Low-Order Model Identification of Distributed Parameter Systems by a Combination of Singular Value Decomposition and the Karhunen−Loève Expansion

In this work, a new system identification method that combines the characteristics of singular value decomposition (SVD) and the Karhunen−Loève (KL) expansion for distributed parameter systems is presented. This method is then demonstrated on two nonlinear reactor systems that can be described by systems of partial differential equations (PDEs). The results indicate that this new method provides satisfactory low-order models when compared to models developed using either the SVD approach or the KL expansion in a Galerkin method. In particular, it has the advantage of not requiring an exact PDE model, which is necessary for the KL solution and it captures the dynamics of the process in contrast to the SVD solution. This has important implications especially for applications such as control that require low-order models for implementable solutions.