Part 2: Measurement SystemBehaviour
Part 2: Measurement System Behaviour
Lecture 4Behaviour AnalysisofMeasurementSystems
Lecture 4 Behaviour Analysis of Measurement Systems
Learning Objectives relate generalized measurement system models to dynamicresponse,: describe and analyze models of zero-, first-, and second-order measurement systems and predict their generalbehavior, calculate static sensitivity, magnitude ratio, and phase shiftfor a range of systems and input waveforms, state the importance of phase linearity in reducing signaldistortion,analyze the response of a measurement system to acomplex input waveform, anddetermine the response of coupled measurement systems
Learning Objectives • relate generalized measurement system models to dynamic response, • describe and analyze models of zero-, first-, and secondorder measurement systems and predict their general behavior, • calculate static sensitivity, magnitude ratio, and phase shift for a range of systems and input waveforms, • state the importance of phase linearity in reducing signal distortion, • analyze the response of a measurement system to a complex input waveform, and • determine the response of coupled measurement systems
GENERALMODELFORAMEASUREMENTSYSTEMAll input and output signals can be broadly classified asbeingo static,。 dynamic, oro some combination of the two
GENERAL MODEL FOR A MEASUREMENT SYSTEM All input and output signals can be broadly classified as being o static, o dynamic, or o some combination of the two
MeasurementSystem(O)InitialconditionsOutputsignalInputsignalMeasurementsystemF(t)operationy(t)the primary task of a measurement system is to sense an input signal and totranslatethat information intoa readilyunderstandable and quantifiable outputform
Measurement System the primary task of a measurement system is to sense an input signal and to translate that information into a readily understandable and quantifiable output form
MeasurementSystem ModelReal measurement systems can be modelled by consideringtheir governing system equations.d"yay+aoy=F(t)anan-adm-dmdtwheredxXbm+boxFotm<nDdtm-1drmdt
Measurement System Model Real measurement systems can be modelled by considering their governing system equations
DynamicMeasurementsFor dynamic signals, signal amplitude, frequency, andgeneral waveform information is needed to reconstruct theinput signal.Because dynamic signals vary with time, the measurementsystem must be able to respond fast enough to keep up withthe input signal
Dynamic Measurements • For dynamic signals, signal amplitude, frequency, and general waveform information is needed to reconstruct the input signal. • Because dynamic signals vary with time, the measurement system must be able to respond fast enough to keep up with the input signal
MeasurementSystemModelIn lumped parameter modelling, the spatially distributed physicalattributes of a system are modelled as discrete elements.An advantage is that the governing equations of the models reducefrom partial to ordinary differential equations.AutomobilestructureMass1y(t)Massy(t)OutputsignalTireVelocityF(t)F(t)Input signalForwardprofileSide profile
Measurement System Model • In lumped parameter modelling, the spatially distributed physical attributes of a system are modelled as discrete elements. • An advantage is that the governing equations of the models reduce from partial to ordinary differential equations
Seismic Accelerometer()Output signalPiezoelectric(voltage)crystalLarge body(a)PiezoelectricaccelerometerattachedtolargebodymjkMassmDamperSpringBodykck(y-x)c(y-x)surface(b)Representationusingmass,(e)Free-bodydiagramspring,anddamper
Seismic Accelerometer (1)
Seismic Accelerometer (2)dxdy+kxm电dtd2dt2dydx6+bo.xalaoy11d2dtdtwe can see that a2 = m, a1= b1 = c, ao= bo = k, and that the forcesdeveloped due to the velocity and displacement of the body becomethe inputs to the accelerometer. If we could anticipate the waveformof x, for example, x(t) = xo sin vt, we could solve for y(t), which givesthemeasurementsystemresponse
Seismic Accelerometer (2) we can see that a2 = m, a1= b1 = c, a0= b0 = k, and that the forces developed due to the velocity and displacement of the body become the inputs to the accelerometer. If we could anticipate the waveform of x, for example, x(t) = x0 sin vt, we could solve for y(t), which gives the measurement system response