Introduction to State Estimation of High-Rate System Dynamics

Engineering systems experiencing high-rate dynamic events, including airbags, debris detection, and active blast protection systems, could benefit from real-time observability for enhanced performance. However, the task of high-rate state estimation is challenging, in particular for real-time applications where the rate of the observer’s convergence needs to be in the microsecond range. This paper identifies the challenges of state estimation of high-rate systems and discusses the fundamental characteristics of high-rate systems. A survey of applications and methods for estimators that have the potential to produce accurate estimations for a complex system experiencing highly dynamic events is presented. It is argued that adaptive observers are important to this research. In particular, adaptive data-driven observers are advantageous due to their adaptability and lack of dependence on the system model.

[1]  Johannes Reuter,et al.  State estimation for fast-switching solenoid valves: A study on practical nonlinear observers and new experimental results , 2015, 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR).

[2]  K. Khayati,et al.  Adaptive observer for a large class of nonlinear systems with exponential convergence of parameter estimation , 2013, 2013 International Conference on Control, Decision and Information Technologies (CoDIT).

[3]  T D Carrigan,et al.  Airbag associated fatal head injury : case report and review of the literature on airbag injuries , 2000 .

[4]  Minyue Fu,et al.  Convergence results of the analytic center estimator , 2000, IEEE Trans. Autom. Control..

[5]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[6]  Lyle H. Ungar,et al.  A hybrid neural network‐first principles approach to process modeling , 1992 .

[7]  Yujiao Zhao,et al.  Unscented Kalman filter and its nonlinear application for tracking a moving target , 2013 .

[8]  Lotfi A. Zadeh A Summary and Update of “Fuzzy Logic” , 2010, 2010 IEEE International Conference on Granular Computing.

[9]  F. Daum Nonlinear filters: beyond the Kalman filter , 2005, IEEE Aerospace and Electronic Systems Magazine.

[10]  Dianguo Xu,et al.  Comparative Study of an Adaptive Sliding Observer and an EKF for Speed Sensor-less DTC IPM Synchronous Motor Drives , 2007, 2007 IEEE Power Electronics Specialists Conference.

[11]  R. Lyapunov Techniques for the Exponential Stability of Linear Difference Equations with Random Coefficients , 2022 .

[12]  Kiyoshi Ohishi,et al.  Wideband Force Control by Position-Acceleration Integrated Disturbance Observer , 2008, IEEE Transactions on Industrial Electronics.

[13]  Kou Yamada,et al.  A design method for unknown input observer for non-minimum phase systems , 2007, ICMIT: Mechatronics and Information Technology.

[14]  Milind E. Rane,et al.  Comparative analysis of linear and non-linear extended state observer with application to motion control , 2014, International Conference for Convergence for Technology-2014.

[15]  Gwi-Tae Park,et al.  Stereovision-based real-time occupant classification system for advanced airbag systems , 2011 .

[16]  Eve Hinman,et al.  Survey of Window Retrofit Solutions for Blast Mitigation , 2004 .

[17]  Wan Kyun Chung,et al.  Design and Performance Tuning of Sliding-Mode Controller for High-Speed and High-Accuracy Positioning Systems in Disturbance Observer Framework , 2009, IEEE Transactions on Industrial Electronics.

[18]  Arthur E. Frazho,et al.  On the convergence of the minimum variance spectral estimator in nonstationary noise , 1991, IEEE Trans. Inf. Theory.

[19]  A. Gelb,et al.  Dual contributions of optimal estimation theory in aerospace applications , 1986, IEEE Control Systems Magazine.

[20]  I. J. Myung,et al.  Tutorial on maximum likelihood estimation , 2003 .

[21]  Tong Zhou On the Convergence and Stability of a Robust State Estimator , 2010, IEEE Transactions on Automatic Control.

[22]  Zhiqiang Gao,et al.  A comparison study of advanced state observer design techniques , 2003, Proceedings of the 2003 American Control Conference, 2003..

[23]  R. Marino Adaptive observers for single output nonlinear systems , 1990 .

[24]  Jae Sik Chung,et al.  A Multiscale Framework with Extended Kalman Filter for Lithium-Ion Battery SOC and Capacity Estimation , 2010 .

[25]  R. Marino,et al.  Global adaptive observers for nonlinear systems via filtered transformations , 1992 .

[26]  Witold Byrski,et al.  On-line fast identification method and exact state observer for adaptive control of continuous system , 2014, Proceeding of the 11th World Congress on Intelligent Control and Automation.

[27]  Zhang Yingchao,et al.  A full sliding mode sensorless control of three-level inverter-fed induction motors , 2008, 2008 IEEE Power Electronics Specialists Conference.

[28]  Marco Tursini,et al.  Adaptive sliding mode observer for speed sensorless control of induction motors , 1999, Conference Record of the 1999 IEEE Industry Applications Conference. Thirty-Forth IAS Annual Meeting (Cat. No.99CH36370).

[29]  D. Luenberger An introduction to observers , 1971 .

[30]  Leonid M. Fridman,et al.  Design of a prescribed convergence time uniform Robust Exact Observer in the presence of measurement noise , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[31]  Goutam Chakraborty,et al.  Robust Unknown Input Observer for Nonlinear Systems and Its Application to Fault Detection and Isolation , 2008 .

