Thermal print head temperature estimation system
View Patent ↗A method estimates the temperature of a thermal print head element during printing. In one embodiment, the temperature is estimated using the resistance of the thermal print head element, which typically changes with the print head element temperature. The change in resistance of the print head element is exploited to indirectly estimate the temperature of the print head element.
1. A computer-implemented method for identifying an estimate {circumflex over (ƒ)}(·) of a function T h =ƒ(R h ) relating resistance R h of a thermal print head element in a thermal print head of a thermal printer to temperature T h of the thermal print head element, the method comprising:
(A) selecting a plurality N of initial temperatures T si ;
(B) heating an insulated chamber containing the thermal print head to the plurality of initial temperatures T si ;
(C) providing the thermal print head element with a plurality N of input powers P i ;
(D) measuring a plurality N of resistances R hi resulting from application of the plurality of input powers P i ; and
(E) identifying the estimate {circumflex over (ƒ)}(·) based on the plurality of initial temperatures T si , the plurality of resistances R hi , and the plurality of input powers P i .
2. The method of claim 1 , further comprising:
(F) identifying a resistance R h of the thermal print head element; and
(G) using the estimate {circumflex over (ƒ)}(·) to predict a temperature T h of the thermal print head element based on the resistance R h .
3. The method of claim 2 , wherein each of the plurality of initial temperatures T si falls within a temperature range, and wherein the predicted temperature T h falls outside of the temperature range.
4. The method of claim 3 , wherein the thermal print head has a maximum permissible temperature, and wherein the predicted temperature T h is higher than the maximum permissible temperature.
5. The method of claim 1 , wherein (E) comprises identifying the estimate {circumflex over (ƒ)}(·) based on a model of change in the temperature T h of the thermal print head element in response of application of input power P to the thermal print head element.
6. The method of claim 5 , wherein the model relates the thermal print head element temperature T h to a heat sink temperature T s and input power P by the equation T h =T s +AP for a given value of A.
7. The method of claim 6 , wherein (E) comprises identifying the estimate {circumflex over (ƒ)}(·) and an estimate  of the parameter A using the equation:
[
f
^
(
·
)
,
A
^
]
=
arg
min
f
(
·
)
,
A
∑
i
1
σ
i
2
(
f
(
R
hi
)
-
T
si
-
AP
i
)
2
,
wherein σ i is a standard deviation of noise on the print head element temperature T h arising from noise in the measurement triplet {R hi ,T si ,P i }.
8. The method of claim 7 , wherein (E) comprises identifying an estimate {circumflex over (x)} of coefficients
x
=
[
x
p
⋮
x
0
]
of a polynomial representation ƒ(R)=x p R h p +x p−1 R h p−1 +. . . +x 0 , of the function ƒ(·), using the equation:
[
x
^
A
^
]
=
(
D
T
WD
)
-
1
D
T
WT
s
,
wherein
T
s
=
[
T
s
1
⋮
T
sN
]
,
W
=
[
1
/
σ
1
2
⋰
1
/
σ
N
2
]
,
D
=
[
R
h
p
-
P
]
,
R
h
p
=
[
R
h
1
p
…
1
⋮
⋮
R
hN
p
…
1
]
,
P
=
[
P
1
⋮
P
N
]
,
and σ i is a standard deviation of noise on the print head element temperature T h arising from noise in the measurement triplet {R hi ,T si ,P i }.
9. The method of claim 6 , wherein (E) comprises identifying the estimate {circumflex over (ƒ)}(·) and an estimate  of the parameter A using the equation:
[
f
^
(
·
)
,
A
^
]
=
arg
min
f
(
·
)
,
A
∑
i
1
f
′
(
R
hi
)
2
(
f
(
R
hi
)
-
T
si
-
AP
i
)
2
,
wherein ƒ′(·) is the first derivative of ƒ(·).
