Higher Order Sliding Mode Based Accurate Tracking of Unmatched Perturbed Outputs

Three approaches for higher-order sliding-mode based unmatched uncertainty compensation are summarized. Firstly, an algorithm is proposed based on the block control and quasi-continuous higher order sliding modes techniques. This method provides for the finite-time exact tracking of a smooth desired signal in spite of unmatched perturbations and allows the reduction of the controller gains in the case of partial knowledge of the system model. Thereafter, the combination of integral high-order sliding modes with the hierarchical quasi-continuous controller is proposed allowing finite-time convergence theoretically. Finally, high-order sliding mode observers are employed for exact state and uncertainties/perturbations reconstruction. A sliding mode control design is proposed which ensures theoretically exact compensation of the uncertainties/perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered for illustrating the feasibility of the proposed approach.

[1]  Han Ho Choi.  Output feedback variable structure control design with an H2 performance bound constraint , 2008, Autom..

[2]  Han Ho Choi,et al.  An LMI-based switching surface design method for a class of mismatched uncertain systems , 2003, IEEE Trans. Autom. Control..

[3]  Leonid M. Fridman,et al.  Integral HOSM Semiglobal Controller for Finite-Time Exact Compensation of Unmatched Perturbations , 2010, IEEE Transactions on Automatic Control.

[4]  Sarah K. Spurgeon,et al.  A nonlinear control strategy for robust sliding mode performance in the presence of unmatched uncertainty , 1993 .

[5]  Alexander G. Loukianov,et al.  Nested integral sliding modes of large scale power system. , 2007, 2007 46th IEEE Conference on Decision and Control.

[6]  B. Molinari.  A strong controllability and observability in linear multivariable control , 1976 .

[7]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

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

[9]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[10]  M.J. Yazdanpanah,et al.  Robust tracking of perturbed nonlinear systems by nested sliding mode control , 2005, 2005 International Conference on Control and Automation.

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

[12]  Leonid M. Fridman,et al.  Quasi-continuous HOSM control for systems with unmatched perturbations , 2008, 2008 International Workshop on Variable Structure Systems.

[13]  Leonid M. Fridman,et al.  High order sliding mode observer for linear systems with unbounded unknown inputs , 2010, Int. J. Control.

[14]  A. G. Luk'yanov.  A BLOCK METHOD OF SYNTHESIS OF NONLINEAR SYSTEMS AT SLIDING MODES , 1998 .

[15]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

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

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

[18]  Antonella Ferrara,et al.  Dynamical Adaptive First and Second-Order Sliding Backstepping Control of Nonlinear Nontriangular Uncertain Systems , 2000 .

[19]  Leonid M. Fridman,et al.  Robust exact finite-time output based control using high-order sliding modes , 2011, Int. J. Syst. Sci..

[20]  Y. B. Shtessel,et al.  Multiple time scale flight control using re-configurable sliding modes , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[21]  Arie Levant,et al.  Integral High-Order Sliding Modes , 2007, IEEE Transactions on Automatic Control.

[22]  J. Hedrick,et al.  Multiple-surface sliding control of a class of uncertain nonlinear systemsm , 1996 .

[23]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

[24]  Antonella Ferrara,et al.  On multi-input backstepping design with second order sliding modes for a class of uncertain nonlinear systems , 1998 .

[25]  Leonid M. Fridman,et al.  Singularly perturbed analysis of chattering in relay control systems , 2002, IEEE Trans. Autom. Control..

[26]  Antonella Ferrara,et al.  A combined backstepping/second order sliding mode approach to control a class of nonlinear systems , 1996, Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -.

[27]  Alexander G. Loukianov,et al.  Robust Block Decomposition Sliding Mode Control Design , 2002 .

[28]  Christopher Edwards,et al.  Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty , 2005, Eur. J. Control.

[29]  Arie Levant,et al.  Adjustment of high‐order sliding‐mode controllers , 2009 .

[30]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

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

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

[33]  Sarah K. Spurgeon,et al.  Sliding Mode Control , 1998 .

[34]  Leonid M. Fridman,et al.  High-Order Block Sliding-Mode Controller for a Synchronous Generator With an Exciter System , 2011, IEEE Transactions on Industrial Electronics.

[35]  Wen-Jun Cao,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Trans. Autom. Control..

[36]  B. Draenovi.  The invariance conditions in variable structure systems , 1969 .

[37]  Sarah K. Spurgeon,et al.  Robust implementation of sliding mode control schemes , 1993 .

[38]  Leonid Fridman,et al.  Unmatched uncertainties compensation based on high‐order sliding mode observation , 2013 .