Throttle data

1. Page 7. Shigeoka MS thesis-capture (store) 3/4 data throttle acceleration data in Matlab

avec

tvec

delta

plot(avec,tvec)

integrate to get vvec

integrate to get xvec

MATLAB CODE

delt= 0.001;

t=[0:0.001:0.8] % 801 points

a=[2.001 2.008 2.016 2.022 2.028 2.035 2.041 2.075 2.086 2.095 2.101 2.109 2.206 2.305 2.404 2.506 3.003 3.012......

3.026 3.036 3.044 3.052 3.061 3.076 3.083 3.099 3.106 3.205 3.320 3.460 3.520 3.620 3.760 3.809 3.999 4.009 4.018 4.065.......

4.098 4.223 4.451 4.852 4.876 4.898 4.903 4.926 4.998 5.003 5.016 5.026 5.046 5.086 5.120 5.223 5.445 5.652 .......

5.785 5.785 5.652 5.543 5.431 5.321 5.211 5.101 5.009 4.456 4.362 4.121 4.002 3.678 3.654 3.541 3.210 3.001 2.987 2.951 ........

2.765 2.542 2.321 2.123 2.002 1.998 1.956 1.845 1.122 1.026 1.001 0.998 0.956 0.945 0.932 0.921 0.910 0.887...

2.1 2.01 2.001 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.333 2.345 2.366...

2.37 2.38 2.39 2.40 2.44 2.45 2.46 2.47 2.48 2.49 2.6 2.7 2.8 2.9 3.0 3.001 3.002 3.01 3.02 3.003...

2.999 2.98 2.987 2.900 2.80 2.7 2.6 2.5 2.4 2.3 2.2 0 0.9 0.8 0.7 0.8 -1 -1.1 -1.111 -1.2...

-1.22 -1.23 -1.24 -1.25 -1 .9 -.8 .7 .5 .4 .3 .2 0 0 0.1 0.2 0.3 0.444 0.45 0.46...

0.47 0.48 0.49 0.50 0.51 0.53 0.54 0.55 0.56 .7 .81 .8 .9 .99 1 0.6 0.5 0.4 0.33 0.2222 0.1...

0 0.1 0.112 0.52 0.789 0.89 0.900 0.912 0.913 1.00 1.2 1.11 1.23 1.4 1.32 1.5 1.55 1.56 1.57...

1.58 2.5 1.543 1.2 1.1 1.0 1.01 .99 0.823 0.7 0.4 0.3 0.2 0.1 -.9 -.8 -.803 -.805 -.0800 -.79...

0.15 .3 .45 .6 .9 1.25 1.5 1.8 2.3 2.5 2.8 3.0 3.1 3.11 3.12 3.13 3.2 3.3 3.44 3.5 3.6...

3.6 3.5 3.3 2.9 2.8 2.7 2.6 2.59 2.58 2.3 2 1.9 1.4 1.2 1 -.9 -.8 -.5 -.51 -.50...

-.50 -.50 -.52 -.4 -.2 -.1 0 1 1.1 1.2 1.3 1.4 1.5 1.6 2 2.1 2.5 3 3.4 3.5 3.6...

3.6 3.7 3.8 3.9 4 4.1 4.11 4.12 4.13 4.14 4.2 4.23 4.4 4.5 4.6 4.7 4.8 4.9 4.9 4.9...

4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.7 3.7 3.7 3.7 3.8 3.8 3.8...

3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3 2.8 2.6 2.4 2.2 2 1.5 1.2 1 .5 0 -.9 -.8 -.8 -.8...

-.8 -.7 -.5 -.4 -.32 -.2 0 .1 .12 .13 .14 .15 .16 2.0 2.1 2.2 2.44 2.24 2.5 2.5...

2.5 2.44 2.43 2.42 2.40 2.41 2.40 2.39 2.38 2.37 2.36 2.365 2.34 2.33 2.22 2.21 2.2 2.2...

2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.7 0.6 0.5 0.4 0.3 0.2...

0.2 0.2 0.2 0.3 0.4 0.8 1 1.2 1.3 1.5 1.8 2.0 2.1 2.2 2.4 2.5 2.6 3.0 3.1 3.2...

3.2 3.2 3.3 4 4.0 4.0 4.0 3.9 3.8 3.7 3.6 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5...

2.5 2.5 2.5 2.1 2.0 1.9 1.8 1.7 1.8 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6...

0.5 0.4 0.3 0.2 0.1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0 -.9 -.8 .7 -.6 -.6 -.6 -.6 -.5...

-.5 -.4 -.3 -.2 -.1 -.9-.8 0 1 1.1 1.2 1.3 1.4 1.5 1.66 1.77 1.8 1.82 1.8 1.9 1.9...

1.9 1.98 1.96 1.95 1.94 .193 1.92 1.90 1.89 1.88 1.76 1.4 1.33 1.22 1.21 1.20 1.1...

1.1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 3 3.2 3.5 3.6 3.7 3.7 3.7 3.7...

3.7 3.8 3.8 3.7 3.66 3.55 3.54 3.53 3.52 3.51 3.5 3.4 3.3 3.22 3.21 3.20 3.15 3.1...

3.0 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0...

-.5 -.4 -.3 -.2 -.1 -.9-.8 0 1 1.1 1.2 1.3 1.4 1.5 1.66 1.77 1.8 1.82 1.8 1.9 1.9...

1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.4 3.5 3.6 3.7 3.8 3.9 4.0...

4.0 4.0 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.4 2.3 2.2 2.1...

2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1...

0.9 0.8 0 -.1 -.2 -.3 -.5 -.5 -.5 -.5 -.4 -.2 -.1 0 0 0 0 0.9 1 1.1 1.2 1.3...

