Low-order model identification for implementable control solutions of distributed parameter systems

Accurate solutions of the distributed parameter system (DPS) may be represented as the sum of an infinite series. Control design however, requires low-order models primarily due to implementation limitations. As such, developing low-order models of high fidelity is important if the objective is accurate control of the DPS. When an exact model (system of partial differential equations (PDEs)) of the system is known, this work presents a method to develop a low-order model that assures convergent and consistent projection to a finite space. The resulting low-order model can then be used to design finite dimensional controllers. When there is no available first-principle model of the system, this work introduces a novel system identification method, that combines the characteristics of singular value decomposition (SVD) and the Karhunen-Loève (KL) expansion for DPS to arrive at a low-order model that captures the dominant characteristics of the system. Here as well, the final model form allows for the synthesis of finite order controllers. Two non-linear reactor systems that can be described by systems of PDEs are provided to demonstrate the model identification methods. Feedback controllers are then synthesized based on these models to demonstrate their performance for disturbance rejection.