Lab Overview
Sensors
DAQ
Modeling
Experimentation
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)
Summary
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Lab Overview
In the laboratory, you will experiment with a compound pendulum setup
equipped with a potentiometric sensor to measure rotational displacement
about a fixed support shaft.
Sensor and digital data acquisition (or ‘DAQ’) concepts are introduced.
Learning LabVIEW continues, now programming to control DAQ hardware
for signal analysis.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
When released from an initial angle, the pendulum
oscillates and eventually stops.
Decay of pendulum motion is likely due to energy dissipated by friction in the
pivot and/or in the air. We will determine which dominates by making
measurements from an angle sensor in combination with results from modeling
and simulation.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Lab Objectives
1
Learn sensor concepts, using sensors, and signal conditioning
2
Become familiar with the National Instruments myDAQ data acquisition
hardware
3
Continue learning how to program in LabVIEW, now for data acquisition
4
Develop a LabVIEW program to measure sensor signals using myDAQ
5
Calibrate rotational potentiometer for angle measurement
6
Write LabVIEW programs that analyze signals to generate useful data
7
Run experiments with the compound pendulum and save angular position
measurements over time as the pendulum comes to rest after being released.
8
Use measured data to answer questions about the system (e.g., estimate
system parameters, system energy stored or dissipated, etc.)
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Most modern sensors are electromechanical
We can classify by the sensing
mechanism.
Resistive (potentiometers,
strain gauges, thermistors,
light, etc.)
Capacitive (Very common in
MEMS; accelerometers, stud
sensors, etc.)
Inductive and Magnetic
(proximity, distance, ...)
Piezolelectric (force, ...)
ME 144L Dynamic Systems and Controls Lab (Longoria)
Summary
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Resistive sensors rely on changes in resistance
The resistance of a uniform conductor is given by, R = ρL/A, with ρ
the resistivity, L the length and A the constant cross-sectional area
through 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 inferred
through a signal conditioning circuit (e.g., a voltage-divider)
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Signal conditioning for resistive sensors converts resistance
change to voltage change
Signal conditioning refers to the
devices and processes we use to
modify and/or improve the nature
of a sensor signal. Examples
include filters, amplifiers, etc.
Consider a basic voltage divider,
where
R2
vin
vout =
R1 + R2
ME 144L Dynamic Systems and Controls Lab (Longoria)
By using a voltage divider, we can
transform the resistance change
into a voltage change which is
more readily measured.
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Calibration of the potentiometric sensor
Effectively, the potentiometric sensor is configured like a voltage divider where the
output 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 is
desirable to have a sensor that has a linear relation between the measurand (here
θ) and the measured voltage.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Why we like linear sensor models
Linear model relations between measured voltages, say vm , and a
measurand of interest, ym , make it easy to represent calibration with a
single constant or line (e.g., from regression),
ym = K · vm
Another advantage is that if the relation between a measured voltage
signal and the measurand is linear then when you look at the temporal
trends in the measured signals these are the same for the actual physical
variable(s) of interest.
Having a nonlinear sensor is tolerable, especially since modern computing
can 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 (or
rotation).
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Pre-Lab 1 – sensing circuit
Review the sensing circuit (potentiometer) discussed in the lecture slides. Submit
a description of how the basic potentiometric circuit is used to measure pendulum
angular position. Use diagrams and equations in this description.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Most modern voltage measurements are made using A/D
converters
Most basic electrical measurements
rely on an analog-to-digital (A/D)
converter, which are even included as
part of modern microcontrollers.
ME 144L Dynamic Systems and Controls Lab (Longoria)
In a DMM, signal conditioners infer
other electrical quantities from a
measurement of voltage.
Note the signal conditioners needed to
allow measurement of current and
resistance.
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
For more general purpose measurement and
instrumentation applications, data acquisition devices offer
more functionality
Analog Output (AO)
I
I
Generate DC Voltages
General waveforms (Function Generator)
Digital I/O
I
I
General low (0V) and high (5V) pulses
Read digital pulses
Timing I/O
I
I
Generate pulse trains (square waves)
Read frequency, time values
Always critically evaluate DAQ specifications to determine if your needs can be
met by a particular DAQ device.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
The NI myDAQ connects via USB
Form factor:
ME 144L Dynamic Systems and Controls Lab (Longoria)
Connections:
Experimentation
Summary
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
What should you know about A/D conversion?
General concepts:
Resolution and range
How fast to sample
How many times to sample
Hardware specific:
Device and configuration
(using NI MAX)
Connecting signals the right
way
What channels to sample
How to deal with the data
There are many different types of software and hardware commercial products for
DAQ. National Instruments products have seen increased application and
adoption in industry, research, etc., including areas that were once considered the
domain of very ‘high-end’ systems.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Analog-to-Digital (A/D) Conversion
The A/D converter (ADC) converts an analog voltage into a binary
number through the process of quantization.
The ADC will have a full-scale voltage range (VF S ) over which it can
operate.
Example: For the NI myDAQ device, there are two analog inputs with
different FS range. What is difference between DC and AC coupled?
The number of bits dictates how many discrete levels will be used to
represent measured voltages.
Example: An 8-bit converter with a VF S = 10 V gives a resolution of
10V/256 = 39.1 mV.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
A/D Conversion: Quantization
A signal entering a computer must be discretized in amplitude and time
(sampling). Amplitude quantization depends on the number of bits in the A/D
converter.
Comparing A/D resolution for n = 3 vs 16:
∆n=3 = VF S /23 = 1.25 V compared to ∆n=16 = VF S /216 = 0.15 mV
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Choosing a sampling or scan rate (scans/sec, or Hz)
The ADC samples according to a scan rate.
