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A Nonparametric Approach to Design Fixed-order Controllers for Systems with Constrained Input

  • Sofiane Khadraoui
  • Hazem Nounou
Regular Papers Control Theory and Applications
  • 15 Downloads

Abstract

This paper presents an approach for designing fixed-structure controllers for input-constrained linear systems using frequency domain data. In conventional control approaches, a plant model is needed to design a suitable controller that meets some user-specified performance specifications. Mathematical models can be built based on fundamental laws or from a set of measurements. In both cases, it is difficult to find a simple and reliable model that completely describes the system behavior. Hence, errors associated with the plant modeling stage may contribute to the degradation of the desired closed-loop performance. Due to the fact that the modeling stage can be viewed only as an intermediate step introduced for the controller design, the concept of data-based control design has been introduced, where controllers are directly designed from measurements. Most existing data-based control approaches are developed for linear systems, which limit their application to systems with nonlinear phenomena. An important non-smooth nonlinearity observed in practical applications is the input saturation, which usually limits the system performance. Here, we attempt to develop a nonparametric approach to design controllers from frequency-domain data by taking into account input constraints. Two practical applications of the proposed method are presented to demonstrate its efficacy.

Keywords

Actuator saturation constrained optimization data-based control frequency response energy consumption safe process operation 

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References

  1. [1]
    R. J. P. Schrama, “Accurate identification for control: the necessity of an iterative scheme,” IEEE Transactions on Automatic Control, vol. 37, no. 7, pp. 991–994, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Ahsan and M. A. Choudhry, “System identification of an airship using trust region reflective least squares algorithm,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1384–1393, 2017.CrossRefGoogle Scholar
  3. [3]
    E. Goberdhansingh, L. Wang, and W. R. Cluett, “Robust frequency domain identification,” Chemical Engineering Science, vol. 47, no. 8, pp. 1989–1999, 1992.CrossRefGoogle Scholar
  4. [4]
    M. Athans, C. E. Rohrs, L. Valavani, and G. Stein, “Robustness of adaptive control algorithms in the presence of unmodelled dynamics,” IEEE Conference on Decision and Control, pp. 3–11, 1982.Google Scholar
  5. [5]
    H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, “Iterative feedback tuning: theory and application,” IEEE Control Systems Magazine, vol. 18, no. 4, pp. 26–41, 1998.CrossRefGoogle Scholar
  6. [6]
    M. C. Campi, A. Lecchini, and S. M. Savaresi, “Virtual reference feedback tuning: a direct method for the design of feedback controllers,” Automatica, vol. 38, no. 8, pp. 1337–1346, 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. D. Rojas and R. Vilanova, “Data-driven robust PID tuning toolbox,” IFAC Conference on Advances in PID Control, Brescia, Italy, vol. 45, no. 3, pp. 134–139, 2012.Google Scholar
  8. [8]
    K. van Heusden, A. Karimi, and D. Bonvin, “Data-driven model reference control with asymptotically guaranteed stability,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 4, pp. 331–351, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    J. C. Spall and J. A. Cristion, “Model-free control of nonlinear stochastic systems with discrete-time measurements,” IEEE Transactions on Automatic Control, vol. 43, no. 9, pp. 1198–1210, 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    A. Karimi, L. Miskovic, and D. Bonvin, “Iterative correlation-based controller tuning,” International Journal of Adaptive Control and Signal Processing, vol. 18, no. 8, pp. 645–664, 2004.CrossRefzbMATHGoogle Scholar
  11. [11]
    H. S. Ahn, Y. Chen, and K. L. Moore, “Iterative learning control: brief survey and categorization,” IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, vol. 37, no. 6, pp. 1099–1121, 2007.CrossRefGoogle Scholar
  12. [12]
