On Sliding Mode Observers for Systems with Unknown Inputs

This paper considers the problem of designing an observer for a linear system subject to unknown inputs. This problem has been extensively studied in the literature with respect to both linear and nonlinear (sliding mode) observers. Necessary and sufficient conditions to enable a linear unknown input observer to be designed have been established for many years. One way to express these conditions is that the transfer function matrix between the unknown input and the measured output must be minimum phase and relative degree one. Identical conditions must be met in order to design a 'classical' sliding mode observer for the same problem. This paper shows how the relative degree condition can be weakened if a classical sliding mode observer is combined with sliding mode exact differentiators to essentially generate additional independent output signals from the available measurements. A simple pedagogical example demonstrates the efficacy of the approach

[1]  T. Floquet *,et al.  On the robust fault detection via a sliding mode disturbance observer , 2004 .

[2]  J. Barbot,et al.  A finite time observer for flux estimation in the induction machine , 2002, Proceedings of the International Conference on Control Applications.

[3]  M. Hautus.  Strong detectability and observers , 1983 .

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

[5]  S. Spurgeon,et al.  On the development of discontinuous observers , 1994 .

[6]  V. Utkin,et al.  Sliding mode observers. Tutorial , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  Jie Chen,et al.  Design of unknown input observers and robust fault detection filters , 1996 .

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

[9]  P. Borne,et al.  A note on sliding observer and controller for generalized canonical forms , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[10]  Jean-Pierre Barbot,et al.  Sliding observer-based feedback control for flexible joints manipulator , 1996, Autom..

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

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

[13]  J. Slotine,et al.  On Sliding Observers for Nonlinear Systems , 1986, 1986 American Control Conference.

[14]  Christopher Edwards,et al.  A comparison of sliding mode and unknown input observers for fault reconstruction , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  Chee Pin Tan,et al.  An LMI approach for designing sliding mode observers , 2001 .

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

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

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

[19]  J. Barbot,et al.  Sliding mode observer for triangular input form , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[21]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[22]  M. Darouach.  On the novel approach to the design of unknown input observers , 1994, IEEE Trans. Autom. Control..

[23]  J. Barbot,et al.  A canonical form for the design of unknown input sliding mode observers , 2008 .

[24]  Martin J. Corless,et al.  State and Input Estimation for a Class of Uncertain Systems , 1998, Autom..

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

[26]  I. Haskara.  On sliding mode observers via equivalent control approach , 1998 .

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

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

[29]  Christopher Edwards,et al.  Sliding mode observers for robust detection and reconstruction of actuator and sensor faults , 2003 .

[30]  Gabriel Abba,et al.  Modeling and robust control of winding systems for elastic webs , 2002, IEEE Trans. Control. Syst. Technol..

[31]  M. Hou,et al.  Design of observers for linear systems with unknown inputs , 1992 .

[32]  Mohamed Djemai,et al.  Sliding Mode Observers , 2002 .

[33]  P. Kokotovic,et al.  The peaking phenomenon and the global stabilization of nonlinear systems , 1991 .

[34]  Noureddine Manamanni,et al.  Exact differentiation and sliding mode observers for switched Lagrangian systems , 2006 .

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

[36]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[37]  Christopher Edwards,et al.  Sensor fault tolerant control using sliding mode observers , 2006 .

[38]  Jie Chen,et al.  Robust detection of faulty actuators via unknown input observers , 1991 .