Dynamic_systems

# Dynamic_systems - Dynamic System Response Author John M...

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Dynamic System Response Author: John M. Cimbala, Penn State University Latest revision: 02 November 2007 – minor correction 31 March 2008 Introduction In an ideal world, sensors respond instantly to changes in the parameter being measured. In the real world, however, sensors require some time to adjust to changes, and in many cases exhibit oscillations that take some time to die out. In this learning module, we discuss the dynamic system response of sensors and their associated electronic circuits. [Much of this material is also covered in M E 370 – Vibration of Mechanical Systems.] Dynamic systems Measuring system Input Output y Consider some generic measuring system with an input and an output, as sketched to the right. The input is the physical quantity or property being measured, s etc. The input is given the symbol x , and is formally called the measurand . The measurin uch as pressure, temperature, velocity, strain, g system converts the measurand into something different, so that we can read, record, and/or changes as the measurand changes. The output is ) can be either static (steady within the time of measurement) or dynamic (unsteady). analyze it. The measuring system can be a sensor like a strain gage (converts strain directly into a change in resistance) or thermocouple (converts temperature directly into a voltage), or a transducer like a pressure transducer (converts pressure into a voltage or current). The output may be mechanical or electrical, and its value given the symbol y . The input (measurand If the measurand is static, the output is generally some factor K times the input, yK x = , where K is called the static sensitivity of the measuring system. For time-dependent (unsteady or dynamic) measure ments, the behavior is described by a differential onse . rder of a dynamic system re measurand x is not constant (static), but is changing with time (dynamic), x = x ( t ). equation. Such systems are called dynamic systems , and their behavior is called dynamic system resp In this learning module, only linear measuring systems are considered. In other words, for static signals, y has a linear relationship with x , namely, y = Kx , rather than some nonlinear relationship like y = K 1 x + K 2 x 2 . O Consider the case whe In an ideal measuring system, output y would respond instantaneously to changes in x , ( ) ( ) yt K xt = . We define n as the order of the dynamic system . The order of an ideal dynamic system is zero, i.e., n = 0 . An ideal measuring system is thus also called a al, but a simple resistor circuit comes close. Consider ll times: zero-order dynamic system . No real system is perfectly ide the resistor as the system, with voltage drop as the input, and current through the resistor as the output, as sketched to the right.

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## This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Penn State.

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Dynamic_systems - Dynamic System Response Author John M...

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