Gradient Based Identification For Dual-Rate Sampled-Data Systems

Multirate systems are abundant in industry; for example, many soft-sensor design problems are related to modeling, parameter identification, or state estimation involving multirate systems. The conventional sample-data systems, whose outputs are sampled at the same rates as the control updating rates, are called single-rate systems. In many industry applications, the outputs are sampled at slower rates than the control updating rates, mostly due to hardware limitation. In this case, there will be two or even more different operation rates in a system. Such systems are named as dual-rate (multirate) systems. Therefore, seaching for effective parameter definication of dual-rate (multirate) systems is not only significant in theory, but also potentially valuable in applications. This thesis is based on the Project "Study of Modelling and Identification of a Class of Nonlinear Systems (The National Nature Science Foundation of China)", and researches parameter identification of dual-rate systems. Based on some existing identification methods of dual-rate (multirate) systems, the thesis mainly focuses on the appropriate model that can be identified with dual-rate input-output data. By using the polynomial transformation technique, new algorithms of parameter identification of dual-rate systems are obtained, and results are presented as follows.1. By using polynomial transformation technique to transform AR model with missing observation data into ARMA model that can be identified with dual-rate input-output data directly, a recursive extended stochastic gradient identification method for the ARMA system with missing observation data is proposed. The stochastic gradient algorithm has low computational effort, but its convergence is relatively slow. In order to improve the tracking performance of the stochastic gradient algorithm, a forgetting factor is introduced to get the recursive extended stochastic gradient algorithm with a forgetting factor. Assume that the system is consistently excited, by applying the stochastic process theorem and the martingale convergence theorem, we can prove that the parameter estimates errors are consistently converge to zero. Finally, we test effectiveness of the algorithm involved by a simulation example.2. Studying identification methods for dual-rate sampled-data ARX models. By using polynomial transformation technique, dual-rate sampled-data ARX model can be transformed into the dual-rate ARMAX model that can be identified with dual-rate input-output data directly, and a forgetting factor based recursive extended stochastic gradient identification method is proposed. Also, assume that the systems are persistent excitation, we prove that the dual-rate parameter estimate methods are consistently convergent. Finally, the simulation example indicate that parameter estimation of the algorithm proposed is satisfying.3. When noise models are AR, MA and ARMA, respectively, we study identification methods for dual-rate sampled-data systems with the colored noise's interfered. By using polynomial trans- formation technique to transform them into the ones that can be identified directly using the observing data, a series of stochastic gradient based identification methods are proposed. Finally, we test the algorithms proposed in thesis by some simulation examples and show their effectiveness.4. Based on the auxiliry model, identify the parameters of the dual-rate sampled OEMA systems by using the dual-rate sampled data directly, and a recursive extended stochastic gradient based the auxiliry model identification method is proposed, and the simulation results indicate that these methods proposed are effective. Compared with the polynomial transformation technique, the algorithm we presented reduces the computational efforts obviously, and the estimate error ratio is also satisfying.Finally, a simple conclusion and prospect of this thesis is given. The difficulties and further objectives of dual-rate problems are also simply outlined in the end.