Date of Award
Doctor of Philosophy
Derrick K. Rollins, Sr.
The continuous-time closed-form algorithms to sinusoidal input changes are proposed and presented for single-input, single-output (SISO) Hammerstein and Wiener systems with the first-order, second-order, and second-order plus lead dynamics. By simulation on theoretical Hammerstein and Wiener systems, the predicted responses agree exactly with the true process values. They depend on only the most recent input change. The algorithms to SISO Hammerstein and Wiener systems can be conveniently extended to the multiple-input, multiple-output (MIMO) systems as shown by the two-input, two-output examples and demonstrated by the simulated seven-input, five-output continuous stirred tank reactor (CSTR). The predictions and the simulated theoretical responses agree exactly and the predicted multiple CSTR outputs are close to the true process outputs. The proposed algorithms can predict the responses closer to the true values when comparing with the piece-wise step input approximation of the sinusoidal input changes on a simulated MIMO CSTR. In addition, as the noisy process input could be decomposed as summation of sinusoidal signals imposed on a step input change; the proposed algorithms can be employed to predict outputs for the noisy process inputs once the decomposition is done and the predicted noisy process outputs are shown to be close to the true ones, and are much better than the predictions based on the perfect filtering of the input signals.;The estimating equations based on the moment method are proposed for the Wiener dynamic process with stochastically correlated process input disturbances or noises and they work well for the parameter estimation. No one has ever proposed such method before. This approach has led to stable and robust estimators that have reasonable estimation errors and there is no need to measure the input disturbances or noises, or to calculate the time derivative of the observed output variable. Only the original process output observations over time are needed. The original model can be shifted to an approximate model under some conditions. This approximation is acceptable based on some analysis and derivation. The estimating equation methodology was shown to work well for the approximate model, while other existing methods do not work at all.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Zhai, Dongmei, "Continuous-time block-oriented nonlinear modeling with complex input noise structure " (2005). Retrospective Theses and Dissertations. 1690.