Identification For Dual-rate Sampled-data Systems

In modern industry systems, the control variables are constrained by physical and me-chanical factors of the systems and the quality of control, thus are sampled by different data sampling/holding rates, this dual-rate or multirate data-sampled systems exist widely in the process control industry. The dual-rate or multirate sampled-data systems are different from the conventional uniformly sampled discrete-time systems, and traditional identification methods cannot be applied to such multirate systems. The dissertation studies identification algorithms for the dual-rate sampled-data systems, thus has theoretical significance and academic values. The main contributions are as follows:1. For autoregressive time series models with missing data, since the conventional identi-fication methods cannot directly utilized to such models, the polynomial transformation tech-nique is employed to transform the model into a new one that excluding the immeasurable data, a least squares algorithm is proposed to identify the model and convergence properties are ana-lyzed. Furthermore, the proposed algorithm is extended to autoregressive moving average time series models with missing data. The simulations verify the effectiveness of the algorithms.2. For the dual-rate sampled equation error systems, the system input can be measured at each sampling time, while the observed system output are small, thus the conventional identifi-cation methods cannot be applied to these systems. The polynomial transformation technique is employed and a recursive extended least squares algorithm is presented to identify the dual-rate model. Notice that the least squares algorithm needs to compute the covariance matrix, leading to large computational load. The stochastic gradient algorithm has much less compu-tation but has slow convergence rate. A modified stochastic gradient algorithm is proposed by adding a convergence index, which accelerate the convergence rate. The convergence properties are analyzed and simulations are performed.3. For the computational burden problem caused by the transformation technique, the hierarchical identification principle is employed that decomposes the system into several sub-systems with smaller dimension and less parameters, a hierarchical least squares algorithm is proposed. Compared with the least squares algorithm, the proposed algorithm reduces the computational load. The theoretical analysis and the simulations verify the effectiveness of the algorithms.4. For the dual-rate sampled output error systems, since the parameter estimation of the conventional identification methods for the output model is biased, a bias compensation based hierarchical estimation algorithm is proposed. The theoretical analysis and the simulations clarify that the estimation of the proposed algorithm is unbiased. 5. For a class of nonuniformly sampled-data systems, the multi-innovation identification algorithm is employed by expanding the innovation scalar in the stochastic gradient algorithm to an innovation vector. Then, the limited sampled data can be taken full use of in the algorithm, and improve the convergence rate. The length of the innovation affects the convergence rate of the algorithm. Convergence analysis and the simulations are performed.