Simplification of large linear systems using two-step iterative method

Graduation date: 1980The order of the practical system (e.g. nuclear power\ud plants, electrical power network and chemical plant) is\ud quite large. However, there are many limitations in computing\ud facilities for the large system. Because of these\ud limitations, it is often necessary to reduce the order of\ud the large system using an approximation.\ud Here the simple iterative technique which is free of\ud certain shortcomings of the previous method is proposed\ud for the approximation of large linear systems by a low-order\ud model. A measure of the goodness of the model is the\ud value of the integral-square error between the step responses\ud of the exact and the simplified system.\ud The proposed technique consists of a two-step iterative\ud scheme. In the first step, the optimum residues are\ud obtained by the minimization of the objective function,\ud while the poles (or eigenvalues) are kept constant. In\ud the second step, the poles (or eigenvalues) are optimized\ud while the residues remain fixed. This procedure is continued\ud cyclically until the objective function is satisfactorily\ud minimized.\ud The necessary and sufficient conditions for existence\ud of an optimum are satisfied in each step. The residues,\ud poles (or eigenvalues) and objective functions always converge\ud monotomically. The resulting reduced-order model\ud obtained by this method is stable if the original system is\ud stable. The method can be applied not only to single-variable\ud systems, but also to systems with repeated poles\ud (or eigenvalues) and to multivariable systems. The results\ud are superior to those obtained previously in the steady-state\ud and transient responses, and the value of the\ud integral-square error.\ud Illustrative examples are presented