# US 9,438,449 B2 · Data sampling method and system, and application method and system thereof in parameter identification

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- Number: US 9,438,449 B2
- Document ID: US9438449B2
- Status: Granted
- Kind: B2
- Application number: 14/437,972
- Filed: 2013-10-23
- Published: 2015-10-01
- Granted: 2016-09-06
- Earliest claimed: 2012-10-23
- Applicants: Yushan Hao
- Inventors: Yushan Hao
- Web page: https://patentgrep.com/patent/US9438449B2

## CPC

- H04L 25/0262: {Arrangements for detecting the data rate of an incoming signal}
- G06F 7/535: Dividing only
- H03M 1/0626: {by filtering}
- H04L 25/068: {by sampling faster than the nominal bit rate}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

The present invention relates to a data sampling method: sampling a physical quantity according to a sampling frequency fs≦fsh, fsh=ζmax/ε being the upper limit of the sampling frequency; and a data sampling method and system: sampling a physical quantity with a sampling frequency satisfying Nyquist theorem, firstly performing low-pass filtering on an obtained sampled sequence, and then re-sampling, the re-sampling frequency fs≦ζmax/ε, where ε is the Z-domain error of a sampling system, and ζmax the maximum error of an S-domain. The present invention also relates to a parameter identification method and system which firstly adopt the above data sampling method and system to obtain sampled data, and then utilize the sampled data to perform dynamic and/or static parameter identification. The data sampling method and system and the parameter identification method and system of the present invention solve technical difficulties such as relatively large errors in sampled data, digital control instability, and parameter identification failure.

## Claims

### Claim 1

A data sampling method for converting an analog signal to a digital signal, comprising the following steps:
S1: sampling, by an analog-to-digital converter, and analog signal y of a physical quantity with a sampling frequency satisfying Nyquist theorem to obtain a sampled sequence Y1;
S2: performing, by a digital low-pass filter, on the sampled sequence Y1 to obtain a filtered sampled sequence Y2;
S3: re-sampling, by a processor, the filtered sampled sequence Y2 to obtain a sampled sequence Y at a re-sampling frequency frs and said frs≦fsh=ζmax/ε; where ε is a Z-domain error of a sampling system and ζmax is a maximum error of S-domain,
S4: outputting the sampled sequence Y.

### Claim 2 (depends on 1)

The data sampling method according to claim 1, wherein a cut-off frequency of said digital low-pass filter is fc and said fc≦0.5×frs.

### Claim 3 (depends on 1)

The data sampling method according to claim 1, wherein the Z-domain error of said sampling system ε≧δ, where said δ is a cut-off error of the sampling system.

### Claim 4 (depends on 3)

The data sampling method according to claim 3, wherein the cut-off error δ of the sampling system is associated with δadc and δcpu, where δadc is a half of resolution ratio of the analog-to-digital converter and δcpu is a cut-off error of expressing digits for value in a computer.

### Claim 5 (depends on 3)

The data sampling method according to claim 3, wherein the Z-domain error of said sampling system satisfies that ε=kα·δ, where said kα is a safety factor lager than 1 and its value is determined by random disturbance level during sampling, a computation error of value in the sampling system or a combination thereof.

### Claim 6 (depends on 1)

The data sampling method according to claim 1, wherein said maximum error ζmax in S-domain is determined by an application system and includes ζmax determined by acceptable error of S-domain zero-poles of the application system, or ζmax determined correspondingly by an acceptable maximum error σmax of a time-domain differential equation of the application system.

### Claim 7

A data sampling system for converting an analog signal to a digital signal, comprising:
an analog-to-digital converter for sampling an analog signal y of a physical quantity with a sampling frequency satisfying the Nyquist theorem to obtain a sampled sequence Y1;
a low-pass filter for implementing digital low-pass filtering on the sampled sequence Y1 to obtain a filtered sampled sequence Y2;
a processor configured to re-sample the filtered sampled sequence Y2 to obtain a sampled sequence Y at a re-sampling frequency frs and said frs≦fsh=ζmax/ε; where ε is a Z-domain error of a sampling system and ζmax is a maximum error of S-domain.

### Claim 8 (depends on 7)

The data sampling system according to claim 7, wherein a cut-off frequency of said low-pass filter is fc with said fc≦0.5×frs.

### Claim 9

A parameter identification system comprising:
a data sampling system for converting an analog signal to a digital signal, including:
an analog-to-digital converter for sampling an analog signal v of a physical quantity with a sampling frequency satisfying the Nyquist theorem to obtain a sampled sequence Y1;
a low-pass filter for implementing digital low-pass filtering on the sampled sequence Y1 to obtain a filtered sampled sequence Y2;
a processor configured to re-sample the filtered sampled sequence Y2 to obtain a sampled sequence Y at a re-sampling frequency frs and said frs≦fsh=ζmax/ε, where ε is a Z-domain error of a sampling system and ζmax is a maximum error of S-domain, wherein the processor is configured to perform dynamic state parameter identification and static state parameter identification according to the sampled sequence Y.

### Claim 10 (depends on 9)

The parameter identification system according to claim 9, wherein the processor is configured to, according to the sampled sequence Y, identify an order and parameter of an ARMAX model using an identification method in an adaptive control, identify a parameter using a reference model method, or identity a parameter using a Kalman filter.

### Claim 11 (depends on 9)

The parameter identification system according to claim 9, wherein the processor is configured to:
calculate a stable state value according to the sampled sequence Y; and
according to the stable state value, estimate a static state parameter using a parameter estimation method, a correlation coefficient method, a linear regression method, a linearizable linear regression method, or a least square method.

### Claim 12 (depends on 11)

The parameter identification system according to claim 11, wherein the processor is configured to:
according to the sampled sequence Y, judge whether a current sample value is in a stable state process or a transient state process based on a “t” distribution or a simplification thereof, or a output result of a filter, wherein said filter is a Kalman filter or αβγ filter;
when the current sample value is in the stable state process, calculate an average value as the stable state value according to the sampled sequence Y; and
when the current sample value is in the transient state process, calculate a force component as the stable state value according to the sampled sequence Y.

### Claim 13 (depends on 12)

The parameter identification system according to claim 12, wherein the processor is configured to:
n+1th derivative of y, with n=0, 1, . . . , according to the sampled sequence Y until

ⅆ
n
+
1
⁢
y
ⅆ
t
n
+
1

≤
ɛ
is satisfied, thereby determine n, where ε is a constant approximate to 0;
perform variable substitution of
x
=
ⅆ
n
⁢
y
ⅆ
t
n
,
and calculate data sequence {xk} based on the sampled sequence Y;
receive the data sequence {xk} and judge whether a current value xk is in the transient state process or in the stable state process;
when the current value xk is in the stable state process, calculate an average value xk as the stable state value {circumflex over (x)}k according to {xk} and proceed to recovery; and
when the current value xk is in the transient state process, make k=1 and proceed to exit;
at recovery, calculate a force component ŷk according to equation ŷk=a0+a1·t+a2·t2+a3·t3+ . . . +an·tn, wherein
a
n
=
1
n
!
·
x
^
k
and a0, a1, a2, . . . , an-1 is a constant determined based on a derivative equation, the analog signal y and an initial value of all-order derivatives thereof.