CN108759875A - A kind of sensor dynamic compensation method based on System Discrimination and frequency response correction - Google Patents
A kind of sensor dynamic compensation method based on System Discrimination and frequency response correction Download PDFInfo
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Abstract
The present invention is a kind of sensor dynamic compensation method based on System Discrimination and frequency response correction, and time domain identification method is combined with frequency domain design method, the design of sensor dynamic compensator is used for, to effectively improve the time-frequency domain dynamic measurement performance of sensor.First, step response experiment is carried out to obtain its dynamic calibration experiment data to sensor；Secondly, the single compensation device that sensor is recognized using identification method, for reducing the time domain dynamic measurement error of sensor；Then, according to sensor, Frequency Response after single compensation carries out error and transfinites the looping construct of model analysis and second compensation device, for the frequency response correction after single compensation, to widen the Measurement bandwidth of sensor；Finally, in the application, the measurement of sensor is exported into Mobile state successively using single compensation device and second compensation device and is compensated, so that it is guaranteed that effectively improving the time domain trace performance and frequency domain measurement bandwidth that sensor dynamic measures.
Description
Technical field
It is especially a kind of suitable for sensor dynamic measurement error the present invention relates to Sensor's Dynamic Error alignment technique
The real-time dynamic compensation technology of time domain, solving existing sensor time domain dynamic compensation technology and being unable to effective compensation low order error transfinites
The problem of sensor dynamic Measurement bandwidth can not be widened when mode.
Background technology
Sensor dynamic measurement error is limiting sensor dynamic Measurement bandwidth, restrict its dynamic test performance it is important because
Element.Carrying out dynamic compensation in real time to sensor measurement data in is reduction sensor dynamic measurement error, improves its dynamic
The important channel of measurement performance.The key of sensor dynamic compensation is the design of dynamic compensator.Currently, dynamic compensator
Design method has very much, such as zero-pole assignment method, identification method etc..Zero-pole assignment method is dependent on the dynamic of sensor
States model, mainly constructing compensator makes its zero pole point and pole-zero cancellation unreasonable in sensor model, and introduces system
Desired zero pole point, to make sensor-level join dynamic compensator after reach desired dynamic property, this method is in sensor
It is difficult to obtain satisfied compensation effect when non-minimum phase system and smaller leading positive zero.Identification method is in itself with zero
Method of Pole Placement is similar, but this method is independent of sensor dynamic model, but passes through the reality output of sensor and expectation
Output identification obtains the parameter of sensor dynamic compensator, usually can obtain preferable dynamic compensation effect.Common system is distinguished
Knowledge method has least square method, prediction error Parameter Estimation Method and neural network etc..Since dynamic compensation is carried out in time domain,
In these processes also mainly from time domain angle so that sensor through dynamic compensate after output and desired output between
The minimum criterion of time domain error come recognize obtain sensor dynamic compensator.Although the compensator that identification method obtains
The step response regulating time and overshoot of sensor usually can be effectively reduced in time domain, to obtain relatively good compensation effect
Fruit, if but the error of higher-order modal components is much larger than lower mode component error in sensor output signal, and identification method obtains
The compensator obtained then often ignores the compensation of the lower mode smaller to amplitude components.At this moment, if lower mode component error
Exceed allowable error band, although can then cause compensator that the time domain dynamic error that sensor measurement exports can be greatly reduced,
The dynamic Measurement bandwidth of sensor cannot effectively be widened.It is convenient for statement, the modal components beyond allowable error band are claimed below
It transfinites mode for error.If in addition, sensor there are non-minimum phase link and dominate positive zero it is smaller, often system is made to distinguish
Although step response regulating time can be shortened but can lengthen the rise time to also result in sensing by knowing obtained dynamic compensator
The Measurement bandwidth of device is lowered.In view of these situations, identification method is difficult often in time domain response time, overshoot and frequency domain
A relatively good balance is obtained between Measurement bandwidth, to influence the dynamic compensation effect exported to sensor measurement.
Invention content
The invention solves existing sensor time domain dynamic compensation technology be unable to effective compensation low order error transfinite mode when
The problem of to widen sensor dynamic Measurement bandwidth, provides a kind of based on System Discrimination design sensor single compensation
Device based on frequency response correcting structure sensor second compensation device and exports the method compensated into Mobile state to sensor measurement.
