sensors · 2018. 11. 26. · transducer: changes one form of energy to another measurement chain...

Sensors

Francesco Ferrante, PhD

[email protected]

Department of Physics, Engineering, Earth, and Environmental Sciences, and

Mechanics

Grenoble Image Parole Signal Automatique

Université Grenoble Alpes

Control Systems Technologies

—–

Graduate Course

Master in Systems, Control, and Information Technologies

—–

September 10, 2018

Université Grenoble Alpes - 1/28

mailto:[email protected]

Outline

1. Generalities on Sensors

2. Temperature Sensors

3. Position Sensors

4. Accelerometers


Outline



3. Position Sensors

4. Accelerometers


Sensors

◮ Sensor: a device that responds to a physical stimulus andconverts it into a signal

◮ Transducer: changes one form of energy to another

Measurement chain

ConditioningSensor Transducer

MeasurementPhysical stimulus Physical Signal Electrical Signal

◮ Temperature, Flow, Mass, Level (Process Control)

◮ Position, speed, acceleration (Motion Control)

Variables of interest in Control Systems


Characteristics of a Sensor

◮ accuracy: agreement ofmeasured values with a givenreference

◮ repeatability: capability ofreproducing as output similarmeasured values for differentmeasurements of the samequantity

◮ stability: for a given inputyou always get the sameoutput

◮ range: the limits betweenwhich the measured inputcan vary.

◮ resolution: minimal changeof the input necessary toproduce a detectable changeat the output


Characteristics of a Sensor◮ sensitivity: variation of the

output signal over variationof the input (sensor gain)

◮ frequency response:

dynamics of the sensor fromDC to the highestmeasurable frequency

◮ calibration curve:

relationship between themeasurand and the signalgenerated by the sensor

◮ linearity: the closeness ofthe calibration curve to aspecified straight line

◮ Rangeability=20:1

◮ fullscale =100 kg s−1

◮ accuracy= 1%Provides measurements with an accuracy of 1% within the range[5, 100]kg s−1

Example-Rangeability

◮ Hysteresis: differencebetween output readings forthe same measurand,depending on the trajectory

x (input)

y (output)


Calibration

1. supply the sensor with a set of n samples xi

2. for each xi, repeat the measurement mi times to getyi,1, yi,2, . . . , yi,mi

3. for each i = 1, 2, . . . , n take the average yi =∑mi

j=1 yi,j

4. select a curve from a specific class, e.g., linear, polynomial, etc

5. get the best fitting parameters to interpolate{(x1, y1), (x2, y2), . . . , (xn, yn)} (least squares algorithm).

lin

explog

x

y


Dynamic Characteristics

Sensors are considered static but actually have their own dynamics!

hA(T∞ − T (t)) = mcdT (t)

dt

where h is the convection coefficient, A is the surface area of the sensor,T is the temperature, m is the TC mass, and c is the heat capacity.

Example:Thermocouple

Therefore, it is important to define dynamical parameters to fullycharacterize a sensor.

◮ The response time: the time it takes for the output tosettle, e.g., at 95% of the value of the input.

◮ The rise time: the time taken for the output to rise to somespecified percentage of the steady-state output.

◮ The settling time: the time taken for the output to settle towithin some percentage of the steady-state value.


Outline



3. Position Sensors

4. Accelerometers


Thermocouples

◮ Input: Temperature difference

◮ Output: Voltage

◮ Supply: Self-supplied (thermoelectric)

◮ Characteristic: Nonlinear

Some numbers...

◮ Temperature range: −200÷ 2760◦C

◮ Output Voltage: −10÷ 50 mV

◮ Sensitivity: 10÷ 50 µV ◦C−1


Thermocouples

Thomas Johann Seebeck(Tallinn 1770–Berlin1831).

In 1821, T. J. Seebeck noticed that atemperature gradient induces an electricalvoltage gradient.

Seebeck Effect

◮ S Seebek coefficient

M1

T2T1

Vg(T1, T2)

Vg(T1, T2) =

∫ T2

T1

S(T )dT


Thermocouples

Thomas Johann Seebeck(Tallinn 1770–Berlin1831).

