Nonlinear observer for simultaneous states and unknown parameter estimation

This paper presents the design of an observer for the simultaneous estimation of states and unknown parameter for a class of nonlinear systems whose nonlinearity satisfies a bounded Jacobian condition. The paper presents two alternate observers based on the structure of the system. The conditions for the existence of these observers can be expressed as a linear matrix inequality and solved using standard solvers. The case of time-varying parameter and multiple unknown parameter have also been investigated. The use of the developed methodology is demonstrated through illustrative examples.

[1]  R. Rajamani,et al.  A systematic approach to adaptive observer synthesis for nonlinear systems , 1995, Proceedings of Tenth International Symposium on Intelligent Control.

[2]  Christiaan Moons,et al.  Parameter identification of induction motor drives , 1995, Autom..

[3]  T. Kataoka,et al.  Application of an extended Kalman filter to parameter identification of an induction motor , 1989, Conference Record of the IEEE Industry Applications Society Annual Meeting,.

[4]  Jennifer Stephan,et al.  Real-time estimation of the parameters and fluxes of induction motors , 1992, Conference Record of the 1992 IEEE Industry Applications Society Annual Meeting.

[5]  Martin Guay,et al.  Performance Improvement in Adaptive Control of Linearly Parameterized Nonlinear Systems $ $ , 2010, IEEE Transactions on Automatic Control.

[6]  Tor Arne Johansen,et al.  Adaptive Nonlinear Observer for Electropneumatic Clutch Actuator With Position Sensor , 2012, IEEE Transactions on Control Systems Technology.

[7]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[8]  Rajesh Rajamani,et al.  Quantitative fault estimation for a class of nonlinear systems , 2006, 2006 American Control Conference.

[9]  M. Gevers,et al.  Stable adaptive observers for nonlinear time-varying systems , 1987 .

[10]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[11]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[12]  Y. Sato,et al.  On-line estimation of induction motor parameters by extended Kalman filter , 2002 .

[13]  Salim Ibrir.  Global estimation of nonlinear systems with unknown-input coefficients , 2010, 2010 IEEE International Symposium on Intelligent Control.

[14]  M. Spong.  Modeling and Control of Elastic Joint Robots , 1987 .

[15]  R. Marino,et al.  Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems , 1995, IEEE Trans. Autom. Control..

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

[17]  Yousef Abdel-Rehim.  Parameter identification of induction motor , 2015 .

[18]  Tor Arne Johansen,et al.  Nonlinear observer and parameter estimation for electropneumatic clutch actuator , 2010 .

[19]  Thomas A. Lipo,et al.  An extended Kalman filter approach to rotor time constant measurement in PWM induction motor drives , 1992 .

[20]  Kyongsu Yi,et al.  Observer Based Identification of Nonlinear Vehicle Suspension Parameters , 1993, 1993 American Control Conference.

[21]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[22]  Rajesh Rajamani,et al.  Nonlinear Observer for Bounded Jacobian Systems, With Applications to Automotive Slip Angle Estimation , 2011, IEEE Transactions on Automatic Control.

[23]  G. Besançon,et al.  On adaptive observers for state affine systems , 2006 .