ME 3870

Measurement & Data Analysis

Open Project Lab Report

Lab 2 – Group 2

12/9/16

I. Executive Summary

The group’s objective for this project was to measure the wind speed by creating an

accurate anemometer. From its trials, the group found its anemometer could gather useful data at

lower speeds, but higher speeds would make the system unstable due to design limitations. The

sensor used in the measurement system was an optical sensor, primarily to collect rotational data.

The static calibration was done to develop a relationship between rpm and wind speed in mph.

The static sensitivity was 61.6560 rpm/mph. The total error was 0.5014 mph. The dynamic

calibration was done to further inspect the sensor in terms of how was the data collected, what

type of response was developed, and what factors were affecting its accuracy. It was determined

that the amount of light reflected into the sensor had a major influence in the voltage output, but

it did not affect the dynamic characteristics of the response. The variance in voltage due to

resistance, brightness, and time did not play a significant role in determining the rpm of the

pinwheel. Overall, the anemometer prototype was successful in proving that it is a viable design

to measure wind speed.

II. Introduction

With wind power having such a wide variety of uses and consequences, it is important to

be able to continually characterize its speed. Gathering data on how fast the average wind speed

is can help engineers to design better wind turbines in order to harness the energy, while

knowing when and how often speeds reach dangerously high levels could provide a useful

analysis on how sturdy local structures need to be. With today’s developing technology, wind

energy continues to have a vast amount of untapped potential. However, due to its inherently

random nature, it is difficult to constitute a “one size fits all” system. Knowing this, the group set

out to create a sensor which would aid engineers in their campaign to optimize wind technology.

This was the driving force behind the objective to perform a viable calibration for an optical

sensor when paired with a rotating pinwheel. In doing so, the result would be the ability to take

accurate wind speed measurements through the comparison between speed and rotation.

Throughout the developmental process, the idea behind the team’s trials was if it could discover

how the optical sensor measures data and use that knowledge to create a proper analysis

methodology for it.

Important Equations:

K theoretical=full scale output rangefull scale input range (1)

RPM= 60time difference betweentwo peaks (2)

m=n¿¿ (3)

b=¿¿ (4)

OS=y p 1− y⋈ 1

y⋈1=e

−π ζ 1

√1−ζ 12

(5)

ωd=2 π

2 (t b 1−t p1 ) (6)

ωn 1=ωd 1

√1−ζ 12 (7)

System= 1s2

ωn 12 +

2 ζ1 sωn 1

+1 (8)

Limitations:

Without greater funding and more accurate measuring equipment, there were several

major limitations to the prototype. The pinwheel was assumed to be gyrating in a perfectly

circular fashion, when in fact it would slightly vacillate. This was due to its flexible composition

and loose tolerance in its material. The group tried to limit this effect by adding multiple

cardboard to support it, but error was only lessened, not eliminated. Additionally, the optical

sensor takes 2 seconds to reach steady state, making the collection of useful data a challenge.

The static calibration was done according to the speed on the car dashboard. However, the speed

displayed was not accurate at low velocity. The actual speed could not be kept constant. For this

experiment, it was assumed whatever speed being displayed on the dashboard was the actual

speed.

III. Experimental Materials and Methods

The optical sensor was consisted of a LED and a transistor. The resistance used for LED

was 220 ohms and the resistance for the transistor was 68,000 ohms. Both elements were

provided with 5V through myDAQ, which was connected to the computer for data acquisition

and transmission.

The static calibration was done in car, which had a numerical speed display on the

dashboard to monitor the speed. This experiment was performed in an indoor garage, so that the

effect of wind was minimized. The pinwheel was first held still in the air to measure if there was

any interference in the surroundings that could cause the pinwheel to rotate. Next, the pinwheel

was held out of the window and fixed in one position relative to the car while the car was

moving forward at 2 mph. The data was collected in the Labview for 10 seconds after the car

passed over the initial accelerating stage and reached a steady speed. The data was then imported

into MATLAB for graphing and analyzing. The time difference between two consecutive peaks

was calculated. This value represented the time for the pinwheel to complete one revolution at 2

mph. Considering the uneven force distribution of wind exerted on the pinwheel blades may

cause the pinwheel to have different rotational speed over time, the average value of all time

differences within a range of continuous peaks was calculated. This procedure was repeated for

another 6 times, from 6 mph to 8 mph, in the increment of 1 mph each time.

The design stage uncertainty was assumed to be zero, this would be further explained in the

results and discussion section below. The linearity error was calculated after the relationship

between rpm and mph was approximated with linear least square regression line.

The dynamic calibration was done by sending in a step input to the sensor on two

different light source, a LED flashlight and reflective tape. The LED flashlight represented the

brightest light available, which served as a standard measurement to show the full voltage drop.

