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ME411 Engineering Measurement & Instrumentation Winter 2017 – Lecture 5 1

ME411 Engineering Measurement & Instrumentation

Nov 12, 2021



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ME411 Engineering Measurement & Instrumentation• Coefficients represent physical parameters – obtained by considering governing equations
• With this knowledge, we could predict the output with knowledge of the input!!
• This will then allow us to better design our measuring system…
Model of a Measurement System
• Fortunately, most measurement systems can be modelled using zero, 1st or 2nd order linear ODEs
• Even complicated systems can usually be thought of as a combination of these simpler cases
• Zero-order system
• Used to model the non-time
dependent system response to
1st-order system
• Measurement systems that have a storage system
• = a1/ao is called the time constant – will always have a dimension of time
• Let’s now consider some special types of input signals and observe how the system responds…
K = 1/ao = Static sens
1st-order system – Step input
1st-order system – Step input
• Time constant, • Time required for system to achieve 63.2% of
• Property of the system!
1st-order system – Example
1st-order system – General Periodic
Dynamic error:
K = 1/ao = Static sens
• As usual, we can’t solve a non-homogenous 2nd order ODE without first solving the homogenous case determines the transient response of the system
• damping ratio internal energy dissipation
• Depending on the value of , three solutions are possible:
2nd-order system
• < 1: oscillation!
• Settling time: Time for output to reach ±10% of KA
• Best damping?? 0.6 – 0.8, but depends…
2nd-order system – Terminated ramp input
25 From Doebelin - Measurement Systems Application and Design 5th ed
2nd-order system – Impulse
2nd-order system – General Periodic
2nd-order system – General Periodic
Image credits
• All images from Figliola and Beasley, Mechanical Measurements 5th edition unless otherwise stated