A method for the determination of approximate system transfer functions

Abstract

Upon examining various experimental techniques for obtaining data which are useful in the determination of approximate system transfer functions of arbitrary systems, it has been concluded that pulse testing is the most generally applicable method. Non-linear regression techniques have been used to fit empirical transfer function forms to pulse test data which have been reduced to the useful frequency response form (or directly to frequency response data). General techniques are discussed briefly and are applied specifically to first-, second-, and third-order system models. A simple statistical test was used to select the simplest adequate representation from the suggested transfer function forms. Several examples have been presented to illustrate the use of the method. They justify the conclusion that the transfer function representation, which is of great utility in process control and dynamic stability studies on linear systems, can be obtained from easily procured experimental data.