| For a dual-rate system with fast input and very slow output data, which means the output sampling time is greatly longer than the regular input sampling time, we develop a two-stage method combining Newton-Raphson algorithm and the finite impulse response model to identify the fast single-rate model. The method is also applied to develop a composition observer for an industrial distillation column. The main contributions could be summarized as follows:1) By using the least-squares criterion, the dual-rate system identification is converted into an optimization problem, solution to which can be iteratively derived by Newton-Raphson method. The technique dealing with the initialization and local minimum problems is also proposed and demonstrated with detailed examples.2) To overcome the bias for colored noises, a two-stage method is later proposed. A finite impulse response models is first developed from the dual-rate samples by using the combined least-squares criterion and Newton-Raphson method; based on the original fast input signal and the derived slow rate model output, a single-and-fast-rate output error model can be eventually developed.3) A recursive identification algorithm of dual-rate system based on Newton-Raphson method is proposed and demonstrated with detailed examples.4) Those identification methods are also applied to build a composition observer for an industrial distillation column. |
