Exact differentiation and sliding mode observers for switched Lagrangian systems

Abstract The main topic of this paper is the problem of constructing observers for switched mechanical systems, which includes, as a specific case, the design of observers based on the high order sliding mode technique. The high order sliding mode is used to overcome the chattering phenomena occurring, which induce some irrelevant and undesirable phenomena for mechanical systems. The proposed approach, based on the Fliess canonical form, also allows observers to give an estimate of the discrete location of the system, which indicates the dynamic evolution. The convergence of the observers is proved and a stick–mass–friction system is used to illustrate the efficiency of the proposed hybrid observers.

[1]  Andrea Balluchi,et al.  A hybrid observer for the driveline dynamics , 2001, 2001 European Control Conference (ECC).

[2]  Eliathamby Ambikairajah,et al.  A hybrid state estimation scheme for power systems , 2002, Asia-Pacific Conference on Circuits and Systems.

[3]  A. Levant,et al.  Higher order sliding modes and arbitrary-order exact robust differentiation , 2001, 2001 European Control Conference (ECC).

[4]  S. Shankar Sastry,et al.  Observability of Linear Hybrid Systems , 2003, HSCC.

[5]  M. D. Di Benedetto,et al.  A Nonlinear Observer for Flexible Mechanisms using Canonical Forms , 1990, 1990 American Control Conference.

[6]  J. J. Slotine,et al.  Tracking control of non-linear systems using sliding surfaces with application to robot manipulators , 1983, 1983 American Control Conference.

[7]  Eduardo Sontag.  On the Observability of Polynomial Systems, I: Finite-Time Problems , 1979 .

[8]  Arturo Zavala-Río,et al.  On the control of complementary-slackness juggling mechanical systems , 2000, IEEE Trans. Autom. Control..

[9]  Carlos Canudas de Wit,et al.  Sliding observers for robot manipulators , 1991, Autom..

[10]  Vibration Reduction of a Harmonically Excited Beam with One-sided Spring Using Sliding Computed Torque Control , 1997 .

[11]  P. Lucibello,et al.  Nonlinear observer for a class of mechanical systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[12]  Driss Boutat,et al.  About the observability of piecewise dynamical systems , 2004 .

[13]  Daniel E. Koditschek,et al.  From stable to chaotic juggling: theory, simulation, and experiments , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[14]  Noureddine Manamanni,et al.  SLIDING MODE OBSERVER FOR TRIANGULAR INPUT HYBRID SYSTEM , 2005 .

[15]  Manuel de la Sen,et al.  Design of linear observers for a class of linear hybrid systems , 2000, Int. J. Syst. Sci..

[16]  Karl Henrik Johansson.  Hybrid control systems , 2004 .

[17]  A. Juloski,et al.  Two approaches to state estimation for a class of piecewise affine systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[18]  Michel Fliess,et al.  Generalized controller canonical form for linear and nonlinear dynamics , 1990 .

[19]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[20]  B. Brogliato,et al.  On the control of finite-dimensional mechanical systems with unilateral constraints , 1997, IEEE Trans. Autom. Control..

[21]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[22]  A. Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).