Modified Discrete LQ Control Algorithm for Situations with the Scan Period Variance

  • Jan CvejnEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 466)


Computer-based control systems, especially if they run under general-purpose operating systems, often exhibit variance of the scan period of processing inputs and outputs. Although this fact is usually not taken into account when discrete control algorithms are used, it can cause worse performance of the control loop in comparison to the theoretical case. In this paper we describe a modified discrete LQ control algorithm that takes disturbances of the scan period into account and partially compensates their influence. We also show that such a controller can be implemented even on low-performance hardware platforms, if they are equipped with a sufficient amount of memory.


Optimal control LQ controller Linear systems Discrete control 


  1. 1.
    Cvejn, J.: Compensation of the scan-period irregularities in lqg control systems. Arch. Control Sci. 18, 3 (2008)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere Corp, New York (1975)Google Scholar
  3. 3.
    Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, Berlin (1995)zbMATHGoogle Scholar
  4. 4.
    Stengel, R.F.: Stochastic Optimal Control: Theory and Application. Wiley, New York (1986)zbMATHGoogle Scholar
  5. 5.
    Pappas, T., Laub, A.J., Sandell Jr, N.R.: On the numerical solution of the discrete-time algebraic riccati equation. IEEE Trans. Autom. Control 25, 631–641 (1980)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kleinman, D.L.: Stabilizing a discrete, constant linear system with application to iterative methods for solving the riccati equation. IEEE Trans. Autom. Control 19, 252–254 (1974)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Faculty of Electrotechnics and InformaticsUniversity of PardubicePardubiceCzech Republic

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