A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version

Authors:
Ruth Curtain;Orest Iftime;Hans Zwart
Affiliations:
University of Groningen, Department of Mathematics, P.O. Box 800, 9700 AV, Groningen, The Netherlands;University of Groningen, Department of Economics and Econometrics, Nettelbosje 2, 9747 AE, Groningen, The Netherlands;University of Twente, Department of Applied Mathematics, P.O. Box 217, 7500 AE, Enschede, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

In this paper we consider a long string of SISO systems which in the limit becomes a scalar infinite spatially invariant system. We compare the LQR control for long-but-finite strings with the LQR control for the corresponding infinite strings. We give analytical and numerical examples where these are quite different and we investigate the cause. In addition, we obtain sufficient conditions for the LQR solutions to be similar as the length of the string increases.