Discrete-Time Sliding-Mode State and Unknown Input Estimations for Nonlinear Systems

This paper addresses the problems of discrete-time state and unknown input/fault estimation for continuous-time nonlinear systems with multiple unknown inputs. Taylor series expansion and a nonlinear transformation are used to convert the nonlinear continuous-time system into a discrete-time model. The conditions for the observability of unknown inputs w.r.t. outputs are discussed. The novelty lies in the formulation of multiple sliding-mode estimator for the states that are directly influenced by unknown inputs, which cannot be decoupled by nonlinear transformation. This framework allows for the estimation of unknown inputs from the multiple sliding modes. The existence of discrete-time sliding mode is guaranteed, and the relation between the boundary layer thickness and the sliding-mode gain design that will eliminate chattering and the boundedness conditions is obtained. The proposed technique can be applied for fault detection and isolation. Simulation results with application to three-phase motor are given to demonstrate the effectiveness of the proposed method.

[1]  Asif Sabanoviç,et al.  Sliding-Mode Control for High-Precision Motion of a Piezostage , 2007, IEEE Transactions on Industrial Electronics.

[2]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[3]  Vadim I. Utkin,et al.  Sliding mode control design principles and applications to electric drives , 1993, IEEE Trans. Ind. Electron..

[4]  Cristian Lascu,et al.  Sliding-mode observer and improved integrator with DC-offset compensation for flux estimation in sensorless-controlled induction motors , 2006, IEEE Transactions on Industrial Electronics.

[5]  S. Żak,et al.  State observation of nonlinear uncertain dynamical systems , 1987 .

[6]  U. Ozguner,et al.  Equivalent value filters in disturbance estimation and state observation , 1999 .

[7]  Sarah K. Spurgeon,et al.  Hyperplane design techniques for discrete-time variable structure control systems , 1992 .

[8]  K. Furuta Sliding mode control of a discrete system , 1990 .

[9]  S. Drakunov Sliding-mode observers based on equivalent control method , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[10]  J. Aplevich,et al.  Lecture Notes in Control and Information Sciences , 1979 .

[11]  A. J. Koshkouei,et al.  Sliding mode state observation for non-linear systems , 2004 .

[12]  Wen-Fang Xie,et al.  Sliding-Mode Observer Based Adaptive Control for Servo Actuator with Friction , 2007, 2007 International Conference on Mechatronics and Automation.

[13]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[14]  M. Zeitz,et al.  Extended Luenberger observer for non-linear multivariable systems , 1988 .

[15]  A. J. Koshkouei,et al.  Sliding mode state observers for SISO linear discrete-time systems , 1996 .

[16]  Y.C. Soh,et al.  Observer with multiple sliding modes for a class of nonlinear uncertain systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[17]  S. Żak,et al.  Comparative study of non-linear state-observation techniques , 1987 .

[18]  Vadim I. Utkin,et al.  Direct torsion control of flexible shaft in an observer-based discrete-time sliding mode , 1998, IEEE Trans. Ind. Electron..

[19]  Yi Xiong,et al.  Sliding mode observer for nonlinear uncertain systems , 2001, IEEE Trans. Autom. Control..

[20]  Andrzej Bartoszewicz,et al.  Discrete-time quasi-sliding-mode control strategies , 1998, IEEE Trans. Ind. Electron..

[21]  Chee Pin Tan,et al.  Sliding mode observers for fault detection and isolation , 2002 .

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

[23]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[24]  Veluvolu Kalyana Chakravarthy,et al.  Sliding mode observers and unknown input estimations for nonlinear systems , 2007 .

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

[26]  Ali Keyhani,et al.  Sliding-Mode Flux Observer With Online Rotor Parameter Estimation for Induction Motors , 2007, IEEE Transactions on Industrial Electronics.

[27]  V. Utkin Variable structure systems with sliding modes , 1977 .

[28]  Y. Soh,et al.  Robust observer with sliding mode estimation for nonlinear uncertain systems , 2007 .

[29]  B. Drazenovic,et al.  The invariance conditions in variable structure systems , 1969, Autom..

[30]  Ching Chuen Chan,et al.  A novel sliding-mode observer for indirect position sensing of switched reluctance motor drives , 1999, IEEE Trans. Ind. Electron..

[31]  Yeng Chai Soh,et al.  Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems , 2007 .