Introduction to Modeling

Define the terms System Surroundings Input/output Transducer

Distinguish between sensors and actuators For a given transducer, identify the

appropriate inputs and outputs For a given transducer, find find/calculate

span, full scale output, sensitivity, accuracy, and resolution

Distinguish between static and dynamic response characteristics of transducers

For a given transducer, find find/calculate

response time, overshoot, gain, and phaseshift, and

Explain the concept of resonance

Some definitions

System:Region of space set aside for analysis

Boundary:Defines a system such that everything within it is the system

Surroundings:Everything outside the system

Interactions between the system and surroundings:• Inputs from surroundings to the system• Outputs from system to the

surroundings.

boundary

system

surroundings“Stuff” can be a physical quantity (p. ej., masa, energía) or something more abstract (p. ej, information, a signal, or a reading)

Levels of modeling

An automotive airbag system

A block diagram

Levels of modeling

Levels of modeling

Levels of modeling

This is the “MEMS” you would buy.

Levels of modeling

This is the “MEMS” you would buy.

MEMSsensor

This is the “MEMS” we usually model.

Levels of modeling

MEMSsensor

This is the “MEMS” we usually model.

• How many inputs/outputs are there?

• What are the inputs? • What are the outputs?

• What is the relationship between the inputs and the outputs?

• What do we need to know about what is inside the “black box” in order to find those relationships?

Transducers

Most MEMS are transducers.

Sensors

• Input is some physical quantity whose value we wish to know (p. ej., temperatura)

• Output is some other physical quantity (p. ej., voltage) whose value correlates to the measurand

Sensors measure something

Actuators

• Input is usually a voltage or some other electrical signal

• Output is physical motion of some kind

Actuators move something

Sensor or actuator?

Thermometer

Input

Output

Thermocouple

Input

Output

Sensor or actuator?

Bimetallic micro-valve

Input

Output

(http://www.konicaminolta.com)

Ink jet print head

Input

Output

Sensor or actuator?

Digital micromirror device

Input

Output

Capacitive accelerometer

Input

Output

Sensor or actuator?

Comb drive

Input

Output

“Micro-reactor” microfluidic device

Input

Output

Loading

The act of measuring alters the thing we’re trying to measure

loading

Power input to transducers

Many sensors require a voltage supply as a second input to provide power for signal conditioning—circuits that help convert the output signal to a form useful for the application

Sensors and actuators require different amounts of input power. Sensors are low input-power devices; actuators are high-input-power

devices

Power input Converted into the actuation outputControl input Tells the system what to do

Transducer characteristics

Static response characteristicsSpan (or full scale input)Range of input values over which a transducer produces output values with acceptable accuracy

UnitsSame as input. (p. ej., Pa for a pressure sensor)

Full-scale output (FSO)Range of output values corresponding tothe span.

UnitsSame as output (p. ej., V for a pressure sensor)

For an actuator? μm

Transducer characteristics

Static response characteristicsSensitivity Constant of proportionality between output and input for a linear transducer.

Slope of the best-fit line.

UnitsOutput units/input units.

Accuracy How close the transducer output is to

• (sensor) true value of the measurand, or• (actuator) the desired output effect.

Accuracy is determined by a calibration procedure

Transducer characteristics

Static response characteristics

Resolution

• (sensor) smallest detectable change in the measurand

Unitsunits of the measurand

• (actuator)smallest change in output that can effected by changing the input

Unitsunits of the output effect(e.g., μm for displacement)

Te toca a ti

For the PX26-001DV model differential pressure transducer:

1. What is the measurand?2. What is the span?3. What is the full-scale output?4. Determine the system sensitivity. 5. Can this transducer be used to measure ΔP, for P1 = 25 psi and P2 = 24.5 psi?

Explain your answer.

Dynamic versus static response

MEMSTransducer

Steady input Steady output

Time varying input

Time varying output

Static response

Dynamic response

Step input Sinusoidal input

Time

Time

Response to step input

MEMSTransducer

Response timeTime required for output to reach new steady state value

OvershootAmount the initial response exceeds the desired value

TimeTime

or

Response to sinusoidal input

MEMSTransducer

Time Time

y(t)

Amplitude ratio (or gain)Ratio of the output amplitude to the input amplitude• Usually reported in decibels (dB)• dB = 20log(gain). Can change as a function of the input frequency

Can be magnified at some frequencies and attenuated (reduced) at others.

FrequencyAmplitudePhase

Same as frequency larger, smaller, or the same In or out phase

Response to sinusoidal input

Resonance Large magnification at certain frequencies and not others

Phase shift• Amount of by which an output

sine wave is “misaligned” with the input

• Usually reported as phase angle φ = ωt

resonance frequenciesin phase out of phase

Response to sinusoidal input

(not time)

Show

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ain

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Bode plot

Volunatarios para temas

1. Resistive sensing Piezoresistive sensing Magnetoresistive sensing Thermo-resistive sensing ______________________

2. Capacitive sensing Piezoelectric sensing ______________________

3. Resonant sensing Variable-frequency resonator Variable-amplitude resonator ______________________

4. Thermoelectric sensing Thermo-electric cooling ______________________

5. Magnetic sensing

Reluctance sensing Inductive sensing ______________________

6. Capacitive actuation Piezoelectric actuation ______________________

7. Thermo-mechanical actuation Bimetallic actuation Thermopneumatic actuation Shape memory alloy actuation Hot arm actuation ______________________

8. Magnetic actuation Magnetostrictive actuation ______________________