Robust observer with sliding mode estimation for nonlinear uncertain systems

To handle the state estimation of a nonlinear system perturbed by a scalar disturbance distributed by a known nonlinear vector, we incorporate a sliding mode term into a nonlinear observer to realise a robust nonlinear observer. By linking the observability of the unknown input to the output measurement, the so-called matching condition is avoided. The measurable output estimation error is the sliding surface. In the sliding mode, the reduced-order error system is free from the disturbance, and the convergence of the estimation error dynamics is proven. The unknown input/disturbance is estimated from the sliding mode. Under a Lipschitz condition for the nonlinear part, the nonlinear observers are designed under the structural assumption that the system is observable with respect to any control input. The proposed robust nonlinear estimator is applied to state and unknown input estimation of a bioreactor. The simulation results demonstrate the effectiveness of the proposed method.

[1]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[2]  D. Luenberger.  Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

[3]  F. Thau.  Observing the state of non-linear dynamic systems† , 1973 .

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

[5]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[6]  F Rikus Eising,et al.  Between controllable and uncontrollable , 1984 .

[7]  J. Hedrick,et al.  Nonlinear state estimation using sliding observers , 1986, 1986 25th IEEE Conference on Decision and Control.

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

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

[10]  Costas Kravaris,et al.  Geometric methods for nonlinear process control. 2. Controller synthesis , 1990 .

[11]  Stanislaw H. Zak,et al.  On the stabilization and observation of nonlinear/uncertain dynamic systems , 1990 .

[12]  C. Kravaris,et al.  Geometric methods for nonlinear process control. 1. Background , 1990 .

[13]  Denis Dochain,et al.  ADAPTIVE CONTROL OF BIOREACTORS , 1990 .

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

[15]  D. Dochain,et al.  On-Line Estimation and Adaptive Control of Bioreactors , 2013 .

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

[17]  J. Gauthier,et al.  High gain estimation for nonlinear systems , 1992 .

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

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

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

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

[22]  J. Gauthier,et al.  Erratum Observability and Observers for Nonlinear Systems , 1995 .

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

[24]  C. Moog,et al.  New algebraic-geometric conditions for the linearization by input-output injection , 1996, IEEE Trans. Autom. Control..

[25]  H. Khalil,et al.  A separation principle for the stabilization of a class of nonlinear systems , 1997 .

[26]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[27]  Masoud Soroush.  State and parameter estimations and their applications in process control , 1998 .

[28]  R. Rajamani,et al.  Existence and design of observers for nonlinear systems: Relation to distance to unobservability , 1998 .

[29]  Olivier Bernard,et al.  Nonlinear observers for a class of biological systems: application to validation of a phytoplanktonic growth model , 1998, IEEE Trans. Autom. Control..

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

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

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

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

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

[35]  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..

[36]  Y. Soh,et al.  Discrete-time sliding mode observer design for a class of uncertain nonlinear systems , 2006, 2006 American Control Conference.

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