Iterative Identification For Multivariable Systems Based On Equation-Error Models

With the development of control theory and industrial technology, the identification ofmany industrial systems can not obtain the ideal results only using the identification principleof single-variable system, but to multivariable system. Therefore, the research of multivariablesystem identification has significant value in theory and application. The thesis is based on"TheNational Nature Science Foundation of China", and presents the identification algorithm for aclass of multivariable systems based on equation-error models. The author reads and researchesa lot of relevant literature, and deep studies the identification of multivariable systems basedon equation-error models. the innovation reserch result in the thesis as follows:1. A transfer matrices is derived from a linear discrete-time multivariable system state-spacemodel with color noises, and then a multivariable systems with moving average noisesmodel is obtained. Further multivariable systems with autoregressive noises models andmultivariable systems with autoregressive moving average noises models are obtained interms of di?erent color noises models.2. A hierarchical gradient-based iterative algorithm is presented for multivariable systemswith moving average noises models. The basic idea is to decompose the MIMO system intotwo virtual subsystems based on the hierarchical identification principle, one containing aparameter vector and the other containing a parameter matrix. To solve the di?culty ofthe information matrix including unmeasurable noise terms, the unknown noise terms arereplaced with their iterative residuals, which are computed through the preceding parameterestimates. At each iteration the algorithm performs a hierarchical computational process.Comparing with recursive least-squares algorithm, The presented algorithm makes full useof all data and thus can generate highly accurate parameter estimates at each iteration.Refer to the derivation of hierarchical gradient-based iterative algorithm , a hierarchicalleast square iterative algorithm is also presented for multivariable systems with movingaverage noises models. Comparing with hierarchical gradient-based iterative algorithm,the hierarchical least-squares iterative algorithm only need dozens of iteration to generatehighly accurate parameter estimates for a multivariable system. The hierarchical gradient-based iterative algorithm and hierarchical least-squares iterative algorithm are also givenin the case of interactive noises for the multivariable systems with moving average noisesmodels. The simulation results indicate that the proposed algorithm works quite well. 3. For the multivariable systems with moving average noises models, a hierarchical gradient-based iterative algorithm and a hierarchical least-squares iterative algorithm are presentedbased on the hierarchical identification principle and iterative identification principle. Thederivation is similar to the multivariable systems with moving average noises models. Thehierarchical gradient-based iterative algorithm and hierarchical least-squares iterative al-gorithm are also given in the case of interactive noises for the multivariable systems withmoving average noises models. The simulation results indicate that the proposed algorithmworks quite well.4. For the multivariable systems with autoregressive moving average noises models, a hierar-chical gradient-based iterative algorithm and a hierarchical least-squares iterative algorithmare presented based on the hierarchical identification principle and iterative identificationprinciple. The multivariable systems with moving average noises models and the multivari-able systems with autoregressive noises models can be viewed as the special circumstancesof the multivariable systems with autoregressive moving average noises models. So thealgorithms of multivariable systems with autoregressive moving average noises models aremore representative. The hierarchical gradient-based iterative algorithm and hierarchicalleast-squares iterative algorithm are also given in the case of interactive noises for the mul-tivariable systems with moving average noises models. The simulation results indicate thatthe proposed algorithm works quite well.A simple conclusion is given in the end , the di?culties and further rasearch of the thesisare alse outlined in the end, for example, the proposed algorithms are lack of theoretical proof,the computational load is too large at each iteration, and so on.