The technical solution adopted in the present invention is：First, dynamic calibration experiment is carried out to sensor using step response method,
Obtain the step response experimental data of sensor；Secondly, the single compensation device that sensor is recognized using identification method, for dropping
The time domain dynamic measurement error of low sensor；Then, the Frequency Response analysis according to sensor after single compensation restricts its survey
The error of amount bandwidth transfinites mode, and carry out second compensation device looping construct and secondary cycle compensation after error transfinite mode
Analysis, until it is expected that the error free mode that transfinites in Measurement bandwidth, the second compensation device obtained accordingly are used for sensor in sensor
After single compensation each error transfinite mode frequency response correction, to widen the Measurement bandwidth of sensor；Finally, in the application, it adopts
The second compensation device of the single compensation device and construction that are designed with System Discrimination exports into Mobile state the measurement of sensor mend successively
It repays, to improve the dynamic following performance of its time domain measurement and effectively widen its frequency domain measurement bandwidth.Wherein, second compensation device
Transmission function is made of proportional component, secondary differential element and order Oscillating link, and load transfer function coefficient transfinites according to each error
The amplitude frequency curve of mode calculates.
The present invention techniqueflow be：Dynamic step response tests 1 → single compensation device identification 2 → second compensation device cycle
3 → sensor time domain dynamic compensation 4 is constructed, as shown in Figure 1.
The dynamic step response experiment 1, as uses step response method to carry out dynamic calibration experiment to sensor, to obtain
Take its step input signal x (t) and response output signal y (t).
The single compensation device identification 2 is the input signal x (t) tested according to the step response of sensor and response
Output signal y (t) designs the single compensation device G of sensor in time domain using identification method1(s)。
The second compensation device looping construct 3 restricts to be analyzed according to Frequency Response of the sensor after single compensation
The error of its Measurement bandwidth transfinites mode, and carries out error after the looping construct and second compensation of second compensation device and transfinite mode
Cycle analysis, until it is expected the error free mode that transfinites in Measurement bandwidth in sensor.The recycle stream of second compensation device looping construct 3
Journey be precompensation frequency response calculate 5 → error transfinite mode judge 6 → low order error transfinite model analysis 7 → second compensation device construct
8, loop stop conditions are that the error mode that transfinites judges that 6 judging result is the error free mode that transfinites.
Precompensation frequency response calculates 5：The step is to calculate the single compensation device and cycle structure that sensor is designed through front successively
Frequency response function after the second compensation device compensation made, calculating are divided into a precompensation frequency response calculating and secondary cycle precompensation frequency
It rings and calculates two kinds of situations.Precompensation frequency response calculates, and as enters the cycle for the first time after 3 flow of second compensation device looping construct
When precompensation frequency response calculate, first calculate separately out the frequency response function G of sensor0The frequency response function G of (j ω) and single compensation device1
Then the two is multiplied to obtain precompensation frequency response M of the sensor after single compensation by (j ω)1(j ω) and its amplitude versus frequency characte | M1(j
ω) |=| G0(jω)G1(jω)|；Secondary cycle precompensation frequency response calculates, and as enters 3 flow of second compensation device looping construct
The precompensation frequency response after the 2nd cycle calculates afterwards, and the second compensation of (i-1)-th looping construct is first calculated in ith cycle
Device G2,i-1(s) frequency response function G2,i-1(j ω), then by the precompensation frequency response M of (i-1)-th cycle calculationsi-1(j ω) and G2,i-1
Precompensation frequency response M of (j ω) the mutually multiplied sensor in ith cyclei(j ω) and its amplitude versus frequency characte | Mi(j ω) |=| Mi-1(j
ω)G2,i-1(jω)|。
The error mode that transfinites judges 6：The step is the expectation Measurement bandwidth [0, ω in sensorbd] in analyze Mi(jω)
With the presence or absence of amplitude beyond allowable error band etolError transfinite mode mi.If MiThere is error to transfinite mode in (j ω), then carries out
Follow-up low order error transfinites model analysis 7 and second compensation device construction 8, and recycles；If MiThe error free mode that transfinites in (j ω),
Then second compensation device looping construct 3 terminates.