10. The method of claim 9 , wherein (E) comprises identifying an estimate {circumflex over (x)} of coefficients
x
=
[
x
p
⋮
x
0
]
of a model of the function ƒ(·) by:
(E) (1) producing a current estimate of {circumflex over (ƒ)}′(·);
(E) (2) computing a weight matrix
W
=
[
1
/
f
^
′
(
R
h
1
)
2
⋰
1
/
f
′
^
(
R
hN
)
2
]
based on the
current estimate of {circumflex over (ƒ)}(·); and
(E) (3) producing a current estimate {circumflex over (x)} of x based on the computed weight matrix W;
(E) (4) using the current estimate {circumflex over (x)} to produce an estimate {circumflex over (ƒ)}(·) of the function ƒ(·);
(E) (5) computing a new estimate of {circumflex over (ƒ)}′(·) from the estimate {circumflex over (ƒ)}(·); and
(E) (6) repeating (E)(2)-(E)(5) at least once.
11. The method of claim 6 , wherein (E) comprises:
(E)(1) identifying a plurality of regions corresponding to a plurality of ranges of resistances;
(E)(2) for each of the plurality of regions, producing a polynomial approximation of the function ƒ(·) within the region for the corresponding one of the plurality of ranges of resistances.
12. The method of claim 11 , wherein the polynomial approximation for each of the plurality of regions is a linear approximation.
13. The method of claim 11 , wherein (E) further comprises:
(E)(3) producing a continuous approximation of the function ƒ(·) based on the plurality of polynomial approximations produced in (E)(2).
14. The method of claim 6 , wherein (E) comprises identifying the estimate {circumflex over (ƒ)}(·) as an estimate
f
^
(
R
h
)
=
∑
m
=
1
M
x
^
m
B
m
p
(
R
h
)
,
wherein B m p (·|k m , . . . , k m+p ) is the m th B-spline of order p for a knot sequence k 1 ≦k 2 ≦. . . ≦k M+p , and wherein m ranges from 1 to M.
15. The method of claim 14 , wherein (E) comprises:
(E)(1) sorting the plurality of resistances R hi ;
(E)(2) placing a knot at every (N/M) th one of the sorted plurality of resistances; and
(E)(3) identifying estimates {circumflex over (x)} and  using the equation
[
x
^
A
^
]
=
(
D
T
W
D
)
-
1
D
T
W
T
s
,
wherein
x
^
=
[
x
^
1
⋮
x
^
M
]
,
T
s
=
[
T
s
1
⋮
T
s
N
]
,
W
=
[
1/σ
1
2
⋰
1/σ
N
2
]
,
D
=
[
B
1
P
(
R
h
1
)
⋯
B
M
P
(
R
h
1
)
-
P
1
⋮
⋰
⋮
⋮
B
1
P
(
R
N
)
⋯
B
M
P
(
R
h
N
)
-
P
N
]
,
and σ i is a standard deviation of noise on the print head element temperature T h arising from noise in the measurement triplet {R hi ,T si ,P i }; and
(E)(4) identifying the estimate {circumflex over (ƒ)}(·) using the equation
f
^
(
R
h
)
=
∑
m
=
1
M
x
^
m
B
m
p
(
R
h
)
.
16. The method of claim 1 , wherein (A) comprises selecting the plurality of initial temperatures T si to maximize SNR, wherein
SNR
=
1
N
∑
i
Δ
T
si
2
σ
i
2
,
ΔT si =T si − T s , wherein
T
_
s
=
1
N
∑
i
T
si
,
and wherein σ i is a standard deviation of noise on the print head element temperature T h arising from noise in the measurement triplet {R hi ,T si ,P i }.
17. The method of claim 16 , wherein (A) comprises selecting the plurality of initial temperatures T si to be uniformly distributed.
18. An apparatus for identifying an estimate {circumflex over (ƒ)}(·) of a function T h =ƒ(R h ) relating resistance R h of a thermal print head element in a thermal print head of a thermal printer to temperature T h of the thermal print head element, the apparatus comprising:
means for selecting a plurality N of initial temperatures T si ;
means for heating an insulated chamber containing the thermal print head to the plurality of initial temperatures T si ;
means for providing the thermal print head element with a plurality N of input powers P i ;
means for measuring a plurality N of resistances R hi resulting from application of the plurality of input powers P i ; and
means for identifying the estimate {circumflex over (ƒ)}(·) based on the plurality of initial temperatures T si , the plurality of resistances R hi , and the plurality of input powers P i .