Lab Overview Sensors DAQ Modeling Experimentation Summary Introduction to Sensors and Data Acquisition Experimenting with a compound pendulum Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin Fall 2014 ME 144L Dynamic Systems and Controls Lab (Longoria)
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In the laboratory, you will experiment with a compound pendulum setupequipped with a potentiometric sensor to measure rotational displacementabout a fixed support shaft.
Sensor and digital data acquisition (or ‘DAQ’) concepts are introduced.
Learning LabVIEW continues, now programming to control DAQ hardwarefor signal analysis.
ME 144L Dynamic Systems and Controls Lab (Longoria)
The resistance of a uniform conductor is given by, R = ρL/A, with ρthe resistivity, L the length and A the constant cross-sectional areathrough which current flows.
Resistance changes either by a geometric (A, L) or material change(ρ) in the resistive element.
Resistance can be directly measured (by an ohmmeter) or inferredthrough a signal conditioning circuit (e.g., a voltage-divider)
ME 144L Dynamic Systems and Controls Lab (Longoria)
Signal conditioning for resistive sensors converts resistancechange to voltage change
Signal conditioning refers to thedevices and processes we use tomodify and/or improve the natureof a sensor signal. Examplesinclude filters, amplifiers, etc.
Consider a basic voltage divider,where
vout =
[R2
R1 +R2
]vin By using a voltage divider, we can
transform the resistance changeinto a voltage change which ismore readily measured.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Effectively, the potentiometric sensor is configured like a voltage divider where theoutput voltage is related to the change in shaft position.
Calibration builds a relation between the output voltage and angular position.
We seek relation θ = f(vout), where vout is the measurable output voltage. It isdesirable to have a sensor that has a linear relation between the measurand (hereθ) and the measured voltage.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Linear model relations between measured voltages, say vm, and ameasurand of interest, ym, make it easy to represent calibration with asingle constant or line (e.g., from regression),
ym = K · vm
Another advantage is that if the relation between a measured voltagesignal and the measurand is linear then when you look at the temporaltrends in the measured signals these are the same for the actual physicalvariable(s) of interest.
Having a nonlinear sensor is tolerable, especially since modern computingcan easily represent the model.NOTE: It is expected that when calibrations are conducted, the regression may introduce a ‘y-intercept’ (i.e.,ym = K · vm + b). This model is more generally called affine, meaning there is a linear relation with some translation (orrotation).
ME 144L Dynamic Systems and Controls Lab (Longoria)
Review the sensing circuit (potentiometer) discussed in the lecture slides. Submita description of how the basic potentiometric circuit is used to measure pendulumangular position. Use diagrams and equations in this description.
ME 144L Dynamic Systems and Controls Lab (Longoria)
A signal entering a computer must be discretized in amplitude and time(sampling). Amplitude quantization depends on the number of bits in the A/Dconverter.
Comparing A/D resolution for n = 3 vs 16:
∆n=3 = VFS/23 = 1.25 V compared to ∆n=16 = VFS/2
16 = 0.15 mV
ME 144L Dynamic Systems and Controls Lab (Longoria)
Read about how data acquisition is accomplished using LabVIEW in GettingStarted with LabVIEW tutorial. Create a NI-DAQmx Simulated Device. Whendeciding on a type of device to simulate, choose E series (e.g., PCI-6025E).
Refer to and/or follow the following instructions:
1 Refer to online note that explains how:http://zone.ni.com/devzone/cda/tut/p/id/3698
2 If you did not install NI-DAQmx device drivers on your own computer, oryou prefer not to, then you need to use the METER lab for this purpose.The NI-DAQmx drivers are required if you will use LabVIEW to control DAQhardware.
3 Using a NI-DAQmx Simulated Device: study from page 4-1 to 4-6 ofChapter 4 in the Getting Started with LabVIEW tutorial. This exampleshould simulate collection of 2 channels of data; when the “while” loop isstopped the data should be saved to a LabVIEW measurement file. Here iswhat the menu sequence might look like.
ME 144L Dynamic Systems and Controls Lab (Longoria)
4 Here is a sample screen shot of a front panel for a VI you should create forcapturing two (simulated) signals. Here is what the block diagram mightlook like.
