Gradient Type Identification Methods For Two-Input Multirate Systems

Along with the development of modern industry, multirate systems have wider applications in automatic field. In many practical industry applications, the conventional sampled-data systems are unable to meet the needs of industrial productions. This requires the sampling periods of the samplers in the control systems should be different from those of the holds. In this case, there will be two or even more different operation rates in a system. Such systems are named as multirate systems. Therefore, researching effective parameter identification of multirate systems is not only significant in theory, but also potentially valuable in applications This thesis studies gradient type identification methods for two-input multirate systems, which is based on "The National Nature Science Foundation of China". After related references are referred by the author, the stochastic gradient type identification methods for two-input multirate systems are studied and convergence properties of some parameter estimation methods are analyzed. The results are presented as follows.1. For the multirate systems with two different input sampling periods, this thesis derives the discrete-time state-space models and the corresponding transfer function models are derived. Further different two-input multirate stochastic system models are obtained in terms of different stochastic noise models.2. A stochastic gradient algorithm is presented for two-input multirate controlled autoregres-sive models. Since the stochastic gradient algorithm has low computational effort, but its convergence is relatively slow. In order to increase convergence speed and improve parameter estimation accuracy, a forgetting factor is introduced to get the stochastic gradient algorithm with a forgetting factor (forgetting gradient algorithm for short). Assume that the system is persistently exciting, and the noise term is uncorrelated with zero mean, by applying the stochastic process theory and the martingale convergence theorem, we can prove the convergence properties of stochastic gradient algorithm. Finally, we test convergence properties of the proposed algorithm involved by a simulation example.3. When the noise models are MA and AR, respectively, we study identification methods for two-input multirate equation error models with the colored noises. For the different noise models contained in these models, the corresponding stochastic gradient algorithms are presented by replacing the unmeasurable noise terms in the information vector with their iterative estimates. Then simulation examples are given to demonstrate the methods for these models. 4. Based on the auxiliary model identification idea, identify the parameters of two-input multi-rate output error type models. Replacing the unknown true outputs (or noise-free outputs) in the information vector with the outputs of the auxiliary model and the unmeasurable noise terms in the information vector with the estimated residuals. The thesis researches on auxiliary model based stochastic gradient identification algorithms for the two-input multi rate output error systems, auxiliary model based extended stochastic gradient identification for the two-input multirate output error moving average models and auxiliary model based extended stochastic gradient identification for the two-input multirate output error autore-gressive moving average models. The convergence properties of the auxiliary model based stochastic gradient identification algorithms are proved. The following simulation examples illustrate the properties of these methods are effective.Finally, the conclusions of this thesis is given. The difficulties and further objectives of stochastic gradient type identification methods of multirate problems are also simply outlined in the end.