Identification and Control of Linear Distributed Parameter Systems Through the Use of Experimentally Determined Singular Functions

Abstract

A new method is presented for the identification of linear Distributed Parameter Systems (DPS) given only limited a priori information about the physical process. Knowledge of the locations of a finite number of spatially varying control actuators and the locations of point measurements is assumed. Basic information from the system inputs and outputs is used to identify approximate spatial characteristics of the DPS. The identification procedure results in a pseudo-modal input/output model for the system, Identification of the spatial character of the process is accomplished by assuming the general model of a linear time-invariant compact unsymmetric integral operator. The kernel of this integral operator is expressed in terms of two sets of orthonormal basis functions, known as singular functions, whose existence is given by singular value theory. Approximations to these singular functions are determined numerically from input/output data using Galerkin's method and the Singular Value Decomposition. Application of this procedure to DPS described by both a self-adjoint and a non-self-adjoint parabolic PDE model is demonstrated. The usefulness of the identified model for an example control system design is shown