Low order error transfinites model analysis 7：The step is judge that 6 get the wrong sow by the ear the poor mode that transfinites in the error mode that transfinites
In the case of, precompensation frequency response M of the analysis second compensation device looping construct 3 in ith cyclei(j ω) is in the expectation of sensor
Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode miType, error transfinites frequency bandAnd extreme point
Frequency.The typical error mode that transfinites is divided into 4 classes by the present invention according to following judgment rules：
MD1 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd it only exists a wave crest or only deposits
In a trough, then it is assumed that the frequency range transfinites mode there are a MD1 class error；If the mode is Mi(j ω) it is expected to measure
Bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable iti, miError transfinite frequency bandmiWave crest or trough extreme value dot frequency be ωem。
MD2 classes：In a Continuous Band [ωl,ωh] in, | Mi(j ω) | there is a pair of adjacent wave crest and trough, and removes wave
Except intermediate zone between peak, trough | | Mi(j ω) | -1 | > etol, then it is assumed that the frequency range transfinites mould there are a MD2 class error
State；If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable iti, mi
Error transfinite frequency bandmiWave crest and trough extreme value dot frequency be ωe1And ωe2And ωe1<
ωe2。
MD3 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two
A trough, two wave crests or the sum of two trough extreme points and the in-between difference in magnitude of reversed extreme point E≤3etol, then regarding should
It transfinites mode there are a MD3 class error in Continuous Band；If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in
Lowest-order error transfinite mode, then it is m to enable iti, miError transfinite frequency bandmiExtreme point frequency
Rate is taken as the average value ω of the extreme value dot frequency of two wave crests or two troughsem。
MD4 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two
The sum of the extreme point of a trough, two wave crests or two troughs and the in-between difference in magnitude of reversed extreme point E > 3etol, then regard
It transfinites mode there are continuous two MD4 class errors in the Continuous Band；If lower mode therein is Mi(j ω) it is expected to survey
Measure bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable itiIf miContinuous Band [the ω at placel,ωh] in
The frequency of intermediate reversed extreme point is ωm, then miError transfinite frequency bandmiWave crest or trough
Extreme value dot frequency be ωem。
Above-mentioned MD3 and MD4 classes error transfinites in mode, continuous two wave crests or two trough extreme points and in-between anti-
The sum of difference in magnitude to extreme point E is calculated as follows：
E=| A1-B |+| A2-B |
In above formula, A1, A2 are respectively the extreme point amplitude of continuous two wave crests or two troughs, and B is two wave crests or two
The amplitude of reversed extreme point among a trough.
Second compensation device construction 8：The step is to be directed to Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order miss
Difference transfinites mode mi, construct corresponding second compensation device G2,i(s), for transfiniting mode m to erroriCarry out frequency response school
Just.Second compensation device G2,i(s) it is made of proportional component, secondary differential element and order Oscillating link using following one
Transmission function characterizes.
Enable ζ1/ζ2=λ, ωn1/ωn2=β, obtains G2,i(s) amplitude versus frequency characte is as follows
It is above-mentioned | G2,i(j ω) | tracing pattern have following feature：As β=1, | G2,i(j ω) | only there are one wave crests
Or trough, and the extreme value dot frequency of wave crest or trough is ωn2, extreme point amplitude be λ；As β ≠ 1, | G2,i(j ω) | there is a pair
Adjacent wave crest and trough, and when β < 1 trough in preceding, wave crest rear, when β > 1 wave crest in preceding, trough in rear, wave crest, trough
Extreme value dot frequency productAs ω → 0, | G2,i(j ω) | → 1, and as ω →+∞, |
G2,i(jω)|→1/β2.Accordingly, the present invention transfinites mould for the low order error 4 quasi-representative errors in model analysis 7 that transfinite
State, point the following two kinds situation calculates all kinds of errors using following methods to transfinite the second compensation device G of mode2,i(s) parameter.
Situation one：MD1, MD3, MD4 the quasi-representative error in model analysis 7 that transfinites for the low order error transfinite mode
mi, secondary compensator G2,i(s) calculating step is：
1. taking β=1, ωn2=ωem, enable correction frequency band
2. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency
ωkPlace enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating
Formula is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1, q2,…,qN]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points.
3. solving above-mentioned equation group using least square method obtains λ and ζ2。
4. according to ζ1=λ ζ2、ωn1=ωn2Calculate ζ1、ωn1。
5. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniIn (j ω)
Error transfinites mode miSecond compensation device G2,i(s)。
Situation two：The MD2 quasi-representative errors in model analysis 7 that transfinite for the low order error transfinite mode mi, secondly
Secondary compensator G2,i(s) calculating step is：
1. enabling correction frequency band
2. determining the interval B of β：When due to ω →+∞ | G2,i(jω)|→1/β2, to reduce second compensation device to school
Positive frequency band [ωlow,ωup] outer sensor Frequency Response influence, ensure in the design of second compensation device | 1/ β2-1|≤etol/ 2,
I.e.If MiMode m in (j ω)iWave crest in preceding, trough rear, that is, require | G2,i
(j ω) | trough in preceding, wave crest rear, the interval of β takesIf MiMode m in (j ω)i
Trough in preceding, wave crest rear, that is, require | G2,i(j ω) | wave crest in preceding, trough rear, the interval of β takes
3. unique step takes W β value [β in interval B(1),β(2),β(3),...,β(W)], successively by β(l)Substitution formulaIn β calculate W ωn2ValueWherein, l=1,2,3 ..., W.
4. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency
ωkPlace enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating
Formula is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1, q2,…,qn]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points.
5. successively by β(l)WithAbove formula is substituted into, corresponding W groups parameter lambda is calculated using least square method(l)With
Wherein l=1,2,3 ..., W.
