From Poncelet's invariance principle to Active Disturbance Rejection

This is a brief survey of a little known field of disturbance estimation and subsequent cancellation, a field with a long history and is still rather disorganized. Researchers and results are scattered over almost two centuries, across East and West: from Jean-Victor Poncelet's Principle of Invariance in 1829, to Jingqing Han's conception of Active Disturbance Rejection in 1995 and beyond. But the field in recent years is maturing and coming into a focus with significant practical and theoretical implications abound. It provides a powerful alternative to the modern control paradigm in how real world control problems, of which disturbance rejection is a central theme, are viewed and solved. In this paper a reader will find a brief history of ideas, a new, unifying, problem formulation, and a summary of recent stability analysis results.

[1]  Zhiqiang Gao,et al.  Active disturbance rejection control: a paradigm shift in feedback control system design , 2006, 2006 American Control Conference.

[2]  Michael A. Demetriou,et al.  UIO for fault detection in vector second order systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[4]  Hassan K. Khalil,et al.  Nonlinear Output-Feedback Tracking Using High-gain Observer and Variable Structure Control, , 1997, Autom..

[5]  Zhiqiang Gao,et al.  A Stability Study of the Active Disturbance Rejection Control Problem by a Singular Perturbation Approach , 2009 .

[6]  Fang Wang,et al.  A comparison study of two disturbance rejection control strategies for hydraulic position servo systems , 2004, 30th Annual Conference of IEEE Industrial Electronics Society, 2004. IECON 2004.

[8]  Hassan K. Khalil,et al.  Performance Recovery of Feedback-Linearization-Based Designs , 2008, IEEE Transactions on Automatic Control.

[9]  Zhiqiang Gao,et al.  A survey of state and disturbance observers for practitioners , 2006, 2006 American Control Conference.

[10]  J. Rootenberg,et al.  Some considerations relating to control systems employing the invariance principle , 1964 .

[11]  E Schrijver,et al.  剛体機械系に対する外乱観測器 等価性,安定性および設計 , 2002 .

[12]  Wan Kyun Chung,et al.  A discrete-time design and analysis of perturbation observer for motion control applications , 2003, IEEE Trans. Control. Syst. Technol..

[13]  Antonio Tornambè,et al.  A Decentralized Controller for the Robust Stabilization of a Class of MIMO Dynamical Systems , 1994 .

[14]  C. D. Johnson,et al.  Accomodation of external disturbances in linear regulator and servomechanism problems , 1971 .

[15]  Zhiqiang Gao,et al.  On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics , 2007, 2007 46th IEEE Conference on Decision and Control.

[16]  Kyongsu Yi,et al.  Nonlinear vehicle stability control using disturbance observer , 2002, Proceedings of the International Conference on Control Applications.

[17]  Dan Wang,et al.  Adaptive unknown input observer approach for aircraft actuator fault detection and isolation , 2007 .

[18]  A. S. Vostrikov,et al.  Russia [control education] , 1996 .

[19]  M. Arcak,et al.  A Two-Time-Scale Redesign for Robust Stabilization and Performance Recovery of Uncertain Nonlinear Systems , 2007, 2007 American Control Conference.

[20]  Masayoshi Tomizuka,et al.  Passivity-based versus disturbance observer based robot control : Equivalence and stability , 1999 .

[21]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[22]  Christopher I. Byrnes,et al.  Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection , 2008, Annu. Rev. Control..

[23]  Yoichi Hori,et al.  Robust speed control of DC servomotors using modern two degrees-of-freedom controller design , 1991 .

[24]  Hyungbo Shim,et al.  Adding robustness to nominal output-feedback controllers for uncertain nonlinear systems: A nonlinear version of disturbance observer , 2008, Autom..

[25]  Peter J. Gawthrop,et al.  A nonlinear disturbance observer for robotic manipulators , 2000, IEEE Trans. Ind. Electron..

[26]  Jingqing Han,et al.  From PID to Active Disturbance Rejection Control , 2009, IEEE Trans. Ind. Electron..

[27]  Zhiqiang Gao,et al.  Scaling and bandwidth-parameterization based controller tuning , 2003, Proceedings of the 2003 American Control Conference, 2003..

[28]  Johannes A.G.M. van Dijk,et al.  Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design , 2002 .

[29]  Yi Huang,et al.  An alternative paradigm for control system design , 2001 .