Method of detecting system function by measuring frequency response
View Patent ↗Real time battery impedance spectrum is acquired using one time record, Compensated Synchronous Detection (CSD). This parallel method enables battery diagnostics. The excitation current to a test battery is a sum of equal amplitude sin waves of a few frequencies spread over range of interest. The time profile of this signal has duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known, synchronous detection processes the time record and each component, both magnitude and phase, is obtained. For compensation, the components, except the one of interest, are reassembled in the time domain. The resulting signal is subtracted from the original signal and the component of interest is synchronously detected. This process is repeated for each component.
1. A method for detecting system function of a unit under test by measuring frequency response, the method comprising the steps of:
(a) selecting a number of frequencies over which the function of the unit under test will be tested;
(b) assembling an excitation time record that is the sum of the sinusoids of the frequencies and a duration of greater than or equal to a period of the lowest selected frequency;
(c) conditioning the excitation time record to be compatible with the unit under test;
(d) exciting the unit under test with the excitation time record and simultaneously capturing a response time record with a data acquisition system;
(e) processing the response time record using the following synchronous detection equations to obtain estimated frequency components of magnitude and phase for one of the selected frequencies:
F
out
K
=
1
N
-
R
∑
j
=
R
+
1
N
{
A
K
sin
(
ω
K
(
j
-
1
)
Δ
t
+
ϕ
in
K
)
∑
i
=
1
M
B
i
sin
(
ω
i
(
j
-
1
)
Δ
t
+
ϕ
out
i
)
}
F
out
K
=
1
N
-
R
∑
j
=
R
+
1
N
{
A
K
B
K
2
[
cos
(
ϕ
in
K
-
ϕ
out
K
)
-
cos
(
2
ω
K
(
j
-
1
)
Δ
t
+
ϕ
in
K
+
ϕ
out
K
)
]
+
∑
i
≠
k
=
1
M
A
K
B
i
2
[
cos
(
(
ω
k
-
ω
i
)
(
j
-
1
)
Δ
t
+
ϕ
in
K
-
ϕ
out
i
)
-
cos
(
(
ω
k
+
ω
i
)
(
j
-
1
)
Δ
t
+
ϕ
in
K
+
ϕ
out
i
)
]
}
F
out
K
=
A
K
B
K
2
cos
(
ϕ
in
K
-
ϕ
out
K
)
Fq
out
K
=
1
N
-
R
∑
j
=
R
+
1
N
{
A
K
cos
(
ω
K
(
j
-
1
)
Δ
t
+
ϕ
in
K
)
∑
i
=
1
M
B
i
sin
(
ω
i
(
j
-
1
)
Δ
t
+
ϕ
out
i
)
}
Fq
oiut
K
=
1
N
-
R
∑
j
=
R
+
1
N
{
A
K
B
K
2
[
sin
(
ϕ
out
K
-
ϕ
in
K
)
+
sin
(
2
ω
K
(
j
-
1
)
Δ
t
+
ϕ
in
K
+
ϕ
out
K
)
]
+
∑
i
≠
k
=
1
M
A
K
B
i
2
[
sin
(
(
ω
k
+
ω
i
)
(
j
-
1
)
Δ
t
+
ϕ
in
K
+
ϕ
out
i
)
-
sin
(
(
ω
k
-
ω
i
)
(
j
-
1
)
Δ
t
+
ϕ
in
K
-
ϕ
out
i
)
]
}
Fq
out
K
=
A
K
B
K
2
sin
(
ϕ
out
K
-
ϕ
in
K
)
F
out
K
=
f
out
K
2
+
fq
out
K
2
=
A
K
B
K
2
sin
2
(
ϕ
in
K
-
ϕ
out
K
)
+
cos
2
(
ϕ
in
K
-
ϕ
out
K
)
︸
=
1
=
A
K
B
K
2
≮
F
out
K
=
tan
-
1
(
Fq
out
K
F
out
K
)
=
tan
-
1
(
A
K
B
K
2
sin
(
ϕ
out
K
-
ϕ
in
K
)
A
K
B
K
2
cos
(
ϕ
out
K
-
ϕ
in
K
)
)
=
tan
-
1
(
sin
(
ϕ
out
K
-
ϕ
in
K
)
cos
(
ϕ
out
K
-
ϕ
in
K
)
)
=
(
ϕ
out
K
-
ϕ
in
K
)
Where:
A i amplitude of the i th input sinusoid
B i amplitude response of the i th output sinusoid
ω i radian frequency of the i th sinusoid
Δt time step of data system
φin i phase of the i th input sinusoid
φout i phase response of the i th output sinusoid
N number of points of the response time record
M number different sinusoids of the excitation time record
R the number of points in the response time record that may be discarded
K is the frequency index for the system function being detected;
(f) repeating step (e) to obtain estimated frequency components for each selected frequency;
(g) assembling the estimated frequency components to get an estimated response time record;
(h) subtracting the estimated response time record from the captured response time record to get an error; and
(i) minimizing the error to achieve the frequency response.
2. The method of claim 1 , wherein said error is minimized using the following equations which create a corrected time record and a compensated time record:
f
RK
[
j
]
=
∑
p
=
1
,
p
≠
K
M
(
F
p
sin
(
ω
p
(
j
-
1
)
Δ
t
)
+
F
Qp
cos
(
ω
p
(
j
-
1
)
Δ
t
)
)
;
j
=
R
+
1
:
N
(
11
)
CfK Out [j]=f Out [j]−f RK [j]
Where:
f Out is the original time record
f RK is the correction time record
Cf KOut is the compensated time record
F p estimated in phase amplitude response at the p th frequency
F Qp estimated quadrature amplitude response at the p th frequency
ω p radian frequency of the p th sinusoid
Δt time step of data system
N number of points of the response time record
M number of different sinusoids of the excitation time record
R number of points of the response time record that may be discarded
K is the frequency index for the system function being detected.
3. The method of claim 1 , wherein said error is minimized using a neural network.
4. The method of claim 1 , wherein said unit under test is a battery.