Pole determinations with complex-zero inputs

A method for the determination of the characteristic pole locations in simple systems and components is discussed. The techniques introduced are extended to include more complex systems. The method consists of applying a signal to the system from a "complex-zero-generator" and then observing the system output response on an oscillograph. The system pole locations are determined when the system output goes through a null, which occurs when the zeros generated by the "complex-zero-generator" cancel the system poles. Tests on experimental systems indicate that the pole locations can be determined accurately and rapidly for a wide variety of systems. For testing purposes, a "complex-zero-generator" was built using two square-wave generators with a timed delay between them. This generator gives a signal which can contain complex zeros anywhere in the s-plane. This signal is then applied to a number of systems containing several different relative pole orientations. The system outputs, as photographed on the oscillograph, are studied to develop rules and procedures to determine the pole locations. The rules are then applied to a number of "unknown" systems in order to determine their applicability and a study is made of the errors and limitations involved. The results indicate that the method described is readily applicable to many systems and that, in many instances, the pole locations are determined more accurately and more rapidly than can be done through the use of a steady-state frequency analysis.