Pole-Free vs. Minimum-Norm Right Inverse in Design of Minimum-Energy Perfect Control for Nonsquare State-Space Systems

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 720)

Abstract

In this paper a comparison of energy cost for different types of perfect control structures is presented. It is shown, that there is a possibility to improve the said control strategy for nonsquare LTI MIMO discrete-time state-space systems in terms of robustness through seeking of minimum control energy. It is remarkable, that simulation examples made in Matlab/Simulink environment confirm the potential of pole-free control design not only in the context of maximum-speed and maximum-accuracy properties, but, what is important, in terms of minimum energy behavior.

Keywords

Perfect control Minimum-energy Pole-free approach Parameter matrix inverses State space Robust control design 

References

  1. 1.
    Hunek, W.P., Krok, M.: Pole-free perfect control for nonsquare LTI discrete-time systems with two state variables. In: Proceedings of the 13th IEEE International Conference on Control and Automation (ICCA 2017), Ohrid, Macedonia, pp. 329–334 (2017).  https://doi.org/10.1109/ICCA.2017.8003082
  2. 2.
    Stanimirović, P.S., Petković, M.D.: Computing generalized inverse of polynomial matrices by interpolation. Appl. Math. Comput. 172(1), 508–523 (2006).  https://doi.org/10.1016/j.amc.2005.02.031MathSciNetMATHGoogle Scholar
  3. 3.
    Karampetakis, N.P., Tzekis, P.: On the computation of the generalized inverse of a polynomial matrix. IMA J. Math. Control Inf. 18(1), 83–97 (2001).  https://doi.org/10.1093/imamci/18.1.83MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ben-Israel, A., Greville, T.N.E.: Generalized Inverses, Theory and Applications, 2nd edn. Springer, New York (2003)MATHGoogle Scholar
  5. 5.
    Hunek, W.P.: Pole-free vs. stable-pole designs of minimum variance control for nonsquare LTI MIMO systems. Bull. Pol. Acad. Sci. Tech. Sci. 59(2), 201–211 (2011).  https://doi.org/10.2478/v10175-011-0025-yMathSciNetMATHGoogle Scholar
  6. 6.
    Hunek, W.P.: New interesting facts about minimum-energy perfect control for LTI nonsquare state-space systems. In: Proceedings of the 22nd IEEE International Conference on Methods and Models in Automation and Robotics (MMAR 2017), Miȩdzyzdroje, Poland, pp. 274–278 (2017)Google Scholar
  7. 7.
    Hunek, W.P.: Towards a General Theory of Control Zeros for LTI MIMO Systems. Opole University of Technology Press, Opole (2011)MATHGoogle Scholar
  8. 8.
    Hunek, W.P., Latawiec, K.J., Stanisławski, R., Łukaniszyn, M., Dzierwa, P.: A new form of a \(\sigma \)-inverse for nonsquare polynomial matrices. In: Proceedings of the 18th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR 2013), Miȩdzyzdroje, Poland, pp. 282–286 (2013).  https://doi.org/10.1109/MMAR.2013.6669920
  9. 9.
    Hunek, W.P., Latawiec, K.J., Majewski, P., Dzierwa, P.: An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems. In: Proceedings of the 19th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR 2014), Miȩdzyzdroje, Poland, pp. 451–455 (2014).  https://doi.org/10.1109/MMAR.2014.6957396
  10. 10.
    Dadhich, S., Birk, W.: Analysis and control of extedned quadruple tank process. In: Proceedings of the 13th IEEE European Control Conference (ECC 2014), pp. 838–843 (2014).  https://doi.org/10.1109/ECC.2014.6862290
  11. 11.
    Hunek, W.P.: An application of new polynomial matrix \(\sigma \)-inverse in minimum-energy design of robust minimum variance control for nonsquare LTI MIMO systems. In: Proceedings of the 8th IFAC Symposium on Robust Control Design (ROCOND 2015), Bratislava, Slovakia, pp. 150–154 (2015).  https://doi.org/10.1016/j.ifacol.2015.09.449
  12. 12.
    Hunek, W.P.: New SVD-based matrix \(H\)-inverse vs. minimum-energy perfect control design for state-space LTI MIMO systems. In: Proceedings of the 20th IEEE International Conference on System Theory, Control and Computing (ICSTCC 2016), Sinaia, Romania, pp. 14–19 (2016).  https://doi.org/10.1109/ICSTCC.2016.7790633
  13. 13.
    Hunek, W.P.: An application of polynomial matrix \(\sigma \)-inverse in minimum-energy state-space perfect control of nonsquare LTI MIMO systems. In: Proceedings of the 20th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR 2015), Miȩdzyzdroje, Poland, pp. 252–255 (2015).  https://doi.org/10.1109/MMAR.2015.7283882
  14. 14.
    Levine, W.S. (ed.): The Control Handbook. Electrical Engineering Handbook. CRC Press and IEEE Press, Boca Raton (1996)MATHGoogle Scholar
  15. 15.
    Grimble, M.J.: Controller performance benchmarking and tuning using generalised minimum variance control. Automatica 38(12), 2111–2119 (2002).  https://doi.org/10.1016/S0005-1098(02)00141-3MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Electrical, Control and Computer EngineeringOpole University of TechnologyOpolePoland

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