A Method of Analysis of Large Scale Control Systems in Frequency Domain by System-Decomposition Technique

Abstract

A method of analysis of multi-variable control systems by digital computer is discussed in this paper. A large scale system can be decomposed into a suitable number of subsystems which are represented by signal flow graphs. In this method, the frequency characteristics of each subsystem is calculated by matrix elimination in the first place. Then, a matrix equation of a composed system is made up by rearranging elements of transfer matrices of the subsystems. From this equation, the transfer matrix of the higher class system can be evaluated by matrix elimination, just the same as in the signal flow graph reduction.
This method has much computational advantage to save the time for computation and to use the memory space effectively, as compared with the reduction without the system-decomposition technique. If we introduced a hierarchical system-decomposition or grouping, the computational advantage would be increased remarkably. Especially, a case study, in which parameters of the system are changed, can be carried out with little additional time for computation through an adequate system-decomposition. For this purpose the routine for reduction is proposed in this paper.
In the computer program developed by the authors, the input data can be made up directly in the tabular form from a block-connection diagram and signal flow graphs of a given system.
As an example, a steam temperature control system of reheat boiler is presented to demonstrate the computational advantage of this method.