The reflective tape was tested in order to show how accurate the static calibration was in terms of

receiving signals. The data was analyzed in MATLAB.

IV. Results and Discussion

According to the static calibration, the static sensitivity was given by two methods. From

Table 1, the theoretical static sensitivity was 60.625 rpm/mph, obtained by Equation 1.

Symbol Description ValueFSO Full scale output range, rpm 0−485FSI Full scale input range, mph 0−8

K theoretical Theoretical sensitivity,rpmmph

60.625

K exp Experimental sensitivity, rpmmph

61.6560

Table 1: Static Calibration

The input range was 0 - 8 mph because that was how far the measurement was decided to

be calibrated. The static calibration at 8 mph was performed for multiple times, and the average

output was calculated to be 485 rpm. From Figure 1, the rpm and mph turned out to have linear

relationship and the function was “rpm = 61.6560 * mph – 25.1740”. The slope of the function

was also defined as the experimental static sensitivity. The two sensitivities were very close to

each other.

Figure 1: Static Calibration

eq Quantization error,mph 0.5em Linearity error,mph 0.0321eb Zero drift error,mph 0.0202uT Total uncertainty, mph 0.5014

Table 2: Error

The linearity error was 0.0321 mph, and zero drift error was 0.202 mph. The quantization

error due the car speed was 0.5 mph because the dashboard had the resolution of 1 mph. The

overall error was 0.5014 mph. The design stage error of the static calibration was assumed to be

zero. The resistor possessed a small amount of uncertainty, however, it could be ignored because

the rpm was calculated using the time difference instead of the actual voltage output. The

variance in voltage drop due resistor uncertainty might change the location of the peak, shifting it

left or right on the time scale a little bit depends on the slope of rising or falling, it was taken care

of by taking the average of all time differences. The time shift within one peak was compensated

by the time shift within the next peak. Further uncertainties regard the voltage will be discussed

below.

Figure 2: Static Calibration DataBased on the static calibration data from figure 2, the longer the sensor stayed on the

reflective tape, the greater but wider peaks were generated. In other words, at the lower speed,

the peaks occurred less frequently but had bigger voltage drop. At first, the voltage drop was

assumed to correlate with the amount of the light being reflected onto the optical sensor.

Therefore, square wave was assumed to be the output wave when the same light source passing

in front of the optical sensor. The peak should immediately drop from 5 volts to its steady-state

voltage, which was dependent on the amount of light reflected, and stayed at that level until the

light source was removed and it should go back to 5 volts theoretically, producing an ideal

square wave. However, as the speed was increasing, the sensor spent less and less time staying

on the reflective tape. The voltage drop was cut off in the middle before reaching its steady-state

value. The result turned out to be a sine wave in this experiment. The effect will be further

explained in the dynamic section below.

Inside the optical sensor, the receiver in the transistor converted the light into an

electrical signal. The brighter the light source was, the higher the collector current was, which

led to a bigger voltage drop according to Ohm’s Law. Since the light source was kept the same,

the error associated with light source mainly came from the unsteady reflection of the infrared

light due the vacillating of the reflective tape. The amount of light reflected back was different

for each rpm, which eventually caused the voltage drop to vary throughout ten seconds while

data was being collected.

Ohm’s law also showed that voltage could also be amplified using a bigger resistance,

given a constant current. At first, the voltage drop was nearly undetectable with 10k ohm through

the transistor. When resistance was increased, a larger voltage drop was observed. In this

experiment, the variance within the current was small enough to allow a bigger resistance

produced a larger voltage drop. As a result, 68k ohm’s was utilized for the transistor.

Figure 3: Dynamic Calibration for LED

Figure 4: Dynamic Calibration for Reflective Tape

Reflective tape and LED flashlight were used in the dynamic calibration. The response

for the optical sensor to detect the light source was illustrated. Based on Figure 3 and 4, the

responses turned out to be second order systems. The maximum overshoot was 0.0695. Damping

ratio was 0.6472, and the natural frequency was 7.6669 rad/s. Bode plots were generated to

compared the frequency response. From Figure 5, the system remained nearly the same towards

two different light sources. There was no difference between the light sources with respect to the

response time. The main difference was the steady-state voltage drop between two light sources

that was proven to be correlated with the amount of light being reflected based on the material.

In other words, the reflective tape used in this experiment would not possibly change the

frequency of the source

being reflected on

the sensor when it

passing through with

certain speed.

Dynamic

calibration showed that it

took sensor 2 seconds to

Static-State Voltage Drop

=2.5110 volts

reach steady state, which was equivalent to 7.5 rpm, given that reflective tape covered about a

quarter of the sensoring area. While the rpm was increasing, the sensor had less and less time

staying in the reflective range, which made the voltage dropped before it could rise to the steady

state. The average voltage drop turned out to be smaller and smaller as the rpm was increasing.

