Linear High-Gain Correction Observer in Nonlinear Control

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


The development of innovation technology requires one to provide control processes with better quality indexes. In modern control theory, the algorithms for calculating linear-quadratic regulator (LQR) for linear dynamic systems are known. The classical LQR algorithms do not take into account transport delays of the signals or uncertainty of measured values and models, which causes the task of stabilizing physical systems by classical LQR algorithm to contain significant errors which decrease quality indexes. Most control systems are non-linear, not isolated from the uncertainty of measured values and models. For this reason, in the paper the possibility of calculating a linear-quadratic regulator for non-linear systems, which will provide stability in a wider environment around the reference point for additive noise based on the high-gain disturbance correction observer, are proposed.


High-gain observer Disturbance observer Estimation Correction Nonlinear control Tracking 


  1. 1.
    Bavdekar, A., Deshpande, A., Patwardhan, C.: Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter. J. Process Control 21(4), 585–601 (2011)CrossRefGoogle Scholar
  2. 2.
    Bronsztejn, I., Siemiendiajew, K., Musiol, G., Muhlig, H.: Compendium of Modern Mathematics. PWN, Warszawa (2007)Google Scholar
  3. 3.
    Byrski, W.: Obserwacja i sterowanie w systemach dynamicznych, Uczelniane Wydawnictwo Naukowo-Dydaktyczne AGH, Monografie, vol. 18 (2007)Google Scholar
  4. 4.
    Iyad Hashlamon, I.: A new adaptive extended Kalman filter for a class of nonlinear systems. J. Appl. Comput. Mech. 61(1), 1–12 (2020)Google Scholar
  5. 5.
    Kailath, T.: Linear Systems. Prentice-Hall Inc., Englewood Cliffs (1980)zbMATHGoogle Scholar
  6. 6.
    Khalil, H., Hassan, K.: High-gain observers in feedback control application to permanent magnet synchronous motors. IEEE Control Syst. Mag. 37(3), 25–41 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Khalil, H.: Nonlinear Control, Global edn. Pearson Education Limited, Edinburgh (2015)zbMATHGoogle Scholar
  8. 8.
    Latocha, A.: System sterowania procesami silnie nieliniowymi, Pomiary Automatyka Robotyka, no. 9. Skamer-ACM (1998)Google Scholar
  9. 9.
    Latocha, A.: A robust linear-quadratic moving averaging controller for strongly nonlinear systems. In: NDC 2017 International Conference on Nonlinear Dynamics and Complexity Lodz University of Technology, Post Conference Materials, pp. 1–9 (2017)Google Scholar
  10. 10.
    Latocha, A.: Fast and robust online dynamic system identification. In: Kościelny, J., Syfert, M., Sztyber, A. (eds.) Advanced Solutions in Diagnostics and Fault Tolerant Control, DPS. Advances in Intelligent Systems and Computing, vol. 635. Springer, Cham (2017)Google Scholar
  11. 11.
    Latocha, A.: Robust fault detection, location, and recovery of damaged data using linear regression and mathematical models, IFAC-PapersOnLine 51(24), 300–306 (2018). ISSN 2405-8963.
  12. 12.
    Li, X., Gao, Z., Ai, W., Tian, S.: Differentiator-based disturbance observer. In: IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS), pp. 976–981 (2019).
  13. 13.
    Lurie, B., Enright, P.: Classical Feedback Control. Marcel Dekker, New York (1986)Google Scholar
  14. 14.
    Merola, A., Cosentino, C., Colacino, D., Amato, F.: Optimal control of uncertain nonlinear quadratic systems. Automatica 83, 345–350 (2017) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Mitkowski, W.: Zarys teorii sterowania, Wydawnictwo AGH. Komitet Automatyki i Robotyki PAN (2019)Google Scholar
  16. 16.
    Morari, M., Zafiriou, E.: Robust Process Control, vol. 10. Prince Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  17. 17.
    Witczak, M., Buciakowski, M., Puig, V., Rotondo, D., Nejjari, F., Jozef Korbicz, J.: A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems. J. Process Control 52, 14–25 (2017).
  18. 18.
    Zak, S.: Systems and Control. Oxford University Press, New York, Oxford (2003). School of Electrical and Computer Engineering Purdue UniversityGoogle Scholar
  19. 19.
    Ljung, L., Gunnarsson, S.: Adaptation and tracking in system identification–a survey. Automatica 26(1), 7–21 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Schön, T.B., Wills, A., Ninness, B.: System identification of nonlinear state-space models. Automatica 47(1), 39–49 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Ljung, L.: Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems. IEEE Trans. Autom. Control 24(1), 36–50 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Bernard, P., Marconi, L.: Hybrid implementation of observers in plant’s coordinates with a finite number of approximate inversions and global convergence. Automatica 111, 108654 (2020). ISSN 0005-1098.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical EngineeringAGH University of Science and TechnologyKrakówPoland

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