In 1821, T. J. Seebeck noticed that atemperature gradient induces an electricalvoltage gradient.

Seebeck Effect

◮ S Seebek coefficient

M1M2

T2

T1

V1V2

E

E(T1, T2) =

∫ T2

T1

(S1(T )−S2(T ))dT

Vg is hard to measure, instruments will perturb the structure of thesensor.


Thermocouples–Two junctions

To solve the problem, two junctions at different temperatures areused

Tc Th

V2V2

V1

M1

M2M2

E

E(Th)|Tc= V2(Tc, Th)− V1(Tc, Th) → Why?

◮ the function E(Th) is reported in the data sheets, usually forTc = 0 ◦C

◮ what if Tc = T c 6= 0 ◦C?E(Th)|Tc=T c

= E(Th)|Tc=0 − E(T c)|Tc=0


ThermistorsA thermistor is a type of resistor whoseresistance is dependent on temperature.

◮ NTC thermistors. Resistancedecreases as temperature rises.

◮ NTC thermistors. Resistanceincreases as temperature rises.

The relationship between resistance and temperature can beconsidered approximatively linear

R(T ) = R(T 0) + α(T − T 0)Vc

Rn

R(T )R(T )R(T )+Rn

Vc


ThermistorsA thermistor is a type of resistor whoseresistance is dependent on temperature.

◮ NTC thermistors. Resistancedecreases as temperature rises.

◮ NTC thermistors. Resistanceincreases as temperature rises.

The relationship between resistance and temperature can beconsidered approximatively linear

R(T ) = R(T 0) + α(T − T 0)Vc

Rn

R(T )R(T )R(T )+Rn

Vc

Not the same as the “resistance temperature detectors” (RTDs).Look for the differences!


Overview on Temperature Sensors

Thermocouple Thermistor

Pro

◮ Self-excitable

◮ Robust

◮ Cheap

◮ Covers a widerange of temp.

◮ Very sensitive

◮ Fast

◮ Two-wiresmeasurement

Cons

◮ Nonlinear

◮ Low outputvoltage (noiseprone)

◮ TemperatureRef.

◮ Low sensitivity

◮ Nonlinear

◮ Limited range

◮ Current Ref.

◮ Self-heating


Overview on Temperature Sensors

Thermocouple Thermistor

Pro

◮ Self-excitable

◮ Robust

◮ Cheap

◮ Covers a widerange of temp.

◮ Very sensitive

◮ Fast

◮ Two-wiresmeasurement

Cons

◮ Nonlinear

◮ Low outputvoltage (noiseprone)

◮ TemperatureRef.

◮ Low sensitivity

◮ Nonlinear

◮ Limited range

◮ Current Ref.

◮ Self-heatingLook out there and tell us how good and bad are “resistance tem-perature detectors” (RTDs).


Outline



3. Position Sensors

4. Accelerometers


Position Sensors

Provide an electrical signal proportional to the displacement of abody with respect to a reference position

◮ linear displacements: potentiometers

◮ angular displacements: potentiometers, resolvers, syncros, andencoders (digital)


Absolute Encoders

Provides an encoded version of the absolute position.The most used absolute encoder is the optical encoder.

◮ The optical encoder iscomposed by:◮ a disc is made of glass or

plastic with transparentand opaque areas;

◮ a light source;◮ a photo detector array

that reads the opticalpattern that results fromthe disc’s position

Position is encoded via Gray code. Why?


Absolute Encoders and Gray Code

Frank Gray. 13 September1887–23 May 1969. (Belllabs)

◮ In Binary Code, bit switchingmay not take placesimultaneously

◮ this phenomenon may leadto errors in the decodingprocess

◮ This phenomenon cannotoccur with a Gray coding

◮ Adjacent cells differ only byone bit


Incremental Encoder

Output is a pulse signal that is generated when the transducer diskrotates

◮ The (optical) incrementalencoder is composed by:◮ a disc is made of glass or

plastic with three tracksof transparent and opaqueareas;

◮ a light source;◮ a photo detector


Incremental Encoder◮ At each complete rotation, tracks

A and B generate Nr pulses◮ tracks A and B (channels) are in

quadrature. This enables rotationdirection detection;

◮ track Z is used to define thereference position, in case useful.