    L. H. Keel and S. P. Bhattacharyya, “Controller synthesis free of analytical models: three term controllers,” IEEE Transactions on Automatic Control, vol. 53, no. 6, pp. 1353–1369, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    P. Kallakuri, L. H. Keel, and S. P. Bhattacharyya, “Data based design of PID controllers for a magnetic levitation experiment,” Proceedings of the 18th IFAC World Congress, Milano, Italy, vol. 44, no. 1, pp. 10231–10236, 2011.Google Scholar
  14. [14]
    D. Garcia, A. Karimi, and R. Longchamp, “Data-driven controller tuning using frequency domain specifications,” Industrial and Engineering Chemistry Research, vol. 45, no. 12, pp. 4032–4042, 2006.CrossRefGoogle Scholar
  15. [15]
    A. J. den Hamer, Data-driven Optimal Controller Synthesis: A Frequency Domain Approach, PhD thesis, Technische Universiteit Eindhoven, ISBN: 978-90-386-2338-2, 2010.Google Scholar
  16. [16]
    A. Karimi and G. Galdos, “Fixed-order H¥ controller design for nonparametric models by convex optimization,” Automatica, vol. 46, no. 8, pp. 1388–1394, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    S. Khadraoui, H. Nounou, M. Nounou, A. Datta, and S. P. Bhattacharyya, “A measurement-based approach for designing reduced-order controllers with guaranteed bounded error,” International Journal of Control, vol. 86, no. 9, pp. 1586–1596, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S. Khadraoui, H. Nounou, M. Nounou, A. Datta, and S. P. Bhattacharyya, “A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system,” Journal of Process Control, vol. 36, no. 1, pp. 1–10, 2015.CrossRefGoogle Scholar
  19. [19]
    S. Khadraoui, H. Nounou, M. Nounou, A. Datta, and S. P. Bhattacharyya, “A model-free design of reduced-order controllers and application to a DC servomotor,” Automatica, vol. 50, no. 8, pp. 2142–2149, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    B. M. Chen, T. H. Lee, K. Peng, and V. Venkataramanan, “Composite nonlinear feedback control for linear systems with input saturation: theory and an application,” IEEE Transactions on Automatic Control, vol. 48, no. 3, pp. 427–439, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    D. J. López-Araujo, A. Zavala-Río, V. Santibáñez, and F. Reyes, “Output-feedback adaptive control for the global regulation of robot manipulators with bounded inputs,” International Journal of Control, Automation and Systems, vol. 11, no. 1, pp. 105–115, 2013.CrossRefGoogle Scholar
  22. [22]
    T. H. Kim and H. W. Lee, “Quasi-min-max outputfeedback model predictive control for LPV systems with input saturation,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1069–1076, 2017.CrossRefGoogle Scholar
  23. [23]
    N. Mohsenizadeh, S. Darbha, L. H. Keel, and S. P. Bhattacharyya, “Model-free synthesis of fixed structure stabilizing controllers using the rate of change of phase,” IFAC Conference on Advances in PID Control, Brescia, Italy, vol. 45, no. 3, pp. 745–750, 2012.Google Scholar
  24. [24]
    A. Sala and A. Esparza, “Extensions to ‘virtual reference feedback tuning: A direct method for the design of feedback controllers’,” Automatica, vol. 41, no. 8, pp. 1473–1476, 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    A. Lanzon, A. Lecchini, A. Dehghani, and B. D. O. Anderson, “Checking if controllers are stabilizing using closedloop data,” Proc. of 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 3660–3665, 2006.CrossRefGoogle Scholar
  26. [26]
    B. Zhou and X. Yang, “Global stabilization of the multiple integrators system by delayed and bounded controls,” IEEE Transactions on Automatic Control, vol. 61, no. 12, pp. 4222–4228, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    B. Zhou, “Global stabilization of periodic linear systems by bounded controls with applications to spacecraft magnetic attitude control,” Automatica, vol. 60, no. 1, pp. 145–154, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Y. Wu, R. Lu, P. Shi, H. Su, and Z. G. Wu, “Adaptive output synchronization of heterogeneous network with an uncertain leader,” Automatica, vol. 76, no. 1, pp. 183–192, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Y. Wu, X. Meng, L. Xie, R. Lu, H. Su, and Z. G. Wu, “An input-based triggering approach to leader-following problems,” Automatica, vol. 75, no. 1, pp. 221–228, 2017.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUAE
  2. 2.Electrical and Computer Engineering ProgramTexas A&M University at QatarDohaQatar

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