measurement, sensors, and data acquisition in the two...

ME 144LDynamic Systems and Controls Laboratory

Department of Mechanical EngineeringThe University of Texas at Austin

Measurement, Sensors, and Data

Acquisition in the Two-Can System

Prof. R.G. Longoria

Updated Fall 2010



Goal of this week’s lab

• Gain familiarity with using sensors

• Gain familiarity with using DAQ hardware

• Build familiarity with LabVIEW for DAQ applications

• Build data collection VIs

• Learn how to capture waveforms

• Learn how to save data to a spreadsheet/measurement

files

• Compare model and experiment results; improve

model predictions



Discuss here…

• Measurement and sensor concepts

• Data acquisition concepts

• Analyzing acquired data (signals) for specific

purpose(s)



Measurement System Context

SPower Flow

MeasurementSystem

Outputs for

Knowledge orControl

Sensor

SystemMeasurand

(True Value)

Optional Aux. Power

Signal

Conditioning

Auxiliary Power

•Recorder/Indicator•Processing

•Controller

Transducedsignal

Signal or information

Most modern measurement systems end up transforming

measurands into electrical (or optical) form.

Referent - a system

attribute that appears

relevant (e.g., state

variables)

Measurand - a referent

that is measurable



Sensor Concept• Sensors provide a measurand

by taking advantage of how

material or geometric

properties relate to changes in

a measurable quantity.

• This quantity is either directly

or indirectly converted into a

form useful for processing.

• Functional design around the

sensing mechanism yields a

usable output signal.

Sensor

SystemMeasurand

(True Value)

Optional Aux. Power

Transducedsignal

PrimarySystem

SecondarySystemMeasurand

(True Value)

Transduced

signal

System interactingdirectly with

process undermeasurement



Types of Electromechanical Sensors

• Resistive Sensors

• Capacitive Sensors

• Inductive and Magnetic Sensors

• Piezolelectric Sensors



Electrical Signal Domains

• The conversion of a physical quantity into electrical form is often done to indicate a direct relation. For example, the voltage level may be directly related to pressure.

• In general, however, the information about the physical quantity can be encoded in the signal in many different ways.

• Three major ways to encode a physical signal:

1. analog - in which the magnitude of an electrical quantity is related to the information of interest

2. time - in which the time relationship between changes in signal level is related to the information of interest

3. digital - in which an integer number is represented by binary level signals



Electrical Signal Domains

analog - many

electromechanical

sensors are of this

form;

potentiometers,

thermistors, etc.

digital -

counters, a/d

converters,

etc.

time - some devices generate signals where frequency

is a function of a physical quantity; e.g., a tachometer

From Malmstadt, et al, “

Electronic Meas for Scientists”



Electrical Signal DomainsExample: Thermistor digital thermometer

From Malmstadt, et al, “ Electronic Meas for Scientists”



Example: Analog vs. Digital Tire

Pressure Gauge

Valve Stem

Spring

Graduated

Stem

Pressure

Pm

Air

Leakage,Ql

C

T

1 I

x

x•

0 LeakageQl

Tire

Pressure

CAir

Spring Piston/stem

mass

Calibrate

for Pressure

1

E

Pm

R

valve

ò

dt

Digital tire gauge

(Radio Shack)



Digital Tire Pressure Gauge

Digital tire gauge

(Radio Shack)



Level measurement in two-can

Many ways to measure level in the two-can system.

This is a resistive level sensor we’ve

built for the two-can system.

Height goes as the inverse of resistance

(or impedance) of the water between

the probes.

*As height drops, resistance goes up.



Pressure Sensors

1 psi ~ 28 in of water

Most pressure sensors

feature a diaphragm that

responds to applied

pressure.

A sensing mechanism of

some type converts the

response to a proportional

electrical signal.

This diaphragm contacts

a small beam with strain

gauges.

This diaphragm in the PX409

pressure sensor is micro-

machined to include

piezoresistive strain gauges.



Can Emptying – Measured

Volume vs. Time for Can1

0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Time [sec]

Vo

lum

e [

ml]

This is volume data during a one-can

emptying experiment collected using the

PX409 pressure sensor (calibrated for can

volume)

1 where

g AP gh Ah V C

A C g

ρρ

ρ= = = = ‘hydraulic capacitance’



Digital data acquisition (DAQ)

• Basics about signals and how they are measured

by data acquisition (DAQ) hardware that use

analog-to-digital conversion (ADC).

