A two-step iterative method for discrete-time systems reduction

✍ Scribed by F.F. Shoji; K. Abe; H. Takeda

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 646 KB
• Volume: 315
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(83)90076-5

✦ Synopsis

A two-step iterative method (1,2) f or a reduction in the order of linear continuous- time systems, given in the state equation or the transfer function, is extended to reduce discretetime systems. The method requires the optimization of the residues and eigenvalues (or poles) belonging to an objectivefunction.

The objectivefunction to be minimized is chosen as the finite sum of the squares of the error between the step responses of the reduced model and the original system. This scheme is continued cyclically until the objective function is satisfactorily minimized. By investigating the initial selection of the eigenvalues in the reduced-order model, it isfound that the dominant eigenvalues of the original system give a good approximation. Further, the resulting model is always stable, assuming the original system is stable. As shown in a numerical example, the proposed method is superior to the other methods of model reduction in both steady-state and transient responses, and in the value of the sum of the squares of the error.