Some results on direct reduced order modeling of linear distributed parameter systems

Abstract

Abstract Control of the distributed parameter systems (DPS) usually involves dynamical description of infinite‐dimensional Hilbert or Banach spaces of functions. Generally, it is not possible to implement an infinite‐dimensional feedback controller for the (infinite‐dimensional) DPS. Consequently, the reduced order modeling of DPS becomes extremely crucial for designing the finite‐dimensional feedback controllers. In this paper, we present two conceptually and computationally easy ways of reduced order modeling via the Galerkin method. Subject to a symmetry assumption on the system operator, these two methods are shown to be equivalent. A simple computer algorithm is presented for efficient calculation of the reduced order model upon which the finite‐dimensional controller design can be based.