Things about the future of maybeline newyork

1. 1
Sensors Characteristics

2. 2
A. Static conditions 0
,
0 

dt
dy
dt
dx
B. Dynamic conditions )
(
))
(
(
0
t
x
dt
t
y
d
a
k
k
k 




3. 3
A.1 Static characteristics
)
(x
f
y 
Sensors
x
y
Ko
x
K
y 

 K - scaling factor in linear systems
)
(x
f - polynomial, exponential, logarithmic function
or experimental determination
)
(x
f -result from modeling of the system (sensor)
-univocal process

4. 4
A.1 Static characteristic
A.2 Invers characteristic (function)
Sensors
x
y
- Perturbative parameters like: humidity, temperature, altitude, ….
i

)
,..
,
( 1 n
x
f
y 


i

F = f -1
Sensors
x
y
f
F
]
[
);
1
(
])
[
( 0
0




 T
R
C
T
R 
]
[
;
)
(
])
[
( 0
0
0 C
R
R
R
R
T





f:
F:

5. 5
]
[
]);
[
],
[
( 1 Hz
C
T
mm
x
f
y o


F = f -1
 
25
02
.
0
1000
1000
0106
.
0
]
[ 1
2
0
2













 
y
y
mm
x
])
[
(
1 
 R


A.1 Static characteristic of complex sensors-Vibrating Wire Jointmeter
A.2 Invers characteristic (function) Vibrating Wire Jointmeter

6. 6
Static conditions
A.1, A.2 e.g.
A.1 Thermistor 1k A.2
A.1 Characteristic processing, linearization
   
   















max
max
max
max
min
1
min
1
2
1
2
1
1
;
;
,
,
:
...
;
;
,
,
:
y
y
x
x
y
y
x
x
y
y
x
x
y
y
x
x
n
n
n
n
n
]
,
[
]
,
[
: max
min
max
min y
y
x
x 

0
)
(
)
,
( 



 y
x
y
E
Approximation function of
experimental data

7. 7
Static conditions, example
A.1 GP2Y0A02YK0F A.2
]
55
.
1
8
.
2
[ 

out
V
]
8
.
0
55
.
1
( 

out
V
]
45
.
0
8
.
0
( 

out
V
Γ2(Vout)= 119.22 - 52.40 ∙ Vout;
Γ1(Vout)=71.31-20.36∙ Vout ;
Γ3(Vout)= 223.88-183.19∙ Vout

8. 8
Static conditions
A.1, A.2 e.g. GP2Y0A02YK0F
L
L
E C
C
C 
 3
,
2
,
1
L _ BSLF - Best Straight Line Fit
-Mathematical determination
- Software consideration (Curve expert)

9. 9
Static conditions
A.3 Full Scale input range
Out of range - recalibration, saturate,
- new calibration function
A.4 Full Scale output range
[xmin…xmax]
GP2Y0A02YK0F
)
(x
f
y 
)
(x
f
y  ]
[ max
min y
y
y 

]
45
.
0
8
.
2
[ 

out
V
GP2Y0A02YK0F
cm
L ]
150
15
[ 

ymin  0 for xmin = 0, and: ymin = 0 when xmin  0.
x
y f1
f2
f3
f4
X min X max
Y min
y max

10. 10
Static conditions
A.5 Sensitivity
Relative sensitivity
1
2
1
2
x
x
y
y
S



min
max
min
max
x
x
y
y
S


 Linear system, K=S
If “K” is higher is better,
but the range is lower.
i
i
x
x
dx
dy
S

 Non-linear system
n
x
m
y
II 

 2
:
order x
m
dx
dy
S 


 2











[x]
%
;
2
1
m
dx
dy
x
x
S
X

]
[
);
1
(
])
[
(
:
order 0
0




 T
R
C
T
R
I  


 0
R
dT
dR
S 




 
C
0

11. 11
Static conditions
A.5 Sensitivity with external parameters
A.6 Resolution
- sensorial systems with digital unit
- depend by of ADC’s number of bits
)
,..
,
( 1 n
x
f
y 

