1. A State-Space Modeling via the Galerkin Approximation for a Boundary Control System
- Author
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Akiko Takahashi, Jun Imai, Shigeyuki Funabiki, and Katsuyuki Noso
- Subjects
0209 industrial biotechnology ,Reduced-order models ,Boundary conditions ,Mathematical analysis ,Basis function ,010103 numerical & computational mathematics ,02 engineering and technology ,Mixed boundary condition ,Singular boundary method ,Boundary knot method ,01 natural sciences ,020901 industrial engineering & automation ,Control and Systems Engineering ,Distributed parameter system ,Distributed parameter systems ,Boundary value problem ,0101 mathematics ,Galerkin method ,Method of weighted residuals ,Mathematics ,Gramian matrix - Abstract
For linear distributed parameter systems with a finite number of boundary inputs, we propose a framework to implement the method of weighted residuals using candidate trial functions without boundary homogenization. Proposed scheme utilizes inner product matrix, or Grammian, of the trial functions to separate appropriate homogenized basis functions and the other trial functions matching inhomogeneous boundary conditions. The finite-dimensional approximate model by using the proposed scheme is represented in descriptor form and it is proved to be straightforwardly transformed into state space form. Feasibility of the method is illustrated by a brief controller design example using the approximate model of a heat conduction rod with Dirichlet boundary input.
- Published
- 2016