6. by above-mentioned W groups parameterSecond compensation device amplitude versus frequency characte is substituted into successively | G2,i(jω)
| calculating formula in, obtain W second compensation device amplitude versus frequency characteWherein l=1,2,3 ..., W.
7. in correction frequency band [ωlow,ωup] in examine it is eachReservation meets condition
's
8. retaining from previous stepMiddle selection one makesIt is minimum
'sIts corresponding parameter As error transfinites mode miSecond compensation device optimal solution ginseng
Number β, λ, ζ2、ωn2。
9. according to ζ1=λ ζ2、ωn1=β ωn2Calculate to obtain ζ1、ωn1。
10. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniIn (j ω)
Error transfinites mode miSecond compensation device G2,i(s)。
The sensor time domain dynamic compensation 4, as picks out primary benefit in sensor through single compensation device identification 2
Repay device G1(s) and 3 looping construct of second compensation device looping construct goes out whole p second compensation device G2,i(s) after, for
The practical measurement of sensor exports, and first uses single compensation device G1(s) to the output of sensor carry out single compensation, then according to
P second compensation device G2,i(s) looping construct sequence uses each second compensation device G2,i(s) to the primary of sensor measurement output
Compensation result is compensated successively；Second compensation device G2,1(s) input is single compensation device G1(s) output, second compensation device
G2,i(s) input is second compensation device G2,i-1(s) output, wherein i=2,3 ..., p；Second compensation device G2,p(s) output
For the final dynamic compensation result of sensor measurement output.
This have the advantage that：The single compensation device that time domain system identification method obtains can be utilized to improve sensor dynamic
The time domain trace performance that state measures, can utilize the second compensation device based on frequency response correcting structure not mended once from frequency-domain correction
Repaying the low order error of device effective compensation transfinites mode, to realize that the time domain trace performance measure sensor dynamic and frequency domain are surveyed
Amount bandwidth effectively improves.
Description of the drawings
Fig. 1 is the techniqueflow block diagram of the method for the present invention, i.e., the sensor dynamic based on System Discrimination and frequency response correction is mended
Repay technical solution flow chart；
Fig. 2 is precompensation frequency response in the ith cycle of the second compensation device looping construct flow of the specific embodiment of the invention
Calculate schematic diagram；
Fig. 3, which is the typical error of the specific embodiment of the invention, to transfinite mode schematic diagram；
Fig. 4, which is MD3 the and MD4 quasi-representative errors of the specific embodiment of the invention, to transfinite mode extreme point schematic diagram；
Fig. 5, which is MD1, MD3, MD4 quasi-representative error of the specific embodiment of the invention, to transfinite mode miSecond compensation device G2,i
(s) calculation flow chart；
Fig. 6, which is the MD2 quasi-representative errors of the specific embodiment of the invention, to transfinite mode miSecond compensation device G2,i(s) meter
Calculate flow chart；
Fig. 7 is the sensor time domain dynamic compensation flow chart of the specific embodiment of the invention；
Fig. 8 is the dynamic compensation effect figure using a kind of strain force sensor of the method for the present invention.
Specific implementation mode
The present invention will be further described below in conjunction with the accompanying drawings：
The present invention design philosophy be：The problem big for sensor dynamic measurement error, Measurement bandwidth is low is first based on passing
Sensor dynamic step response experimental data is passed using the single compensation device of time domain system identification method design sensor with being greatly reduced
The time domain dynamic measurement error of sensor improves the time domain dynamic following performance of sensor measurement；Then, for desired Measurement bandwidth
It is not transfinited mode by the error of single compensation device effective compensation inside, carries out frequency response after second compensation device looping construct and second compensation
Cycle analysis, until constructing whole errors transfinites the second compensation device of mode, for being carried out to each error mode that transfinites
Frequency response corrects, and so that its amplitude error is reduced in allowable error band, to effectively improve the frequency domain measurement bandwidth of sensor；According to
This, can first use single compensation device to the practical measurement output signal of sensor in practical applications, use second compensation again
Device successively compensates it into Mobile state, to realize to the time domain dynamic following performance of sensor measurement and frequency domain measurement bandwidth
It effectively improves.
Technical scheme of the present invention flow chart is as shown in Figure 1.First, sensor is obtained by dynamic step response experiment 1
Dynamic calibration experiment data；Secondly, the single compensation device of sensor is obtained by single compensation device identification 2；Again, pass through two
The second compensation for mode that secondary compensator looping construct 3 is analyzed and each error of the structure sensor in desired Measurement bandwidth transfinites
Device；Finally, the second compensation device of the single compensation device and looping construct that recognize is used successively by sensor time domain dynamic compensation 4
Sensor measurement output signal is compensated into Mobile state.
