Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input-output time delays

  • Authors:

  • Hsun-Pang Wang;Leang-San Shieh;Jason S. H. Tsai;Yongpeng Zhang

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Houston, Houston, Texas 77204-4005, USA;Department of Electrical and Computer Engineering, University of Houston, Houston, Texas 77204-4005, USA;Department of Electrical Engineering, National Cheng-Kung University, Taiwan, R.O.C;Engineering Technology Department, Prairie View A&M University, Texas 77446, USA

  • Venue:
  • International Journal of Systems Science
  • Year:
  • 2008

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Abstract

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input-output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input-output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input-output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input-output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.