5 Submit your VI via email to your TA before going to lab
ME 144L Dynamic Systems and Controls Lab (Longoria)
The model for a compound pendulumwas previously derived (seeIntroduction slides) as a 2nd orderODE,
J0θ̈ +mglC sin θ = 0.
with J0 the (mass) moment of inertiaabout the axis of rotation (or pivot),O, J0 = J +ml2C , m is the totalmass, and lC the distance from thepivot to the CG. It was assumed thatthere are no damping torques.If the angle of oscillation about θ = 0is small (< 10 degrees), sin θ ≈ θ thenthe ODE becomes linear,
J0θ̈ +mglCθ = 0.
In standard 2nd order form,
θ̈ + ω2nθ = 0,
where, ωn =√mglC/J0 is the
undamped natural frequency. In this
way, a measurement of the undamped
natural period, Tn = 2π/ωn, can be
used to experimentally determine J0.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Before closing, consider the what can be found out by use of thependulum setup, the sensor(s) provided, and DAQ measurement.
Here are some suggestions:
estimate pendulum moment of inertia
show that for large oscillations, the pendulum period depends onamplitude of oscillation - it is known that as amplitude increases, thenso must period
estimate stored energy, and how energy decreases after each cycle
estimate the total energy over time - this requires that you estimatethe potential energy as well as the kinetic energy. Estimating kineticenergy requires estimating the velocity from the measured position.
Any one of these motivates the need to analyze the signals and the data ina certain way.
ME 144L Dynamic Systems and Controls Lab (Longoria)
In lab, you will make period measurements to experimentally estimate thependulum moment of inertia (about the pivot) based on a model of thependulum. You will need pendulum geometric data found on the course log (useany of these values and update/verify when you go to lab) and assume a nominalvalue for aluminum density. Submit answers to the following items:
1 What are two key assumptions made in relating pendulum moment of inertiato the undamped natural period?
2 Determine the distance to the center of gravity from the pivot, the totalmass of the pendulum, and the mass moment of inertia about the pivot.
3 Calculate the theoretical undamped natural period of the pendulum (inseconds).
4 One factor in the uncertainty in your measurement of the measured periodwill depend on how many samples you measure every second (sample rate).Say you wanted to be able to say that the uncertainty was no more than1%. Given your estimate of the undamped period, what would yourecommend for a sampling rate?
ME 144L Dynamic Systems and Controls Lab (Longoria)
Make notes on how to connect power, sensors, and measured signalsproperly. Simple circuit knowledge is all that is needed, and it canhelp you make sure you collect the signals correctly and don’t damageequipment.
Keep separate issues of software from hardware, but understand theywork together. LabVIEW does not measure signals – instruments dothat. LabVIEW is software that controls hardware. The hardwaredoes the actual data collection.
Similarly, we’ll use LabVIEW to numerically solve equations, butLabVIEW does not “model a physical system”– you do that!
ME 144L Dynamic Systems and Controls Lab (Longoria)
Use this lab to build experience using simple sensors
Use this known physical problem for purposeful learning of DAQusage, signal processing, etc.
Take opportunity to experiment with very basic LabVIEW VI for datacollection.
Experiment with myDAQ for quick data acquisition, testing, andmodel improvement
Data collected in this week’s experiments will be used in the followingweek and compared to results from simulation of the model
ME 144L Dynamic Systems and Controls Lab (Longoria)
NI myDAQ Specifications
Two Differential Analog Input and Analog Output Channels(200 kS/s, 16 bit, +/- 10 Volts)Access matched analog input and output channels in a +/- 10 volt rangethrough the screw terminal connectors or +/- 2 volt range through the3.5mm audio jacks.
+5 , +15, and -15 Volt Power Supply Outputs (up to 500m Watts of Power)USB powered for maximum mobility, myDAQ supplies enough power forsimple circuits and sensors.
Eight Digital Input and Digital Output Lines (3.3 Volt TTL-Compatible)Use software-timed digital lines for interfacing both Low Voltage TTL(LVTTL) and 5 volt TTL digital circuits. Each line is individually selectablefor input or output.
60 Volt Digital Multimeter (DMM) for Measuring Voltage, Current, andResistanceThe isolated DMM includes the capability to measure both AC and DCvoltage and current as well as resistance, diode voltage, and continuity.
ME 144L Dynamic Systems and Controls Lab (Longoria)
NI myDAQ block diagram
ME 144L Dynamic Systems and Controls Lab (Longoria)