[32]  Jerome J. Connor,et al.  Structural Motion Engineering , 2014 .

[33]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[34]  M. Morari,et al.  A discrete adaptive observer and identifier with arbitrarily fast rate of convergence , 1982 .

[35]  Zheng Zhang,et al.  An adaptive sliding-mode observer for induction motor sensorless speed control , 2005, IEEE Transactions on Industry Applications.

[36]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[37]  John N. Chiasson,et al.  Nonlinear speed observer for high-performance induction motor control , 1995, IEEE Trans. Ind. Electron..

[38]  I. Guyon,et al.  Neural networks and applications tutorial , 1991 .

[39]  T. Bui-Thanh,et al.  An active concept for limiting injuries caused by air blasts , 2010 .

[40]  A. Andrews,et al.  Applications of Kalman Filtering to Aerospace: 1960 to Present , 2010 .

[41]  Gregory M. Shaver,et al.  Input observer convergence and robustness: Application to compression ratio estimation , 2013 .

[42]  Kiyoshi Ohishi,et al.  High-performance Load Torque Compensation of Industrial Robot using Kalman-filter-based Instantaneous State Observer , 2015 .

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

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

[45]  James D. Walker,et al.  From Columbia to Discovery: Understanding the impact threat to the space shuttle , 2009 .

[46]  Yang Yingjuan,et al.  Design of a nonlinear adaptive observer for a class of Lipschitz systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[47]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[48]  Abdollah Bagheri,et al.  Structural damage detection using incomplete modal data and incomplete static response , 2013 .

[49]  M. Geetha,et al.  Comparative performance analysis of extended Kalman filter and neural observer for state estimation of continuous stirred tank reactor , 2013, 2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT).

[50]  Fawang Liu,et al.  Numerical solution of the space fractional Fokker-Planck equation , 2004 .

[51]  Jafar Zarei,et al.  Robust sensor fault detection based on nonlinear unknown input observer , 2014 .

[52]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[53]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[54]  G. Das,et al.  A comparative study between Luenberger full order observer and full order observer designed by generalized matrix inverse method , 2014, 2014 First International Conference on Automation, Control, Energy and Systems (ACES).

[55]  Mohammad Reza Mosavi Comparing DGPS corrections prediction using neural network, fuzzy neural network, and Kalman filter , 2006 .

[56]  Gildas Besancon,et al.  Immersion-Based Observer Design , 2007 .

[57]  Eugénio C. Ferreira,et al.  A study on the convergence of observer-based kinetics estimators in stirred tank bioreactors , 1996 .

[58]  H. Kolsky An Investigation of the Mechanical Properties of Materials at very High Rates of Loading , 1949 .

[59]  Nicolas Boizot,et al.  Adaptive-gain observers and applications , 2007 .

[60]  Zhenwei Cao,et al.  A comparative study of observer design techniques for state of charge estimation in electric vehicles , 2012, 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA).

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

[62]  Stephen A. Billings,et al.  Approximate observability of infinite dimensional bilinear systems using a Volterra series expansion , 2015, Syst. Control. Lett..

[63]  H.M. Hafez,et al.  A comparison between Kalman filters and recurrent neural networks , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

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

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

[66]  Fred Daum New exact nonlinear filters: theory and applications , 1994, Defense, Security, and Sensing.

[67]  Mohammad Javad Yazdanpanah,et al.  Adaptive state observer for Lipschitz nonlinear systems , 2013, Syst. Control. Lett..

[68]  S. Billings Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains , 2013 .

[69]  P. Swerling Modern state estimation methods from the viewpoint of the method of least squares , 1971 .

[70]  Reachability State Feedback , .

[71]  Torsten Jeinsch,et al.  Dynamic nonlinear unknown input observer for fault detection of induction motors , 2015, 2015 23rd Iranian Conference on Electrical Engineering.

[72]  Bernard Derrida Introduction to neural network models , 1988 .

[73]  Hassan K. Khalil,et al.  High-gain observers in nonlinear feedback control , 2009, 2009 IEEE International Conference on Control and Automation.

[74]  M. Boutayeb,et al.  Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems , 1997, IEEE Trans. Autom. Control..

[75]  R. Ortega An on-line least-squares parameter estimator with finite convergence time , 1988 .

[76]  Wei Xu,et al.  A comparative study of Luenberger observer, sliding mode observer and extended Kalman filter for sensorless vector control of induction motor drives , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[77]  Lihua Xie,et al.  Fault Detection and Isolation of Nonlinear Systems: An Unknown Input Observer Approach With Sum-of-Squares Techniques , 2012 .

[78]  Yan Wang,et al.  Observer design for differentiable Lipschitz nonlinear systems with time-varying parameters , 2014, 53rd IEEE Conference on Decision and Control.

[79]  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.

[80]  G. Besançon An Overview on Observer Tools for Nonlinear Systems , 2007 .

[81]  E. Kamen A recursive parameter estimator yielding exponential convergence under sufficient excitation , 1989 .

[82]  Hao-Chi Chang,et al.  Sliding mode control on electro-mechanical systems , 1999 .

[83]  Zi-li Deng,et al.  Convergence of self-tuning Riccati equation for systems with unknown parameters and noise variances , 2010, World Congress on Intelligent Control and Automation.