Some Fundamental Limitations on Indirect Testing of Dynamic Systems

Abstract

The measurement of several system parameters from a few testpoints for checkout purposes finds a close parallel in plant identification for adaptive control. Where in the latter ase statistical reduction techniques are common, in the former case a severe testing-time limitation must be faced. Against this background, measurement of a maximum of system parameters with a minimum of observations from a stimulus and a response connection was investigated. Investigations were limited to methods that will produce a consistent set of linear equations in the system parameters under observation. The stimulus has to contain to number of different components equal to the number of parameters under test, which components can be chosen from an orthogonal or independent set. The responses to these stimulus components, however, are in general not independent. The result is a fundamental lack of resolution depending on the complexity of the system under test and placement of a practical upper limit on the number of parameters that can be observed. Quantitative measures of error propagation from observation to solution have been developed Turingnumber, propagation of variance) to investigate this lack of resolution and to minimize it by proper test method design. Resolution can be further improved by repeated measurements. For checkout, however, time-consuming bruteforce approaches are to be avoided. From a large set of test methods investigated, it appeared that the best results are obtained by using sine-wave stimuli. Also a unique test method will be presented, instrumentable with a few simple low-pass filters.