However, each peak was still distinguishable and relatively stable at low rpm, which

corresponded to the speed range from 2 mph to 5 mph. The maximum voltage drop was within

20% of the average drop. At high rpm, a portion of data showed steady voltage drop and the time

difference between two consecutive peaks could be obtained.

Figure 5: Bode plot of second order system

V. Conclusion

The static calibration showed the sensitivity of the measurement was 61.656 rpm/mph,

with total error being 0.5014 mph. The voltage drop was affected by three factors: the brightness

of the light source, the amount of time sensor stayed in the light source and the resistor used for

the transistor. Only the last one could be predefined manually. The error associated with all three

factors were all voltage related. Therefore, they did not play an important role in the time

differences. The dynamic calibration showed that damping ratio was 0.6472 and natural

frequency was 7.6669 rad/s. The amount of light will affect the voltage output, but it did not

change the dynamic characteristics of the sensor, which can pick up the light signal through

reflective tape as fast as it did with strong LED flashlight.

VI. Appendices

Group Members and Responsibilities:

David Roth - Introduction, Experimental Procedure

Yizhou Lu - Executive summary, Results and Discussion

Chien Liu - Results and Discussion, Appendices

Symbol Description Value

FSO Full scale output range,

rpm

0−485

FSI Full scale input range, mph 0−8

K theoretical Theoretical sensitivity,rpmmph

60.625

n Number of data points 8

P Confidential level 0.95

v Probability 0.975

f Degree of freedom 7

t Student t-distribution 1.9616

variable

m Slope, rpmmph

61.6560

b Y-intercept, rpm −25.1740

se Standard deviation of

output,rpm

17.7685

sm Standard deviation of

slope, rpmmph

2.5160

sb Standard deviation of y-

intercept, rpm

12.6739

K exp Experimental sensitivity,

rpmmph

61.6560

K theoretical=FSOFSI

=485 rpm8 mph

=60.625 rpmmph

v=0.5∗(1+P )=0.5∗(1+0.95 )=0.975

f =n−1=7

m=n¿¿

b=¿¿

se=√∑i=1

n

(m x i+b− y i)2

n−2 =17.7685rpm

sm=√ n se2

n¿¿¿

sb=√se2¿¿¿

K exp=m=61.6560 rpmmph

ri Input range,mph 8

eq Quantization error,mph 0.5

em Linearity error,mph 0.0321

eb Zero drift error,mph 0.0202

uT Total uncertainty, mph 0.5014

eq=ucar=0.5 mph

em=t sm r i

m √n=0.0321 mph

eb=t sb

m√n=0.0202mph

uT=√eq2+em

2 +eb2=0.5014 mph

Symbol Description Value

y⋈ 1 Amplitude at t⋈1, volt 4.693

y p1 1stPeak Amplitude at

t p 1=2.275 s, volt

5.019

yc 1 1stConcave Amplitude at

t b 1=2.8125 s, volt

4.613

OS Overshoot 0.0695

ωd1 Damped natural frequency,

rads

5.8448

ζ 1 Damping ratio 0.6472

ωn 1 Natural frequency,rad

s7.6669

OS=y p 1− y⋈1

y⋈1=0.0695

ωd 1=2 π

2(t b 1−t p 1)=5.8448 rad

s

OS=e−π ζ 1

√1−ζ 12

=0.0695⟹ ζ 1=0.6472 rads

ωn 1=ωd 1

√1−ζ 12=7.6669 rad

s

System= 1s2

ωn 12 +

2 ζ 1 sωn 1

+1

Symbol Description Value

y⋈ 2 Amplitude at t⋈1, volt 4.673

y p2 1stPeak Amplitude at

t p 1=4.638 s, volt

4.894

yc 2 1stConcave Amplitude at

t b 1=5.287 s, volt

4.543

OS Overshoot 0.0473

ωd 2 Damped natural frequency,

rads

4.8407

ζ 2 Damping ratio 0.6967

ωn 2 Natural frequency,rad

s6.7482

