Synthetic Sensing: Temperature Sensors and AccelerometersMediaRobotics Lab, February 2010

References:

Fraden: Handbook of Modern SensorsFeynman: Lectures on Physics

Position, velocity, acceleration are related (and can be expressed, in approximation, by Newton's laws of motion)

Velocity is the first derivative (distance over time) and acceleration is the second derivative.

Given noise (and the difficulty of measuring the desired parameters directly), this approach does not help much in practice.

Linear velocity over large distances is often measured via GPS, for example.

Velocities over small distances are measured via a displacement of a moving component (inertial mass) inside a box; one that lags the motion of the box when set into motion. This displacement is then transduced into an electric signal.

One method of measuring displacement is to measure the the voltage created by a magnet moving in a coil (Faraday's law). The voltage is proportional to the velocity of the magnet's motion (provided the coil is divided into two sections and connected in series opposite direction).

Physically, an accelerometer can be modeled as a single-degree-of-freedom device with a reference mass, a spring-like supporting system, a frame and damping properties.

Mf =−kx−b dx /dt

f =d 2 xdt2

−d 2 y dt2

M d 2 xdt2

b dxdt

kx=M d 2 ydt2

The general structure assumes a mass M supported by a spring with stiffness k and damping coefficient b.

Applying Newton's second law ('F = m*a')

Where f is the acceleration of the mass (relative to earth)

Substituting for f gives the characteristic equation (second order differential equation -> oscillating output)

M d 2 xdt2

b dx dt

kx=M d 2 ydt2

x t =∫ g t−tau a taudtau

Using nifty substitutions and the Laplace transform properties, the equation above can be expressed in the time domain as:

When operating in properly designed critically damped mode, the accelerometer should have a flat frequency response range within which accurate measurements are possible

Capacitive accelerometers

A capacitive -acceleration sensor contains two elements: a stationary plate and an inertial mass free to move inside the housing. The elements form a capacitor whose value is a function of the distance d between these elements.

Practical example

analog devices ADXL 103/203 single/dual axis accelerometer

Tilt measurement

One of the most popular applications of the ADXL213 is tilt measurement. An accelerometer uses the force of gravity as an input vector to determine the orientation of an object in space. An accelerometer is most sensitive to tilt when its sensitive axis is perpendicular to the force of gravity (parallel to the earth’s surface). At this orientation, its sensitivity to changes in tilt is highest. When the accelerometer is oriented on axis to gravity, i.e., near its +1 g or –1 g reading, the change in output acceleration per degree of tilt is negligible. Converting Acceleration to Tilt When the accelerometer is oriented so both its X and Y axes are parallel to the earth’s surface, it can be used as a 2-axis tilt sensor with a roll axis and a pitch axis. Once the output signal from the accelerometer has been converted to an acceleration that varies between –1 g and +1 g, the output tilt in degrees is calculated as follows:

PITCH = ASIN(AX/1 g) ROLL = ASIN(AY/1 g)

Apple Iphone Accelerometer

LIS302DL

Apple Iphone Accelerometer

data access in Objective -C

// MainViewController.h// AccelerometerTutorial// Copyright 2009 Paranoid Ferret Productions. All rights reserved.

#import <UIKit/UIKit.h>

@interface MainViewController : UIViewController <UIAccelerometerDelegate> { IBOutlet UILabel *labelX; IBOutlet UILabel *labelY; IBOutlet UILabel *labelZ; IBOutlet UIProgressView *progressX; IBOutlet UIProgressView *progressY; IBOutlet UIProgressView *progressZ; UIAccelerometer *accelerometer;}

@property (nonatomic, retain) IBOutlet UILabel *labelX;@property (nonatomic, retain) IBOutlet UILabel *labelY;@property (nonatomic, retain) IBOutlet UILabel *labelZ;@property (nonatomic, retain) IBOutlet UIProgressView *progressX;@property (nonatomic, retain) IBOutlet UIProgressView *progressY;@property (nonatomic, retain) IBOutlet UIProgressView *progressZ;@property (nonatomic, retain) UIAccelerometer *accelerometer;@end

- (void)viewDidLoad { [super viewDidLoad]; self.accelerometer = [UIAccelerometer sharedAccelerometer]; self.accelerometer.updateInterval = .1; self.accelerometer.delegate = self;}

- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration { labelX.text = [NSString stringWithFormat:@"%@%f", @"X: ", acceleration.x]; labelY.text = [NSString stringWithFormat:@"%@%f", @"Y: ", acceleration.y]; labelZ.text = [NSString stringWithFormat:@"%@%f", @"Z: ", acceleration.z]; self.progressX.progress = ABS(acceleration.x); self.progressY.progress = ABS(acceleration.y); self.progressZ.progress = ABS(acceleration.z);}http://www.switchonthecode.com/tutorials/iphone-tutorial-

reading-the-accelerometer

X: roll around axis from home button to earpiece(0.5 to -0.5)Y: pitch (about the long axis)(0.5 to -0.5)Z: face up – face down(0.5 to -0.5)

Two Iphone apps built around the internal LIS302DL accelerometer.

Temperature Sensors

Taking a temperature measurement requires the transmission of a small portion of an object's thermal energy to the sensor, where it is converted into an electric signal.

Any such sensor, will disturb the measurement site and cause some error in measurement.

Two fundamental modes of sensing temperature: equilibrium and predictive

Equilibrium measurement only complete when there is no (significant) thermal difference between the sensor and the object it measures.Example: thermometer in your mouth.

Predictive measurement is determined by the rate of change of the sensor.

Temperature sensors can also be classified into absolute and relative sensor types. Absolute sensors measure temperature with a fixed reference (0, 25 deg C, etc). Example: thermistor and IC based sensors

Relative type temperature sensors measure the difference between two objects, where one of the objects functions as the reference.Example: thermocouple

Thermal properties are often modeled in analogy to electrical properties. The thermal resistance is inversely related to thermal conductivity, the ability to conduct heat.

From the above diagram one can then write a thermal circuit equation, assuming the energy that flows from the object to the sensor is equal to the energy that outflows from the sensor to the environment.

Tb−Tsr1

=Tb−T0r1r2

Ts=Tb−Tb−T0∗r1r2

=Tb− dT∗r1r2

Where dT is the thermal gradient between object and surroundings.

Including time as a parameter, one can write the following equation

dQ=a1∗Tb−Tsdt

The change in heat energy is equal to the thermal conductivity of the sensor-object interface (a1) multiplied by the temperature difference between the sensor and the object. If the sensor has the specific heat c and the mass m, then the change in heat energy (the absorbed heat) is

dQ=m∗c∗dT

a1∗Tb−Tsdt=m∗c∗dT

From this one can formulate the following first order differential equation:

With the time constant tau defined as: tau=m∗ca1

=m∗c∗r1

The differential equation has this form: dTTb−Ts

= dttau

And this equation has the following solution:

Ts=Tb−dT∗e−t / tau

NTC and PTC thermistors

Thermistors are absolute temperature sensors. They can exhibit either a negative temperature coefficient (NTC) or a positive temperature coefficient (PTC). NTC types are better for precise measurements.

The relationship between temperature and sensor resistance is dependent on numerous parameters and is non-linear. The following polynomial describes the relationship between temperature and the logarithm of a thermistor's resistance

ln R=A0 A1T

A2T 2

A3T 3

Solving for R (assuming the last two terms are negligible)

R=R0∗eb∗ 1

T−

1T0

Where b is a material constant

b=A1B∗T A2T

A3T 2

But beta (b) is not constant, a function of temperature itself ...

Manufacturers of thermistors usually supply data on the sensor in tabulated form:

from the BC2300 datasheet

While you can assume, for the purpose of your assignment, an n-dimensional polynomial to fit the data over a limited range, physics implies an exponential relationship as stated above...

Analog Devices IC temperature sensors

This is a semiconductor sensor that makes use of the fact that p-n junction in a diode and bipolar transistor exhibit strong thermal dependence. If the forward-biased junction is connected to a constant current generator, the resulting voltage becomes a measure of the junction temperature, with a high degree of linearity.

Acoustic temperature sensors

In dry air under normal (atmospheric pressure) the speed of sound is related to the ambient temperature T by the following equation

v≈331.5∗ T273.15

Acoustic temperature sensors are composed of three components:ultrasonic transmitter, ultrasonic receiver, gas filled (sealed) tube

The clock triggers the transmitter and disables the receiver, the piezoelectric crystal flexes and an ultrasonic wave is transmitted through the tube. The receiving crystal is enables and ready for the wave when it arrives. The control circuit calculates the speed of sound by determining the propagation time in the tube, and from that, the corresponding temperature is found