On Mixed Galerkin Modeling for Controller Design of Boundary Control Systems

Jun Imai, Katsuyuki Noso, Akiko Takahashi, Shigeyuki Funabiki

Research output: Contribution to journalArticlepeer-review


A mixed Galerkin formulation for reduced-order modeling is presented for controller design of distributed parameter systems with boundary inputs. A null space approach is established to yield appropriate trial and test functions by using candidate trial functions which are free from boundary conditions. The approach is applicable, with considerably mild conditions on the candidate trial functions, on the interior domain as well as its boundaries. It is shown that this modeling technique yields a finite dimensional descriptor system of index 1, that is equivalent to a state-space representation suitable for controller design model. Effectiveness of the proposed method is demonstrated by an example of a heat conduction rod using polynomial functions which are not preprocessed to meet the boundary conditions.

Original languageEnglish
Pages (from-to)7133-7138
Number of pages6
Issue number1
Publication statusPublished - Jul 2017


  • Boundary conditions
  • Distributed parameter systems
  • Method of weighted residuals
  • Reduced-order models

ASJC Scopus subject areas

  • Control and Systems Engineering


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