APPENDIX F DYNAMIC RESPONSE OF INSTRUMENT SYSTEMS
In our discussions in this text, any temporal variations in the measured quantity have been treated as random variations that contribute to the random uncertainty in the measurement. However, it is also necessary for us to consider additional error sources due to the response of instruments to dynamic, or changing, inputs. An instrument may produce an output with both amplitude and phase (time lag) errors when a dynamic input is encountered.
These dynamic response errors are similar to the variable but deterministic bias errors discussed in Appendix E, and they can be very important in the analysis of a timewise, transient experiment. In the following sections we present the fundamentals needed to estimate these amplitude and phase errors.
F-1 GENERAL INSTRUMENT RESPONSE
The traditional way to investigate the dynamic response of an instrument is to consider the differential equation that describes the output. We assume that the instrument response can be modeled using a linear ordinary differential equation with constant coefficients [1]
where y is the instrument output, x is the input, and n is the order of the instrument.
Instrument response to three different inputs will be discussed: (1) a step change, (2) a ramp input, and (3) a sinusoidal input. These are illustrated in
Figures F.1, F.2, and F.3. Mathematically, ...
Get Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