• How to build simple programs in LabVIEW for

acquiring signals, displaying the data, analyzing

the data, and storing the data for later use.



A/D Converter in DMM

From “Using Your

Meter”

by A.J. Evans, Master Publishing, Inc., 1994.

Although it is not

hard to find an analog

multitester, digital

devices are much more

common.

In a DMM, signal

conditioners convert the

quantity under measure

into a voltage to be read

by an A/D converter.



Computers rely on DAQ

Data Acquisition (DAQ, ‘dak’) hardware is used to form a

communication interface between a computer and the ‘real world’.

There is a lot of DAQ

hardware available from

very low cost to high-

end. Choose as needed

for your application.



DAQ Functions Besides A/D

• Analog Output

– Generate DC Voltages

– General waveforms (Function Generator)

• Digital I/O

– General low (0V) and high (5V) pulses

– Read digital pulses

• Timing I/O

– Generate pulse trains (square waves)

– Read frequency, time values



What do you need to know?

• Resolution and range

• How fast to sample*

• How many times to sample

• Device and configuration (MAX)

• Connecting the signals the right way

• What channels to sample

• How to deal with the data*

The lab experiments are meant to provide experience with these concepts.

General Concepts

Hardware Specific



Analog-to-Digital 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 over which it

can operate.

• The number of bits will dictate how many discrete levels will

be used to represent measured voltages.

• For example, an 8-bit converter with a full-scale voltage of 10

V will give you a resolution of 10V/256 which is 39.1 mV.



A/D ConversionSignal entering the computer must be discretized

in amplitude as well as time (sampling).

Contrast n = 3 versus n = 16

3

16

10

2

10

2

1.25

0.152

V

FS

n V

VV

mV

=∆ = =

=

Resolution:



Choosing a sampling

or scan rate (scans/sec, or Hz)

• The ADC samples according to a scan rate.

• How fast you sample should satisfy the Nyquist

sampling theorem.

• The sampling frequency should be at least two times

the highest frequency present in the signal.

• Not satisfying Nyquist criterion has implications in

how the signal is ‘reconstructed’.



Selecting a sample rate…Depending on your

objective, you

might choose scan

rate to satisfy

Nyquist criterion.

But you might also

want to have

accuracy in time

measurements.

Can you see how you have to balance how fast you sample,

how many samples you get, etc.?



Data Acquisition Usage in Lab

• Build a virtual instruments in LabVIEW to acquire and graph voltage signals from pressure sensors and to conduct calibration.

• The VI should save waveforms to a measurement file for post-processing.

• Analyze the data

– Use to arrive at improved estimates of K flow coefficients

– Compare to simulation results



Methods for finding K

• Simple one-can experiments, measuring volume

and time to empty (last week)

• Use pressure (volume) data over time

– More accurate determination of critical heights,

time values, etc.

– Captures volume-time characteristic (shape)

– Enables comparison to simulation directly or to

analytical model



One-Can Experiments – Case 2

• Qin = 0. 0 out

dVQ

dt= −

outQ

dVK V

dt= −or

constantV ≠

h

Volume is a dynamic state.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

VoKo

2t⋅−

2

1 e

t−

τ eq⋅

t

Linear cans

never empty

eq

dVK V

dt= −

dVK V

dt= −

Nonlinear can2

( ) ,02

o e

KV t V t t T

= − ≤ ≤

Solution:

1

1o

K

V

=

=



Fitting Data to Analytical Solution

2 22( )

2 4o o o

K KV t V t t K V t V

= − = − +

2

( )2

i i i o i

Ke V V t V V t

= − = − −

The analytical solution is a quadratic equation:

There exist general routines that will fit experimental data (i.e., for volume

over time) to polynomials of this form.

Another approach is to derive a solution for K from minimizing the sum of

the squared error,

This results in a formula for K that is a

function of the volume-time data.

2

0ide

dK=



Comparison of Different Methods

0 5 10 15 20 25 30-2

0

2

4

6

8

10x 10

-4

measured

LSE-1

LSE-2

Vo & Te

Simulation results from using

different K values are shown

plotted with measured volume

data.

From LSE

You are expected to derive and test your own methods for finding K using this data.



How do I know my method works?

Simulate the experimental data collection!

Use your K values from the previous

week’s lab work.



Summary

• Use a known physical problem (two-can) for

purposeful learning of DAQ usage, signal

processing, etc.

• Experience with using pressure sensors (off-

the-shelf)

• Take opportunity to experiment with very basic

LabVIEW VI for data collection.

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