On the convergence properties of a 2-sliding control algorithm for non-linear uncertain systems

The second order sliding mode control of uncertain dynamical systems can be expressed in terms of the stabilization of uncertain second-order non-linear systems with incomplete state availability. The existence of the solution strictly depends on the assumptions made on the uncertainties, and global results are not always attainable. In this paper the class of systems for which a suitable variable structure control algorithm ensures finite time global convergence to the sliding manifold is identified. Simulation results highlight the effectiveness of the proposed method.

[1]  A. Isidori Nonlinear Control Systems , 1985 .

[2]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[3]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[4]  Arie Levant,et al.  Higher order sliding modes as a natural phenomenon in control theory , 1996 .

[5]  J. Hedrick,et al.  Nonlinear Observers—A State-of-the-Art Survey , 1989 .

[6]  A. Levant Sliding order and sliding accuracy in sliding mode control , 1993 .

[7]  M. Thoma,et al.  Variable Structure Systems, Sliding Mode and Nonlinear Control , 1999 .

[8]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[9]  F. Garofalo,et al.  Robust Control Via Variable Structure and Lyapunov Techniques , 1996 .

[10]  Giorgio Bartolini,et al.  An improved, chattering free, VSC scheme for uncertain dynamical systems , 1996, IEEE Trans. Autom. Control..

[11]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[12]  Hakan Elmali,et al.  Robust output tracking control of nonlinear MIMO systems via sliding mode technique , 1992, Autom..

[13]  S. V. Emel'yanov,et al.  High-order sliding modes in control systems , 1996 .

[14]  Antonella Ferrara,et al.  APPLICATIONS OF A SUB‐OPTIMAL DISCONTINUOUS CONTROL ALGORITHM FOR UNCERTAIN SECOND ORDER SYSTEMS , 1997 .

[15]  G. Bartolini,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Trans. Autom. Control..

[16]  Antonella Ferrara,et al.  On second order sliding mode controllers , 1998 .

[17]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .