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