  







i
i
f
x
x
f
y 
 i
f



- Parasitic sensitivity
T
K
l
K
T
S
l
l
T
S
T
S
l
R 






























 '
)
1
(
1
)
1
( 0
0
0
0 





   
C
K
m
K 



12. 12
Static conditions
A.5 Error-Accuracy
- function approximation,
- Noise,
- Improper device,…
;
,
x x
X
X 



 
 x
X 

 X estimation of x - true value
100
[%]
or
100
[%] 





x
x
X
x
x
X

 ;
0

x
[%]
100




x
X
R
   ];
[
10
then,
10 6
%
6
% ppm
if ppm 

 




13. 13
Static conditions
A.5.1 Offset Error
y’= f’(x)= f(x)+εoff
A.5.2 Gain Error
y = f(x) linear system
off
x
f 

 )
0
(
' )
0
(
'
)
( 


 x
f
x
f
y off

ideal
min
max
min
max
x
x
y
k
y



real
min
max
min
max '
'
'
x
x
y
k
y


 k
r
y
r
y
C
C
x
x
y
x
x
y
k 







min
max
min
max
min
max
min
max
)
'
'
(
'
, true

14. 14
Static conditions
A.5.3 Non-linear Error
-Caused by approximation
A.5.6 Repeatability Error
..
3
3
2
2
)
(
1
0
)
(
1
0
0
)
(
x
k
x
k
x
g
x
k
k
x
g
x
k
k
i
i
x
i
k
x
f















[%]
100


 R
R



15. 15
Problemes
A given sensor has a specified linearity error of 1 % of the
reading plus 0.1 % of the full-scale output (FSO). A second
sensor having the same measurement range has a specified
error of 0.5 % of the reading plus 0.2 % FSO. For what range
of values is the first sensor more accurate than the second
one? If the second sensor had a measurement range twice
that of the first one, for what range of values would it be the
more accurate?

16. 16
Dinamic conditions
)
(
))
(
(
0
t
x
dt
t
y
d
a
k
k
k 



 
pol
s
a
s
a
s
a
s
X
s
Y
s
H
s
X
s
Y
a
s
a
s
a
t
y
a
dt
t
y
d
a
dt
t
y
d
a
L
k
k
k
k
k
k

























,
j
s
;
...
1
)
(
)
(
)
(
)
(
)
(
...
)
(
))
(
(
...
))
(
(
0
1
0
1
1
1
1


Exponential Growth
Oscilation
Damped oscillator
Over Damped

17. 17
Dynamic conditions
 Potentiometer
 Thermistor
)
(
)
( 0 t
x
a
t
y 

)
(
)
(
))
(
(
0
1 t
x
t
y
a
dt
t
y
d
a 



y
sensitivit
static
1
constant,
time
1
)
(
)
(
)
(
)
(
1
)
(
))
(
(
0
0
1
0
0
1
a
k
a
a
s
k
s
X
s
Y
s
H
t
x
a
t
y
dt
t
y
d
a
a












),
(
1
)
( s
X
s
k
s
Y 













 1
1
1
)
(
s
k
s
k
s
s
k
s
Y  
)
(
)
( 1
s
Y
L
t
y 

)
1
(
)
( 
t
e
k
t
y




signal
step
unit
/
1
))
(
(
)
( s
t
x
L
s
X
if 

zero order
firs order

18. 18
Dynamic conditions
Rising time ( tC )
Response time (tt)
Signal rise
(εM)
)
(
)
(
))
(
(
))
(
(
0
1
2
2
2 t
x
t
y
a
dt
t
y
d
a
dt
t
y
d
a 




 second order

19. 19
LM92 temperature sensor

20. 20
KTY81

21. 21
GP2Y0A02YK0F

22. 22
MPX53

23. 23
S18U