OS=y p 2− y⋈ 2

y⋈2=0.0473

ωd 2=2 π

2(t b 2−t p2)=4.8407 rad

s

OS=e−π ζ 2

√1−ζ 22

=0.0473⟹ ζ 2=0.6967 rads

ωn 2=ωd 2

√1−ζ 22=6.7482 rad

s

System= 1s2

ωn 22 +

2 ζ2 sωn 2

+1

Matlab Code: %% static calibrationclcclearclose speed=[0,2:1:8];for i=2:length(speed)-1 file=strcat(num2str(speed(i)),'.lvm'); Data(:,:,i-1)=load(file); figure (1) subplot(4,2,i-1) plot(Data(:,1,i-1),Data(:,2,i-1))endData8=load('8.lvm');figure (1)subplot(4,2,7)plot(Data8(:,1),Data8(:,2))suptitle('Static Calibration Data')avg(1)=0;time2=[0.5, 1.15, 1.85, 2.55, 3.225, 4, 4.925, 5.85, 6.65, 7.35, 8.025, 8.775, 9.75];for i=1:length(time2)-1 timed2(i)=time2(i+1)-time2(i);end avg(2)=sum(timed2)/(length(time2)-1);time3=[0.4, 0.8, 1.225, 1.6, 2.025, 2.425, 2.85, 3.275, 3.675, 4.025, 4.375, 4.8, 5.225, 5.675, 6.125, 6.525, 6.9, 7.325, 7.675, 8.05, 8.4, 8.775, 9.2, 9.6]; for i=1:length(time3)-1 timed3(i)=time3(i+1)-time3(i);endavg(3)=sum(timed3)/(length(time3)-1);time4=[0.1125, 0.4, 0.6625, 0.9, 1.163, 1.425, 1.675, 1.95, 2.212, 2.475, 2.737, 3, 3.275, 3.525, 3.737, 4.025, 4.275, 4.563, 4.838];for i=1:length(time4)-1 timed4(i)=time4(i+1)-time4(i);endavg(4)=sum(timed4)/(length(time4)-1);time5=[0.125, 0.4, 0.6375, 0.8875, 1.163, 1.425, 1.688, 1.962, 2.225, 2.513];for i=1:length(time5)-1 timed5(i)=time5(i+1)-time5(i);endavg(5)=sum(timed5)/(length(time5)-1);avg(5)=0.2222;time6=[2.375, 2.55, 2.712, 2.913, 3.087, 3.288, 3.462];for i=1:length(time6)-1 timed6(i)=time6(i+1)-time6(i);endavg(6)=sum(timed6)/(length(time6)-1);time7=[2.862, 3, 3.15, 3.3, 3.45, 3.587];for i=1:length(time7)-1 timed7(i)=time7(i+1)-time7(i);endavg(7)=sum(timed7)/(length(time7)-1);

time8=[1.581, 1.7, 1.844, 1.994, 2.119, 2.244, 2.525, 2.369, 2.525, 2.65, 2.794, 2.919, 3.065];for i=1:length(time8)-1 timed8(i)=time8(i+1)-time8(i);endavg(8)=sum(timed8)/(length(time8)-1);rpm(1)=0;for i=2:length(avg) rpm(i)=60/avg(i); endfigure (2)plot(speed,rpm)hold on[m, b, sdm, sdb, R2]=llsr(speed,rpm);for i=1:length(speed) y(i)=m*speed(i)+b;endplot(speed,y)hold offtitle('Static Calibration')legend('raw data','linear least square regression')xlabel('wind speed, mph')ylabel('rotational speed, rpm')P=0.95;v=0.5*(1+P);n=length(Data);f=n-1;t=tinv(v,f);ri=8;% linearity errore_m=t*sdm*ri/(m*sqrt(n));e_b=t*sdb/(m*sqrt(n));e_q=0.5;u=sqrt(e_q^2+e_m^2+e_b^2);% dynamic calibration  syms xData=load('dynamic1.lvm');figure (1)plot(Data(:,1),Data(:,2))title('Dynamic Calibration for LED')xlabel('Time, s')ylabel('Voltage, volt')start_y=0.04164;start_t=1.5;ss=4.693;os_y=5.019;os_t=2.275;bs_y=4.613;bs_t=2.8125;os=(os_y-ss)/ssT=(bs_t-os_t)*2wd=2*pi/T%zeta=0.6471;y=solve(exp(-pi*x/sqrt(1-x^2))==os,x);zeta=double(subs(y(1)))wn=wd/sqrt(1-zeta^2)s=tf('s');

sys=1/(s^2/wn^2+2*zeta*s/wn+1); Data2=load('dynamic2.lvm');figure (2)plot(Data2(:,1),Data2(:,2))title('Dynamic Calibration for Reflective Tape')xlabel('Time, s')ylabel('Voltage, volt')start_y2=2.162;start_t2=3.862;ss2=4.673;os_y2=4.894;os_t2=4.638;bs_y2=4.543;bs_t2=5.287;os2=(os_y2-ss2)/ss2T2=(bs_t2-os_t2)*2wd2=2*pi/T2%zeta2=0.6967;y=solve(exp(-pi*x/sqrt(1-x^2))==os2,x);zeta2=double(subs(y(1)))wn2=wd2/sqrt(1-zeta2^2)s=tf('s')sys2=1/(s^2/wn2^2+2*zeta2*s/wn2+1); figure (3)bode(sys)hold onbode(sys2)legend('flashlight','reflective tape')