1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.11 1.1 1 0.9 0.8 0.7 0.6 0.5 .4 .3 .2 0.1 0.1...

-.1 -.5 -.6 -.7 -.8 -.9 -1 -2 -2 -2 - -1 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.7...

1.7 1.8 1.8 1.9 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.9 2 2.1 2.22 2.3 2.4...

2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.33 3.4 3.5 3.6 3.7 4.0 4.0 4.0 4.0 3.9 3.9...

3.9 3.8 3.7 3.6 3.55 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.3]% 801 points

V=delt*cumtrapz(a); % V is the velocity of the data

d=delt*cumtrapz(V);% d is displacement of the data

plot(t,a,t,V,t,d)

xlabel('Time (seconds)','fontsize',12,'fontweight','b','color','r');

ylabel('Acceleration (m/s^2), Velocity (m/s), Displacement (m)','fontsize',12,'fontweight','b','color','r');

hleg1 = legend('Acceleration','Velocity','Displacement');

title ('Filtered Acceleration Data for 3/4 or max throttle')

%delt=0.001

V=delt*cumtrapz(a); % V is the velocity of the data

d=delt*cumtrapz(V);% d is displacement of the data

plot(t,a)

xlabel('Time (seconds)','fontsize',12,'fontweight','b','color','r');

ylabel('Acceleration (m/s^2)','fontsize',12,'fontweight','b','color','r');

hleg1 = legend('Acceleration');

title ('Filtered Acceleration Data for 3/4 or max throttle')

plot(t,V)

xlabel('Time (seconds)','fontsize',12,'fontweight','b','color','r');

ylabel('Velocity (m/s)','fontsize',12,'fontweight','b','color','r');

hleg1 = legend('Velocity');

title ('Filtered Velocity Data for 3/4 or max throttle')

plot(t,d)

xlabel('Time (seconds)','fontsize',12,'fontweight','b','color','r');

ylabel('Position (m)','fontsize',12,'fontweight','b','color','r');

hleg1 = legend('Displacement');

title ('Filtered Position Data for 3/4 or max throttle')

Z = TRAPZ(t,a)% Integrate to get vvec

D = TRAPZ(Z)% Integrate to get xvec

%TRAPZ Trapezoidal numerical integration.

%Z = TRAPZ(X,Y) computes the integral of Y with respect to X using

%the trapezoidal method. X and Y must be vectors of the same

%length, or X must be a column vector and Y an array whose first

%non-singleton dimension is length(X). TRAPZ operates along this

%dimension.

_________________________________________________________________

Z =

1.1540

D =

Z =

1.1540

D =

Z =

1.1540

D =

Z =

1.1540

D =

Z =

1.1540

D =

Z =

1.1540

D =

2. Pass acceleration vector through a LPF

H(s) = d/ s+d

d=large (no filter)

d=pi

d small- lots of low pass filter

d large- little low pass filtering

MATLAB CODE:

a=[ 2 2.1 2.5 3 5 4 3.9 1.9 1.2 1.8 2.5 -1.8 1.5 1.3 1.1...

2 4.4 2.3 2.2 1.9 1.8 .5 1 .5 .1 1.9 3 1 -.9 -1.3 .3 .5 1.9 3.9 3 3.2 3.5 -1.5...

1.7 2 1.9 1 2 0.1 -.1 .5 2 3.9 3 2.5 1 -1.5 0 1.5 1 .5 1.7 2 1 0 -1 1 2 4 2 1 0 0.3...

0.5 0.2 0.1 2 1 0 -1.5 0 1 2 4 2 1.8 ]; %81 points

t=[ 0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 .12...

.13 .14 .15 .16 .17 .18 .19 .2 .21 .22 .23 .24 .25 .26 .27 .28 .29 .3 .31 .32 .33 .34 .35...

.36 .37 .38 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50 .51 .52 .53 .54 .55...

.56 .57 .58 .59 .60 .61 .62 .63 .64 .65 .66 .67 .68 .69 .70 .71 .72 .73 .74 .75 .76 .77...

.78 .79 .80]; %81 points

num= pi % a= pi given on page 22

den=[1 pi] % denominator of the trasfer function

sys=tf (num,den)

[y,t] = lsim(sys,a,t)

plot(t,y)

xlabel('Time (seconds)','fontsize',12,'fontweight','b','color','r');

ylabel('filtered acceleration (m)','fontsize',12,'fontweight','b','color','r');

hleg1 = legend('Displacement');

title ('Filtered Position Data for 3/4 or max throttle')

grid on

cutoff frequency of 40Hz

Flapping Frequency = 5.6 Hz

[KSS. pg 11] n = the number of components = 10

num= pi % a= pi given on page 22

den=[1 pi] % denominator of the trasfer function

sys=tf (num,den)

bode(sys)

Youtube :

Simulink / Matlab Video Tutorial and Example - Low Pass Filter - Bode Plots (Part 2)

Youtube- Simulink Low pass filter

http://www.youtube.com/watch?v=oDqTg3gweuw

the simplest lowpass filter

https://ccrma.stanford.edu/~jos/filters/Matlab_Filter_Implementation.html

% simplpm1.m - matlab main program implementing % the simplest lowpass filter: % % y(n) = x(n)+x(n-1)} N=10; % length of test input signal x = 1:N; % test input signal (integer ramp) B = [1,1]; % transfer function numerator A = 1; % transfer function denominator y = filter(B,A,x); for i=1:N disp(sprintf('x(%d)=%f\ty(%d)=%f',i,x(i),i,y(i))); end

Matlab code to construct and apply a low-pass filter to acceleration data

http://nees.org/resources/474/download/Using_MATLAB_to_Analyze_Data_Stored_On_NEEScentral.pdf