The dynamic step response experiment 1, as uses step response method to carry out dynamic calibration experiment to sensor, to obtain
Its dynamic calibration experiment data is taken, for the identification of subsequent single compensation device and second compensation device construction.When experiment, to sensor
Apply step excitation, passes through step input signal x (t) and step response the output letter of signal collecting device synchronous acquisition sensor
Number y (t).
The single compensation device identification 2 is the input signal x (t) tested according to the step response of sensor and response
Output signal y (t) designs the single compensation device G of sensor in time domain using identification method1(s)。
The second compensation device looping construct 3 restricts to be analyzed according to Frequency Response of the sensor after single compensation
The error of its Measurement bandwidth transfinites mode, and carries out error after the looping construct and second compensation of second compensation device and transfinite mode
Cycle analysis, until it is expected the error free mode that transfinites in Measurement bandwidth in sensor.The recycle stream of second compensation device looping construct 3
Journey be precompensation frequency response calculate 5 → error transfinite mode judge 6 → low order error transfinite model analysis 7 → second compensation device construct
8, loop stop conditions are that the error mode that transfinites judges that 6 judging result is the error free mode that transfinites.
Precompensation frequency response calculates 5 calculating schematic diagram as shown in Fig. 2, being one for calculating sensor and being designed successively through front
The second compensation device of secondary compensator and looping construct compensation after frequency response function, be divided into a precompensation frequency response calculate and it is secondary
It recycles precompensation frequency response and calculates two kinds of situations.Precompensation frequency response calculates, and as enters 3 flow of second compensation device looping construct
Precompensation frequency response when recycling for the first time afterwards calculates, and first calculates separately out the frequency response function G of sensor0(j ω) and single compensation
The frequency response function G of device1Then the two is multiplied to obtain precompensation frequency response M of the sensor after single compensation by (j ω)1(j ω) and
Its amplitude versus frequency characte | M1(j ω) |=| G0(jω)G1(jω)|；Secondary cycle precompensation frequency response calculates, and as enters second compensation
Precompensation frequency response after 3 flow of device looping construct after the 2nd cycle calculates, and (i-1)-th cycle is first calculated in ith cycle
The second compensation device G of construction2,i-1(s) frequency response function G2,i-1(j ω), then by the precompensation frequency response of (i-1)-th cycle calculations
Mi-1(j ω) and G2,i-1Precompensation frequency response M of (j ω) the mutually multiplied sensor in ith cyclei(j ω) and its amplitude versus frequency characte |
Mi(j ω) |=| Mi-1(jω)G2,i-1(jω)|。
The error mode that transfinites judges 6, as in the expectation Measurement bandwidth [0, ω of sensorbd] in analyze MiWhether (j ω)
There are amplitudes beyond allowable error band etolError transfinite mode mi.If MiThere is error to transfinite mode in (j ω), then carries out follow-up
Low order error transfinites model analysis 7 and second compensation device construction 8, and recycles；If MiThe error free mode that transfinites in (j ω), then two
Secondary compensator looping construct 3 terminates.
Low order error transfinites model analysis 7, as error transfinite mode judge 6 get the wrong sow by the ear difference transfinite mode the case where
Under, precompensation frequency response M of the analysis second compensation device looping construct 3 in ith cyclei(j ω) is measured in the expectation of sensor
Bandwidth [0, ωbd] in lowest-order error transfinite mode miType, error transfinites frequency bandWith extreme value dot frequency.
The typical error mode that transfinites is divided into 4 classes by the present invention according to following judgment rules, and schematic diagram is as shown in Figure 3：
MD1 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd it only exists a wave crest or only deposits
In a trough, then it is assumed that the frequency range transfinites mode there are a MD1 class error；If the mode is Mi(j ω) it is expected to measure
Bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable iti, miError transfinite frequency bandmiWave crest or trough extreme value dot frequency be ωem。
MD2 classes：In a Continuous Band [ωl,ωh] in, | Mi(j ω) | there is a pair of adjacent wave crest and trough, and removes wave
Except intermediate zone between peak, trough | | Mi(j ω) | -1 | > etol, then it is assumed that the frequency range transfinites mould there are a MD2 class error
State；If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable iti, mi
Error transfinite frequency bandmiWave crest and trough extreme value dot frequency be ωe1And ωe2And ωe1<
ωe2。
MD3 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two
A trough, two wave crests or the sum of two trough extreme points and the in-between difference in magnitude of reversed extreme point E≤3etol, then regarding should
It transfinites mode there are a MD3 class error in Continuous Band；If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in
Lowest-order error transfinite mode, then it is m to enable iti, miError transfinite frequency bandmiExtreme point
Frequency is taken as the average value ω of the extreme value dot frequency of two wave crests or two troughsem。
MD4 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two
The sum of the extreme point of a trough, two wave crests or two troughs and the in-between difference in magnitude of reversed extreme point E > 3etol, then regard
It transfinites mode there are continuous two MD4 class errors in the Continuous Band；If lower mode therein is Mi(j ω) it is expected to survey
Measure bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable itiIf miContinuous Band [the ω at placel,ωh] in
The frequency of intermediate reversed extreme point is ωm, then miError transfinite frequency bandmiWave crest or trough
Extreme value dot frequency be ωem。
Above-mentioned MD3 and MD4 classes error transfinites in mode, continuous two wave crests or two trough extreme points and in-between anti-
The sum of difference in magnitude to extreme point E is calculated as follows：
E=| A1-B |+| A2-B |
In above formula, A1, A2 are respectively the extreme point amplitude of continuous two wave crests or two troughs, and B is two wave crests or two
The amplitude of reversed extreme point among a trough, as shown in Figure 4.
