Advertisement

Time-Varying Perfect Control Algorithm for LTI Multivariable Systems

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

Abstract

In this paper, a new approach to perfect control design is proposed. The novel application of polynomial degrees of freedom in calculation of generalized matrix inverse has enabled a new branch of perfect control-oriented robust scenarios. Crucially, the obtained closed-loop system has revealed to be internally time-varying even though the general input-output behavior is still time-invariant. Simulation instances made in Matlab/Simulink environment show some interesting peculiarities covering the perfect control speed and energy.

Keywords

Multivariable perfect control LTV control algorithm Nonunique matrix inverses Robustification 

References

  1. 1.
    Hunek, W.P.: Towards a General Theory of Control Zeros for LTI MIMO Systems. Opole University of Technology Press, Opole (2011)zbMATHGoogle Scholar
  2. 2.
    Latawiec, K.J., Korytowski, A.: A direct solution of the perfect regulation problem for LTI discrete-time systems. In: Proceedings of the 14th National Automatic Control Conference (KKA 2002), Zielona Góra, Poland, pp. 165–168 (2002). (in Polish)Google Scholar
  3. 3.
    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
  4. 4.
    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
  5. 5.
    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/18.1.83MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hunek, W., Krok, M.: Parameter matrix \(\sigma \)-inverse in design of structurally stable pole-free perfect control for second-order state-space systems. In: Proceedings of the 24th International Conference on Automation and Computing (IEEE ICAC 2018) (2018).  https://doi.org/10.23919/IConAC.2018.8748977
  7. 7.
    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.2005.02.031MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ben-Israel, A., Greville, T.N.E.: Generalized Inverses. Theory and Applications, 2nd edn. Springer, New York (2003)zbMATHGoogle Scholar
  9. 9.
    Hunek, W.P., Majewski, P.: Perfect reconstruction of signal - a new polynomial matrix inverse approach. EURASIP J. Wirel. Commun. Networking 2018(107), 8 (2018).  https://doi.org/10.1186/s13638-018-1122-5CrossRefGoogle Scholar
  10. 10.
    Noueili, L., Chagra, W., Ksouri, M.: New iterative learning control algorithm using learning gain based on \(\sigma \) inversion for nonsquare multi-input multi-output systems (2018).  https://doi.org/10.1504/IJMIC.2018.095829
  11. 11.
    Hunek, W.P., Krok, M.: A study on a new criterion for minimum-energy perfect control in the state-space framework. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 233(7), 779–787 (2019)Google Scholar
  12. 12.
    Gutierrez de Anda, M.A., Sarmiento Reyes, A., Hernandez Martinez, L., Piskorowski, J., Kaszynski, R.: The reduction of the duration of the transient response in a class of continuous-time LTV filters. IEEE Trans. Circuits Syst. II: Express Briefs 56(2), 102–106 (2009)Google Scholar
  13. 13.
    Ozgun, M., Tsividis, Y., Burra, G.: Dynamic power optimization of active filters with application to zero-if receivers. IEEE J. Solid-State Circuits 41(6), 1344–1352 (2006)CrossRefGoogle Scholar
  14. 14.
    Tsividis, Y., Krishnapura, N., Palaskas, Y., Toth, L.: Internally varying analog circuits minimize power dissipation. IEEE Circuits Devices Mag. 19(1), 63–72 (2003)CrossRefGoogle Scholar
  15. 15.
    Petersen, K.B., Pedersen, M.S.: The Matrix Cookbook. Technical University of Denmark, November 2012Google Scholar
  16. 16.
    Tokarzewski, J.: Finite Zeros in Discrete Time Control Systems. Lecture Notes in Control and Information Sciences, vol. 338. Springer-Verlag (2006).  https://doi.org/10.1007/11587743
  17. 17.
    Niezabitowski, M.: Numerical characteristics of discrete hybrid system. Ph.D. thesis, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Gliwice, Poland (2014)Google Scholar
  18. 18.
    Orlowski, P.: Applications of SVD-DFT decomposition. part 2: feedback stability analysis for time-varying systems. Pomiary Automatyka Kontrola 53(2), 44–47 (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Opole University of TechnologyOpolePoland

Personalised recommendations