How fast you sample should minimally satisfy the Nyquist sampling
theorem.
Nyquist: the sampling rate should be at least two times the highest
frequency present in the signal.
Satisfying the Nyquist criterion helps ensure the signal can be
reconstructed properly.
You need to balance how fast you sample, how many samples you
store, etc.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
In selecting a sample rate, think about time resolution also
Depending on your objective, you might choose scan rate to satisfy Nyquist
criterion, but remember accuracy in time measurements.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
“All grounds are not the same the world ’round.”
Understanding grounds is important in making proper signal connections.
Can you connect them?
Circuit or signal common
Earth ground
Chassis ground
ME 144L Dynamic Systems and Controls Lab (Longoria)
Ground symbols:
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Types of signal sources
Grounded source:
Referenced to system ground
(e.g., earth, building)
Share a common ground with a
DAQ board, oscilloscope, etc.
Some signal generators, power supplies
Floating source:
Isolated from absolute reference
such as earth or building ground
Neither terminal is connected to
a ground
Batteries and battery-powered sources, many sensors
such as thermocouples, etc.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Types of Measurement Systems
You may see these connection options on DAQ hardware.
1
Differential measurement system
2
Referenced single-ended (RSE)
3
Non-referenced single-ended (NRSE)
Example: myDAQ analog input
ME 144L Dynamic Systems and Controls Lab (Longoria)
Summary
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Pre-Lab 2 (1) – learning about LabVIEW DAQ
Read about how data acquisition is accomplished using LabVIEW in Getting
Started with LabVIEW tutorial. Create a NI-DAQmx Simulated Device. When
deciding 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, or
you 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 DAQ
hardware.
3
Using a NI-DAQmx Simulated Device: study from page 4-1 to 4-6 of
Chapter 4 in the Getting Started with LabVIEW tutorial. This example
should simulate collection of 2 channels of data; when the “while” loop is
stopped the data should be saved to a LabVIEW measurement file. Here is
what the menu sequence might look like.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Pre-Lab 2 (2) – learning about LabVIEW DAQ
4
Here is a sample screen shot of a front panel for a VI you should create for
capturing two (simulated) signals. Here is what the block diagram might
look like.
5
Submit your VI via email to your TA before going to lab
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Model for determining pendulum moment of inertia
The model for a compound pendulum
was previously derived (see
Introduction slides) as a 2nd order
ODE,
J0 θ̈ + mglC sin θ = 0.
with J0 the (mass) moment of inertia
about the axis of rotation (or pivot),
2
O, J0 = J + mlC
, m is the total
mass, and lC the distance from the
pivot to the CG. It was assumed that
there are no damping torques.
If the angle of oscillation about θ = 0
is small (< 10 degrees), sin θ ≈ θ then
the ODE becomes linear,
ME 144L Dynamic Systems and Controls Lab (Longoria)
J0 θ̈ + mglC θ = 0.
In standard 2nd order form,
θ̈ + ωn2 θ = 0,
p
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 .
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Experimentation
Before closing, consider the what can be found out by use of the
pendulum 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 on
amplitude of oscillation - it is known that as amplitude increases, then
so must period
estimate stored energy, and how energy decreases after each cycle
estimate the total energy over time - this requires that you estimate
the potential energy as well as the kinetic energy. Estimating kinetic
energy requires estimating the velocity from the measured position.
Any one of these motivates the need to analyze the signals and the data in
a certain way.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Pre-Lab 3 – estimating moment of inertia
In lab, you will make period measurements to experimentally estimate the
pendulum moment of inertia (about the pivot) based on a model of the
pendulum. You will need pendulum geometric data found on the course log (use
any of these values and update/verify when you go to lab) and assume a nominal
value for aluminum density. Submit answers to the following items:
1
What are two key assumptions made in relating pendulum moment of inertia
to the undamped natural period?
2
Determine the distance to the center of gravity from the pivot, the total
mass of the pendulum, and the mass moment of inertia about the pivot.
3
Calculate the theoretical undamped natural period of the pendulum (in
seconds).
4
One factor in the uncertainty in your measurement of the measured period
will 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 than
1%. Given your estimate of the undamped period, what would you
recommend for a sampling rate?
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Some advice:
Make notes on how to connect power, sensors, and measured signals
properly. Simple circuit knowledge is all that is needed, and it can
help you make sure you collect the signals correctly and don’t damage
equipment.
Keep separate issues of software from hardware, but understand they
work together. LabVIEW does not measure signals – instruments do
that. LabVIEW is software that controls hardware. The hardware
does the actual data collection.
Similarly, we’ll use LabVIEW to numerically solve equations, but
LabVIEW does not “model a physical system”– you do that!
ME 144L Dynamic Systems and Controls Lab (Longoria)
Lab Overview
Sensors
DAQ
Modeling
Experimentation
Summary
Summary
Use this lab to build experience using simple sensors
Use this known physical problem for purposeful learning of DAQ
usage, signal processing, etc.
Take opportunity to experiment with very basic LabVIEW VI for data
collection.
Experiment with myDAQ for quick data acquisition, testing, and
model improvement
Data collected in this week’s experiments will be used in the following
week 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 range
through the screw terminal connectors or +/- 2 volt range through the
3.5mm 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 for
simple 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 selectable
for input or output.
60 Volt Digital Multimeter (DMM) for Measuring Voltage, Current, and
Resistance
The isolated DMM includes the capability to measure both AC and DC
voltage 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)