Second compensation device construction 8, is as directed to Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order error it is super
Limit mode mi, construct corresponding second compensation device G2,i(s), for transfiniting mode m to erroriCarry out frequency response correction.Two
Secondary compensator G2,i(s) using a following transmission letter being made of proportional component, secondary differential element and order Oscillating link
It counts to characterize：
Enable ζ1/ζ2=λ, ωn1/ωn2=β, obtains G2,i(s) amplitude versus frequency characte is as follows
It is above-mentioned | G2,i(j ω) | tracing pattern have following feature：As β=1, | G2,i(j ω) | only there are one wave crests
Or trough, and the extreme value dot frequency of wave crest or trough is ωn2, extreme point amplitude be λ；As β ≠ 1, | G2,i(j ω) | there is a pair
Adjacent wave crest and trough, and when β < 1 trough in preceding, wave crest rear, when β > 1 wave crest in preceding, trough in rear, wave crest, trough
The product of extreme value dot frequencyAs ω → 0, | G2,i(j ω) | → 1, and as ω →+∞, |
G2,i(jω)|→1/β2.Accordingly, the present invention transfinites mould for the low order error 4 quasi-representative errors in model analysis 7 that transfinite
State, point the following two kinds situation calculates all kinds of errors using following methods to transfinite the second compensation device G of mode2,i(s) parameter.
Situation one：MD1, MD3, MD4 the quasi-representative error in model analysis 7 that transfinites for the low order error transfinite mode
mi, secondary compensator G2,i(s) calculation process is as shown in figure 5, specifically calculating step is：
1. taking β=1, ωn2=ωem, enable correction frequency band
2. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency
ωkPlace enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating
Formula is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1,q2,…,qN]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points.
3. solving above-mentioned equation group using least square method obtains λ and ζ2。
4. according to ζ1=λ ζ2、ωn1=ωn2Calculate ζ1、ωn1。
5. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniIn (j ω)
Error transfinites mode miSecond compensation device G2,i(s)。
Situation two：The MD2 quasi-representative errors in model analysis 7 that transfinite for the low order error transfinite mode mi, secondly
Secondary compensator G2,i(s) calculation process is as shown in fig. 6, specifically calculating step is：
1. enabling correction frequency band
2. determining the interval B of β：When due to ω →+∞ | G2,i(jω)|→1/β2, to reduce second compensation device to school
Positive frequency band [ωlow,ωup] outer sensor Frequency Response influence, ensure in the design of second compensation device | 1/ β2-1|≤etol/ 2,
I.e.If MiMode m in (j ω)iWave crest in preceding, trough rear, that is, require | G2,i
(j ω) | trough in preceding, wave crest rear, the interval of β takesIf MiMode m in (j ω)i
Trough in preceding, wave crest rear, that is, require | G2,i(j ω) | wave crest in preceding, trough rear, the interval of β takes
3. unique step takes W β value [β in interval B(1),β(2),β(3),...,β(W)], successively by β(l)Substitution formulaIn β calculate W ωn2ValueWherein, l=1,2,3 ..., W.
4. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency
ωkPlace enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating
Formula is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1,q2,…,qn]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points.
5. successively by β(l)WithAbove formula is substituted into, corresponding W groups parameter lambda is calculated using least square method(l)WithIts
Middle l=1,2,3 ..., W.
6. by above-mentioned W groups parameterSecond compensation device amplitude versus frequency characte is substituted into successively | G2,i(jω)
| calculating formula in, obtain W second compensation device amplitude versus frequency characteWherein l=1,2,3 ..., W.
