

[1]  Rafael Kelly,et al.  A measurement procedure for viscous and coulomb friction , 2000, IEEE Trans. Instrum. Meas..

[2]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[3]  Leonid M. Fridman,et al.  Exact compensation of unmatched perturbation via quasi-continuous HOSM , 2008, 2008 47th IEEE Conference on Decision and Control.

[4]  L. Fridman,et al.  Identification based generation of self-excited oscillations for underactuated mechanical systems via two-relay algorithm , 2008, 2008 International Workshop on Variable Structure Systems.

[5]  Leonid M. Fridman,et al.  Generating self-excited oscillations for underactuated mechanical systems via two-relay controller , 2009, Int. J. Control.

[6]  Ronald S. Fearing,et al.  Tracking fast inverted trajectories of the underactuated Acrobot , 1999, IEEE Trans. Robotics Autom..

[7]  Karl Johan Åström,et al.  The Reaction Wheel Pendulum , 2007, The Reaction Wheel Pendulum.

[8]  Leonid M. Fridman,et al.  Generating Self-Excited Oscillations via Two-Relay Controller , 2009, IEEE Transactions on Automatic Control.

[9]  Thierry Floquet,et al.  Second‐order sliding mode control of underactuated mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up/balancing control , 2008 .

[10]  Carlos Canudas-de-Wit,et al.  Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach , 2005, IEEE Transactions on Automatic Control.

[11]  Arie Levant,et al.  Chattering Analysis , 2007, IEEE Transactions on Automatic Control.

[12]  Leonid B. Freidovich,et al.  Transverse Linearization for Controlled Mechanical Systems With Several Passive Degrees of Freedom , 2010, IEEE Transactions on Automatic Control.

[13]  Yu-Ping Tian,et al.  Frequency-Domain Analysis and Design of Distributed Control Systems: Tian/Frequency-Domain Analysis and Design of Distributed Control Systems , 2012 .

[14]  Christine Chevallereau,et al.  Nonlinear control of mechanical systems with an unactuated cyclic variable , 2005, IEEE Transactions on Automatic Control.

[15]  Claudio Urrea,et al.  ORBITAL STABILIZATION OF UNDERACTUATED MECHANICAL SYSTEMS , 2002 .

[16]  Arie Levant,et al.  Quasi-continuous high-order sliding-mode controllers , 2005, IEEE Transactions on Automatic Control.

[17]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[18]  D. P. Atherton,et al.  Nonlinear Control Engineering-Describing Function Analysis and Design , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Arie Levant,et al.  Quasi-continuous high-order sliding-mode controllers , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[20]  Igor Boiko,et al.  Inducing oscillations in an inertia wheel pendulum via two-relays controller: Theory and experiments , 2009, 2009 American Control Conference.

[21]  J. Burdick,et al.  On the periodic motions of simple hopping robots , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.