Typical number of ticks per revolutionNr = 100 ÷ 5000

Resolution of the encoder= 2πNr


Incremental Encoder-Signal Processing Issues

Different approaches to decode

◮ 1X decoding: Trigger on risingeither falling edges of one channel.Nr pulses tour.

◮ 2X decoding: Trigger on risingeither falling edges of both channelsA and B. 2Nr pulses tour.

◮ 4X decoding: Trigger on rising andfalling edges of both channels Aand B. 4Nr pulses tour.

A

B

Z

U/DD Q

clkclk

clear

Simple hardware 1Xdecoding.


Incremental Encoder-4X decoding

Finite-state machine

Ch. A Ch. BState 0 1 1State 1 1 0State 2 0 1State 3 0 0


Speed Estimation

Encoders can be used to estimate angular speed. Differentmethods:◮ Numerical derivative: One step Euler approximation.

θ[k] = θ(kT ) ≈1

T(θ[k]− θ[k])

can be improved by considering finer higher orderapproximations of the derivative. Very noisy!

◮ Filtering: One assumes that

[θ[k]

θ[k]

]

=

[1 T0 1

]

︸︷︷︸

A

[θ[k − 1]

θ[k − 1]

]

︸︷︷︸

x[k−1]

+ v︸︷︷︸

noise

θ[k] =[1 0

]

︸︷︷︸

C

[θ[k]

θ[k]

]

+ w︸︷︷︸

noise

Then a (causal) estimator is designed to reconstruct the missingstate x2 = θ.


Speed Estimation

Encoders can be used to estimate angular speed. Differentmethods:◮ Numerical derivative: One step Euler approximation.

θ[k] = θ(kT ) ≈1

T(θ[k]− θ[k])

can be improved by considering finer higher orderapproximations of the derivative. Very noisy!

◮ Filtering: One assumes that

[θ[k]

θ[k]

]

=

[1 T0 1

]

︸︷︷︸

A

[θ[k − 1]

θ[k − 1]

]

︸︷︷︸

x[k−1]

+ v︸︷︷︸

noise

θ[k] =[1 0

]

︸︷︷︸

C

[θ[k]

θ[k]

]

+ w︸︷︷︸

noise

Then a (causal) estimator is designed to reconstruct the missingstate x2 = θ.

Kalman Filter

x[k] = Ax[k − 1] + L[k]︸︷︷︸

Kalman Gain

(θ(k)− CAx(k − 1))


Outline



3. Position Sensors

4. Accelerometers


Accelerometers

Provide Acceleration measurements based on inertia.

Mechanical energy is converted into an electrical signal. Differenttechnologies:

◮ Piezoelectric: no supply, good linearity, and high bandwidth;◮ piezoresistive : supply is needed, detect static acceleration,

i.e., “gravity”◮ capacitive: large bandwidth, low cost, poor resolution◮ micro electro-mechanical systems. The new Era!


Accelerometers

◮ u body acceleration

◮ x relative position ofthe seismic mass

◮ M mass of theseismic mass

◮ K stiffness

◮ b damping factor

Mu = Mx+Kx+ bx

Assumingum = κy

the transfer function of the sensor is

Um(s)

U(s)= F (s) =

κ

s2 + (b/M)s +K/M


Accelerometers-Frequency Analysis

F (s) =κ

s2 + (b/M)s +K/M ωr =

√

K

M= 2πFr ζ =

b

2

√

1

KM


Homework

Carry out a little research on:Pressure, level detector, and flow sensors.Generate a small report including, principles of operation, type ofoutput signal, circuitry needed to interface with a PLC, the moredetailed the better! Due in two weeks, i.e., October 24.


sensors · 2018. 11. 26. · transducer: changes one form of energy to another measurement chain...

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