7. in correction frequency band [ωlow,ωup] in examine it is eachReservation meets condition
's
8. retaining from previous stepMiddle selection one makesIt is minimum
'sIts corresponding parameter As error transfinites mode miSecond compensation device optimal solution ginseng
Number β, λ, ζ2、ωn2。
9. according to ζ1=λ ζ2、ωn1=β ωn2Calculate to obtain ζ1、ωn1。
10. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniIn (j ω)
Error transfinites mode miSecond compensation device G2,i(s)。
The flow of the sensor time domain dynamic compensation 4 is as shown in fig. 7, be to be distinguished through the single compensation device in sensor
Know 2 and picks out single compensation device G1(s) and 3 looping construct of second compensation device looping construct goes out whole p second compensation devices
G2,i(s) after, the practical measurement for sensor exports, and first uses single compensation device G1(s) one is carried out to the output of sensor
Secondary compensation, then according to p second compensation device G2,i(s) looping construct sequence uses each second compensation device G2,i(s) to sensing
The single compensation result that device measures output is compensated successively；Second compensation device G2,1(s) input is single compensation device G1(s)
Output, second compensation device G2,i(s) input is second compensation device G2,i-1(s) output, wherein i=2,3 ..., p；Secondary benefit
Repay device G2,p(s) output is the final dynamic compensation result of sensor measurement output.
It is the dynamic compensation effect figure using a kind of strain force sensor of the method for the present invention shown in Fig. 8.Sensor
The allowable error band that dynamic measures is ± 5%, it is expected that Measurement bandwidth is 100Hz.First 1 pair is tested using the dynamic step response
Sensor carries out dynamic calibration experiment；The single compensation is used further according to the step response dynamic calibration experiment data of sensor
2 identification of device identification obtains single compensation device G1(s)；Then, it is constructed by the second compensation device looping construct 3 and obtains sensor
A MD2 class error transfinite the second compensation device G of mode2,1(s) the second compensation device for the mode that transfinites with a MD1 class error
G2,2(s)；Finally, using G1(s)、G2,1(s)、G2,2(s) output is measured to sensor step response to be compensated successively.Fig. 8
(a) it is respectively amplitude-versus-frequency curve s0, the single compensation device G of sensor in1(s) amplitude-versus-frequency curve s1 and sensor is through one
Secondary compensator G1(s) the amplitude-versus-frequency curve s2 after compensating；Respectively sensor is through single compensation device G in Fig. 8 (b)1(s) it mends
Amplitude-versus-frequency curve s2, second compensation device G after repaying2,1(s) amplitude-versus-frequency curve s3 and sensor is through G1(s)、G2,1(s)
Amplitude-versus-frequency curve s4 after compensating successively；Respectively sensor is through G in Fig. 8 (c)1(s)、G2,1(s) after compensating successively
Amplitude-versus-frequency curve s4, second compensation device G2,2(s) amplitude-versus-frequency curve s5 and sensor is through G1(s)、G2,1(s)、G2,2(s)
Amplitude-versus-frequency curve s6 after compensating successively；It is respectively that sensor step response curve c0 and step response warp are dynamic in Fig. 8 (d)
Curve c1 after state compensation.As shown in Figure 8, after single compensation and second compensation, time domain dynamic error is substantially dropped sensor
Low, frequency domain measurement bandwidth is also greatly improved.
Claims (5)
1. a kind of sensor dynamic compensation method based on System Discrimination and frequency response correction, for the dynamic calibration according to sensor
Experimental data designs the dynamic compensator of sensor, exports the practical measurement of sensor into Mobile state and compensates, dynamic to improve it
State measure time domain trace performance and frequency domain measurement bandwidth, techniqueflow include：The experiment of dynamic step response, single compensation device are distinguished
Knowledge, second compensation device looping construct, sensor time domain dynamic compensate, it is characterised in that：
The dynamic calibration experiment data for obtaining sensor are first tested by dynamic step response；Identification method identification sensing is used again
The single compensation device of device；Then, according to sensor, Frequency Response after single compensation carries out error and transfinites model analysis and two
The looping construct of secondary compensator obtains the second compensation device of sensor；In actually measuring application, using single compensation device and two
Secondary compensator exports into Mobile state the measurement of sensor compensate successively.
