Transfer Function Measurement Using Analog Modeling Techniques

Analog models provide a cheap and effective method for identification and checkout of a wide range of physical systems via the transfer function concept. This paper reviews the excitation of series, parallel, and pi mode analog models by deterministic stimuli. Errors between the system and model responses may be displayed on a cathode-ray tube, or on an instrument measuring mean-error modulus. Novel methods of tuning the model coefficients by observing the error displays are described and evaluated experimentally. The checkout strategy is particularly suitable for use by technicians since reliable repeatable models are obtained independent of the level of operator understanding of the system under test. These models may then be used as input data for quality control of production items and for preventive maintenance schemes during the life of the system under test. A low-order model is shown to be perfectly adequate for dynamic performance checkout of a complex noisy nonlinear system. Intermediate access points then permit elemental modeling down to replaceable units. For adequate confidence in system dynamic performance, checkout tolerances placed on the model coefficients must be conditional and a suitable tolerance flow chart is included. Although presented on the basis of manual instrumentation, the methodology is suitable for automation and is applicable to self-adaptive systems in which system dynamics change slowly with time.