Identification For Multiple-input Single-Output Systems Based On Output-error Models

With the development of control theory and the requirements of engineering practice, theobjects in industrial control systems are no longer limited to single variable systems with onlyone variable or a few variables, but to multivariable systems with complex characteristics andtoo many variables. The thesis studies the identification problem for multiple-input single-output systems based on output-error models, which uses the least squares identification prici-ple, the instrumental variable method, the auxiliary model identification idea, the hierarchicalidentification principle, the multi-innovation identification theory and iteractive identificationmethod. Findings are as follow:1. For the output-error multiple-input single-output systems with white noise, the r ?1 inputsof the systems are treated as unpredictable noise, r represents for the total input numberof the systems, and form a general noise together with the noise inherent in the system. Aninstrumental variable based recursive least squares algorithm for the output-error multiple-input single-output systems with white noise is presented by means of instrumental variablemethod for single-input single-output systems. The computational e?ciency and identifi-cation accuracy of the instrumental variable based recursive least squares algorithm andthe auxiliary model based recursive least squares algorithm are compared. A hierarchicalleast squares algorithm is proposed based on auxiliary models by Combining the auxiliarymodel identification idea and the hierarchical identification principle.2. Auxiliary model based extended and generalized stochastic gradient algorithms are derivedby replacing the unknown unmeasurable variables in the information vector with the outputof the auxiliary model. An auxiliary model based multi-innovation extended and generalizedstochastic gradient algorithm are proposed for output-error multiple-input single-outputsystems with colored noise by introducing the innovation length and expanding the scalarinnovation to an innovation vector. The two algorithms not only use the current data andinnovation but also use the past data and innovation at each iteration, thus the parameterestimation accuracy and convergence rate can be improved obviously.3. For the multiple-input single-output systems based on output-error models with colorednoise, an auxiliary model is formed by taking advantage of measurable information, anduse the output of the auxiliary model and noise estimates instead of the true output thatunknown and unmeasurable noise in the information vector of identification model. Thena least squares based iterative identification using the auxiliary model algorithm is derived through making use of least squares based iterative algorithm. This algorithm is comparedwith the auxiliary model based extended and generalized recursive least squares algorithm.In conclusion, this theis mainly uses the idea of auxiliary model identification, systemata-cially derives and analyzes several parameters estimation methods based on auxiliary model forthe output-error multiple-input single-output systems. Finally, a brief summary and outlookis made for this topic, which involved a simple introduction about some urgent di?culties andissues needed to be solved, as the proof of the convergence of some identification algorithms,and the applications in industrial control.