System identification and model-based control for a class of distributed parameter systems

A large number of processes in the chemical and petroleum industries are distributed in nature. The diversity of distribution patterns and functions make modeling of distributed parameter systems (DPS) a very challenging problem.; Employment of first-principles about the physics and chemistry will yield mathematical models in the form of systems of linear or nonlinear partial differential equations (PDEs). The analytical and numerical solutions for PDEs are infinite or very high dimension, which are not suitable for implementable control designs. The first objective of this research is to develop a general model reduction methodology to reduce the system of PDEs to a finite dimensional system of ODES, which can be used to synthesize a model-based control. This methodology is based on the identification of empirical eigenfunctions (EEFs) from data and using the Galerkin method to obtain a model with dominant modes. For a system of first-order hyperbolic PDEs, accelerated EEFs are used to find a reduced order model.; In the case where the physics-based modeling approach cannot be applied with confidence, an input/output model developed based on experimental data may suffice. A novel system identification method to develop the model using a data-driven approach is proposed. The method combines the fundamental principles of singular value decomposition (SVD) and Karhunen-Loeve (KL) expansion in the identification of a finite order model. The application of SVD and KL provides natural decoupling of the inputs and outputs while yielding a model that captures the dominant spatial and temporal behavior of the distributed system. The fundamental theorems to assure the accuracy of this method are provided.; Implementable control designs to regulate the DPS are now realizable with a finite order model. Dynamic matrix control (DMC) and Quadratic DMC (QDMC) are selected as control strategies wherein, the merit of the control design is dependent on the fidelity of the identified by SVD-KL method. Sufficient conditions are proposed to tune the QDMC control strategy so that stable closed-loop performance is guaranteed. The regulation of several candidate chemical reactor systems and the hydro-dealkylation process that produces benzene from toluene (HDA) are used to illustrate the potential of this data-driven modeling and model-based control framework for distributed parameter systems.