Control Theory and Technology

, Volume 14, Issue 3, pp 199–208 | Cite as

On ADRC for non-minimum phase systems: canonical form selection and stability conditions

  • Wenchao Xue
  • Yi Huang
  • Zhiqiang Gao


Active disturbance rejection control (ADRC), as proposed by Prof. Jingqing Han, reduces first the plant dynamics to its canonical form, normally in the form of cascade integrators, for which the standard controller can be employed to meet the design specifications. This paper concerns with the selection of the canonical form for non-minimum phase systems. In particular, it is shown that, by employing the well known controllable canonical form, the uncertainties of such systems can be divided into two terms in the state space model, one in the control channel and the other in the output channel. The necessary and sufficient condition is obtained for the stability of the closed-loop system with the proposed canonical form and ADRC. Also, by showing the necessity of the detectability of the extended system as well as certain information of the system-s “zeros”, we present the fundamental guidelines of design ADRC for non-minimum phase uncertain systems.


Active disturbance rejection control (ADRC) extended state observer (ESO) rejector uncertain systems nonminimum phase 


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  1. [1]
    Z. Gao. On the centrality of disturbance rejection in automatic control. ISA Transactions, 2014, 53(4): 850–857.CrossRefGoogle Scholar
  2. [2]
    M. Hou, P. C. Muller. Design of observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 1993, 37(6): 871–874.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D. Soffker, T. J. Yu, P. C. Mullter. State estimation of dynamical systems with nonlinearities by using proportionalintegral observer. International Journal of Systems Science, 1995, 26(9):1571–1582.CrossRefGoogle Scholar
  4. [4]
    M. Nakao, K. Ohnishi, K. Miyachi. A robust decentralized joint control based on interference estimation. IEEE International Conference on Robotics and Automation, Raleigh: IEEE, 1987: 326–331.Google Scholar
  5. [5]
    H. Shim, N. H. Jo. An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer. Automatica, 2009, 45(1): 296–299.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    W.-H. Chen, D. J. Ballance, P. J. Gawthrop, et al. A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics, 2000, 47(4): 932–938.CrossRefGoogle Scholar
  7. [7]
    L. Guo, S. Cao. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions, 2014, 53(4): 846–849.MathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Han. The “extended state observer” of a class of uncertain systems. Journal of Control and Decision, 1995, 10(1): 85–88 (in Chinese).Google Scholar
  9. [9]
    J. Han. From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 2009, 56(3): 900–906.CrossRefGoogle Scholar
  10. [10]
    C. D. Johnson. Real-time disturbance-observers; origin and evolution of the idea–Part 1: The early years. Proceedings of the 40th Southeastern Symposium on System Theory, New Orleans: IEEE, 2008: 88–91.Google Scholar
  11. [11]
    S. Li, J. Yang, W.-H. Chen, et al. Disturbance Observer-based Control: Methods and Applicaitons. Boca Raton: CRC Press, 2013.Google Scholar
  12. [12]
    A. Radke, Z. Gao. A survey of state and disturbance observers for practitioners. Proceedings of the American Control Conference, Minnesota: IEEE, 2006: 5183–5188.Google Scholar
  13. [13]
    Z. Gao. Scaling and bandwidth-parameterization based controller tuning. Proceedings of the American Control Conference, Colorado: IEEE, 2003: 4989–4996.Google Scholar
  14. [14]
    Q. Zheng, Z. Gao. On practical applications of active disturbance rejection control. Proceedings of the 29th Chinese Control Conference, Beijing: IEEE, 2010: 6095–6100.Google Scholar
  15. [15]
    R. Schoenberger. Linestream technologies signs licensing deal with Texas instruments. 2011: Scholar
  16. [16]
    G. Cheng, J. Hu. An observer-based mode switching control scheme for improved position regulation in servomotors. IEEE Transactions on Control Systems Technology, 2014, 22(5): 1883–1891.CrossRefGoogle Scholar
  17. [17]
    H. Liu, S. Li. Speed control for PMSM servo system using predictive functional control and extended state observer. IEEE Transactions on Industrial Electronics, 2012, 59(2): 1171–1183.CrossRefGoogle Scholar
  18. [18]
    J. Linares-Flores, C. Garcia-Rodriguez, H. Sira-Ramirez, et al. Robust backstepping tracking controller for low-speed pmsm positioning system: Design, analysis, and implementation. IEEE Transactions on Industrial Informatics, 2015, 11(5): 1130–1141.CrossRefGoogle Scholar
  19. [19]
    Y. Xia, Z. Zhu, M. Fu, et al. Attitude tracking of rigid spacecraft with bounded disturbances. IEEE Transactions on Industrial Electronics, 2011, 58(2): 647–659.CrossRefGoogle Scholar
  20. [20]
    T. Jiang, C. Huang, L. Guo. Control of uncertain nonlinear systems based on observers and estimators. Automatica, 2015, 59: 35–47.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    G. Sun, X. Ren, D. Li. Neural active disturbance rejection output control of multimotor servomechanism. IEEE Transactions on Control Systems Technology, 2015, 23(2): 746–753.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Q. Li, D. Li, W. Tan. Performance robustness comparison of ADRC and GPC. Proceedings of the Chinese Control Conference, Hefei, China: IEEE, 2012: 4586–4590.Google Scholar
  23. [23]
    H. Xie, K. Song, L. Li, et al. A comprehensive decoupling control method for gasoline hcci combustion. Proceedings of the Chinese Control Conference, Xi’an: IEEE, 2013: 7681–7691.Google Scholar
  24. [24]
    L. Sun, D. Li, Z. Gao, et al. Combined feedforward and model-assisted active disturbance rejection control for non-minimum phase system. ISA Transactions, 2016: DOI 10.1016/j.isatra.2016.04.020.Google Scholar
  25. [25]
    Y. Huang, W. Xue. Active disturbance rejection control: Methodology and theoretical analysis. ISA Transaction, 2014, 53: 963–976.CrossRefGoogle Scholar
  26. [26]
    Q. Zheng, Z. Chen, Z. Gao. A practical approach to disturbance decoupling control. Control Engineering Practice, 2009, 17(9): 1016–1025.CrossRefGoogle Scholar
  27. [27]
    B. Guo, Z. Zhao. On convergence of the nonlinear active disturbance rejection control for MIMO systems. SIAM Journal of Control and Optimization, 2013, 51(2): 1727–1757.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    W. Xue, Y. Huang. Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems. ISA Transaction, 2015, 58: 133–54.CrossRefGoogle Scholar
  29. [29]
    S. Zhao, L. Sun, D. Li, et al. Tracking and disturbance rejection in non-minimum phase systems. Proceedings of the Chinese Control Conference, Nanjing: IEEE, 2014: 3834–2839.Google Scholar
  30. [30]
    C.-T. Chen. Linear System Theory and Design. 3rd ed. New York: Oxford University Press, 1999.Google Scholar
  31. [31]
    D. Yoo, S. S.-T. Yau, Z. Gao. Optimal fast tracking observer bandwidth of the linear extended state observer. International Journal of Control, 2007, 80(1): 102–111.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Department of Electrical and Computer EngineeringCleveland State UniversityClevelandUSA

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