Identification of Multiple First-Order Continuous-Time Dynamic Models From Special Segments in Historical Data

Continuous-time dynamic models are often required for controller design, process monitoring, and operation optimization. This paper proposes an approach to estimate unknown parameters of multiple first-order continuous-time dynamic models from special segments in historical data. The approach is composed by two main steps. First, special segments are defined as the ones with two ends in steady states and the middle part having significant amplitude variations in transient states; the special segments are found automatically by exploiting a piece-wise linear representation technique from a large amount of historical data samples. Second, static gains are estimated by solving a set of linear equations based on steady-state values of inputs and outputs; sums of time constants and delays are obtained by solving another set of linear equations based on integrals of model output errors from data samples in transient states; the sums are used as an optimization constraint for maximizing the fitness value between measured and simulated outputs, from which separated estimates of time constants and delays are yielded. Numerical examples are provided to illustrate the proposed approach and compare with existing ones.