Order reduction of nonlinear dynamic models by subspace identification and stepwise regression

Detailed dynamic nonlinear models are frequently available for chemical processes due the understanding achieved in many areas, such as thermodynamics and kinetics, and the subsequent appearance of rigorous dynamic commercial simulators. These detailed models have been useful in off-line studies; however, their large size has precluded their use in on-line applications such as Nonlinear Model Predictive Control (NL-MPC) and estimation of unmeasured variables by state estimation. This thesis develops a methodology for obtaining Non-Linear Low Order Models (NLLOM) that retain the dominant dynamic characteristics of the detailed model. This methodology is based on a data driven approach which uses the detailed model as a data source. The methodology is broken into two major tasks. In the first task, a Regional Linear Low Order Model (ReLLOM) is developed, and in the second task, appropriate nonlinear terms are augmented to the ReLLOM to form the NLLOM. Techniques are presented for designing simultaneous multiple-input perturbation signals that ensure that the collected data has sufficient information for identifying the ReLLOM and NLLOM structures and parameters. The designed input signals also ease development of the ReLLOM by facilitating removal of certain classes of nonlinearities from the data. The ReLLOM has a discrete state-space structure, each state corresponding directly to an output within the detailed model. The ReLLOM thus has physically meaningful states while state-space models arrived at by system identification in general do not. In order for the ReLLOM to achieve the desired accuracy, the number of states needed may be greater than the number of primary outputs of direct interest. A method based on Key Set Factor Analysis (KSFA) and subspace projections is presented for selecting the optimal set of secondary outputs needed to make the state/output relationship square. Once the ReLLOM is constructed, appropriate nonlinear terms are selected by stepwise regression between a set of candidate nonlinear terms and the nonlinear residuals between the ReLLOM and the data. The selected terms are appended to the ReLLOM to form the NLLOM, and their coefficients are determined using nonlinear parameter estimation. The methodology presented does not rely on process specific heuristics, and thus has wide applicability to processes both inside and outside of chemical engineering.