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A New Adaptive Partially Decentralized PID Controller for Non-square Discrete-time Linear Parameter Varying Systems

  • Ibtissem Malouche
  • Faouzi Bouani
Regular Papers Control Theory and Applications

Abstract

In this paper, a novel partially decentralized adaptive control strategy is presented to deal with a class of Multi Inputs Multi Outputs (MIMO) non-square, Linear Parameter Varying (LPV) systems. The key idea is the design of Proportional Integral Derivative (PID) regulator based on online pairing and tuning of its parameters using the Dynamic Relative Gain Array (DRGA) matrix. The proposed adaptive partially decoupled control scheme operates in a straightforward and systematic way. The convergence of the proposed controller is guaranteed by theoretical analysis, numerical simulations and experimental tests carried out on a non-holonomic two Wheeled Mobile Robot (WMR). Studies of the proposed regulator robustness against additive disturbance and stability over the whole parameter range are given to illustrate the effectiveness of the proposed PID scheme.

Keywords

Adaptive partially decentralized regulation discrete-time state-space linear parameter varying models dynamic relative gain array embedded C code generation microcontrollers stability analysis 

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References

  1. [1]
    D. Kalpana, T. Thyagarajan, and N. Gokulraj, “Modeling and control of non-square MIMO system using relay feedback,” ISA Transactions, vol. 59, pp. 408–417, September 2015.CrossRefGoogle Scholar
  2. [2]
    V. V. Kumar, V. S. R. Rao, and M. Chidambaram, “Centralized PI controllers for interacting multivariable processes by synthesis method,” ISA Transactions, vol. 51, no. 3, pp. 400–409, May 2012.CrossRefGoogle Scholar
  3. [3]
    T. Chiranjeeevi, I. V. V. Vijetha, B. N. CH. V. Chakravarthi, and M. Karthika, “Tuning and control of multi variable systems,” International Journal of Electronics and Electrical Engineering, vol. 2, no. 4, December 2014.Google Scholar
  4. [4]
    P. Dworak, “Squaring down plant model and I/O grouping strategies for a dynamic decoupling of left-invertible MIMO plants,” Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 62, vo. 3, 2014.Google Scholar
  5. [5]
    J. Garridoa, F. Vazqueza, and F. Morillab, “Multivariable PID control by decoupling,” International Journal of Systems Science, 2014.Google Scholar
  6. [6]
    Q. G. Wang, Decoupling Control, Springer-Verlag, Berlin-Heidelberg, 2003.Google Scholar
  7. [7]
    S. Kamoun and M. Kamoun, “A new decentralized implicit adaptive regulator for large-scale systems described by discrete-time state-space mathematical models,” International Journal of Control, Automation, and Systems, vol. 14, no. 3, pp. 733–742, 2016.CrossRefGoogle Scholar
  8. [8]
    F. M. Bayat, N. Mirebrahimi, and M. R. Khalili, “Discretetime fractional-order PID controller: definition, tuning, digital realization and some applications,” International Journal of Control, Automation, and Systems, vol. 13, no. 1, pp. 81–90, 2015.CrossRefGoogle Scholar
  9. [9]
    A. Bagis, “Determination of the PID controller parameters by modified genetic algorithm for improved performance,” Journal of Information Science and Engineering, pp. 1469–1480, 2007.Google Scholar
  10. [10]
    A. G. Alexandrov and M. V. Palenov, “Adaptive PID controllers: state of the art and development prospects,” Automation and Remote Control, vol. 75, no. 2, pp. 188–199, 2014.MathSciNetCrossRefGoogle Scholar
  11. [11]
    F. Kühne, W. F Lages, J. M. Gomes, and Da Silva Jr., “Model predictive control of a mobile robot using linearization,” Mechatronics and Robotics 2004, Aachen, Germany, pp. 525–530, 2004.Google Scholar
  12. [12]
    L. Pacheco and N. Luo, “Mobile robot local trajectory tracking with dynamic predictive control technics,” International Journal of innovative Computing, Information and control, vol. 7, no. 6, pp. 3457–3483, June 2011.Google Scholar
  13. [13]
    J. Keighobadi and Y. Mohamadi, “Fuzzy robust trajectory tracking control of WMRs,” Intelligent Control and Innovative Computing, Springer, 2012.Google Scholar
  14. [14]
    S. Roy, S. Nandy, R. Ray, and S. N. Shome, “Robust path tracking control of nonholonomic wheeled mobile robot: experimental validation,” International Journal of Control, Automation, and Systems, vol. 13, no. 4, pp. 1–9, September 2015.CrossRefGoogle Scholar
  15. [15]
    Q. G. Wang, Z. Ye, W.J. Cai, and C. C. Hang, PID Control for Multivariable Processes, Springer-Verlag, 2008.zbMATHGoogle Scholar
  16. [16]
    E. H. Bristol, “On a new measure of interactions for multivariable process control,” IEEE Trans. Auto. Control, vol. 11, no. 1, pp. 133–134, 1966.CrossRefGoogle Scholar
  17. [17]
    W. Hu, W. J. Cai, and G. Xiao, “Decentralized control system design for MIMO processes with integrators/differentiators,” Industrial and Engineering Chemistry Research, vol. 49, no. 24, pp. 12521–12528, 2010.CrossRefGoogle Scholar
  18. [18]
    M. F. Witcher and T. J. McAvoy, “Interacting control systems: steadystate and dynamic measurement of interaction,” ISA Transactions, vol. 16, no. 3, pp. 35–41, 1977.Google Scholar
  19. [19]
    M. C. Arranz and W. Birk, “A new approach to the dynamic RGA analysis of uncertain systems,” IEEE Multiconference on Systems and Control, San Antonio, Texas, USA, September 3-5, 2008.Google Scholar
  20. [20]
    A. K. Sedigh and B. Moaveni, Control Configuration Selection of Linear Multivariable Plants: The RGA Approach, Springer Berlin Heidelberg, 2009.CrossRefGoogle Scholar
  21. [21]
    I. L. Chien, H. P. Huang, and J. C. Yang, “A simple multiloop tuning method for PID controllers with no proportional kick,” Industrial and Engineering Chemistry Research, vol. 38, no. 4, pp. 1456–1468, 1999.CrossRefGoogle Scholar
  22. [22]
    M. Kurien, A. Prayagkar, and V. Rajeshirke, “Overview of different approaches of PID controller tuning,” International Journal of Research in Advent Technology, vol. 2, no. 1, pp. 167–175, January 2014.Google Scholar
  23. [23]
    I. Malouche, A. Kheriji, and F. Bouani, “Automatic model predictive control implementation in a high-performance microcontroller,” International Conference on Systems, Analysis and Automatic Control, Mahdia, Tunisia, March 2015.Google Scholar
  24. [24]
    STMicroelectronics “RM0090 Reference manual,” 2015.Google 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.Tunis El Manar University, National School of Engineering of Tunis, LR11ES20, Analysis, Conception and Control of Systems LaboratoryTunisTunisia

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