2. a kind of sensor dynamic compensation method based on System Discrimination and frequency response correction as described in claim 1, feature
It is：Second compensation device looping construct measures band to restrict it according to Frequency Response analysis of the sensor after single compensation
Wide error transfinites mode, and carries out error after the looping construct and second compensation of second compensation device and transfinite the cycle point of mode
Analysis, until it is expected the error free mode that transfinites in Measurement bandwidth in sensor；The circulation step of second compensation device looping construct is：Before
Compensation frequency response calculating → error mode judgement → low order error that transfinites transfinites model analysis → second compensation device construction, and cycle terminates
Condition be error transfinite mode judgement result be the error free mode that transfinites；
The precompensation frequency response calculates, to calculate the secondary of single compensation device that sensor is designed through front successively and looping construct
Frequency response function after compensator compensation, calculating is divided into a precompensation frequency response calculating and secondary cycle precompensation frequency response calculates two
Kind situation；Precompensation frequency response calculates, and as enters preceding benefit when recycling for the first time after second compensation device looping construct flow
Frequency response calculating is repaid, the frequency response function G of sensor is first calculated separately out0The frequency response function G of (j ω) and single compensation device1(j ω), so
The two is multiplied afterwards to obtain precompensation frequency response M of the sensor after single compensation1(j ω) and its amplitude versus frequency characte | M1(j ω) |=|
G0(jω)G1(jω)|；Secondary cycle precompensation frequency response calculates, and is as followed into the 2nd time after second compensation device looping construct flow
Precompensation frequency response after ring calculates, and the second compensation device G of (i-1)-th looping construct is first calculated in ith cycle2,i-1(s)
Frequency response function G2,i-1(j ω), then by the precompensation frequency response M of (i-1)-th cycle calculationsi-1(j ω) and G2,i-1(j ω) is multiplied
Obtain precompensation frequency response M of the sensor in ith cyclei(j ω) and its amplitude versus frequency characte | Mi(j ω) |=| Mi-1(jω)G2,i-1
(jω)|；
The error transfinite mode judgement, as in the expectation Measurement bandwidth [0, ω of sensorbd] in analyze MiWhether (j ω) deposits
In amplitude beyond allowable error band etolError transfinite mode mi；If MiThere is error to transfinite mode in (j ω), then carries out follow-up low
Rank error transfinites model analysis and second compensation device construction, and recycles；If MiThe error free mode that transfinites in (j ω), then secondary benefit
Device looping construct flow is repaid to terminate；
The low order error transfinites model analysis, and the difference that as gets the wrong sow by the ear in the error transfinites mode judgment step transfinites mould
In the case of state, precompensation frequency response M of the analysis second compensation device looping construct flow in ith cyclei(j ω) is in sensor
Expectation Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode miType, error transfinites frequency bandWith
Extreme value dot frequency；
The second compensation device construction, is as directed to Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order error transfinite
Mode mi, construct corresponding second compensation device G2,i(s), for transfiniting mode m to erroriCarry out frequency response correction.
3. a kind of sensor dynamic based on System Discrimination and frequency response correction as described in claim 1 and claim 2 compensates
Method, it is characterised in that：Typical error is transfinited in the model analysis of transfiniting of low order error in second compensation device looping construct flow
Mode is divided into tetra- class of MD1, MD2, MD3, MD4；Typical error transfinites the type of mode, precompensation frequency response Mi(j ω) is in sensor
Expectation Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode mi、miError transfinite frequency bandAnd mi's
The judgment rule of extreme value dot frequency is：
MD1 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd it only exists a wave crest or only exists one
A trough, then it is assumed that the frequency range transfinites mode there are a MD1 class error；If the mode is Mi(j ω) is in desired Measurement bandwidth
[0,ωbd] in lowest-order error transfinite mode, then it is m to enable iti, miError transfinite frequency bandmi
Wave crest or trough extreme value dot frequency be ωem；
MD2 classes：In a Continuous Band [ωl,ωh] in, | Mi(j ω) | there is a pair of adjacent wave crest and trough, and except wave crest,
Except intermediate zone between trough | | Mi(j ω) | -1 | > etol, then it is assumed that the frequency range transfinites mode there are a MD2 class error；
If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in lowest-order error transfinite mode, then it is m to enable iti, miMistake
Difference transfinites frequency bandmiWave crest and trough extreme value dot frequency be ωe1And ωe2And ωe1< ωe2；
MD3 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two waves
Paddy, two wave crests or the sum of two trough extreme points and the in-between difference in magnitude of reversed extreme point E≤3etol, then it is continuous to regard this
It transfinites mode there are a MD3 class error in frequency range；If the mode is Mi(j ω) is in desired Measurement bandwidth [0, ωbd] in most
Low order error transfinites mode, then it is m to enable iti, miError transfinite frequency bandmiExtreme value dot frequency
It is taken as the average value ω of the extreme value dot frequency of two wave crests or two troughsem；
MD4 classes：In a Continuous Band [ωl,ωh] in, | | Mi(j ω) | -1 | > etolAnd there are continuous two wave crests or two waves
The sum of the extreme point of paddy, two wave crests or two troughs and the in-between difference in magnitude of reversed extreme point E > 3etol, then the company is regarded
It transfinites mode there are continuous two MD4 class errors in continuous frequency range；If lower mode therein is Mi(j ω) it is expected to measure band
Width [0, ωbd] in lowest-order error transfinite mode, then it is m to enable itiIf miContinuous Band [the ω at placel,ωh] in centre
The frequency of reversed extreme point is ωm, then miError transfinite frequency bandmiWave crest or trough pole
Value dot frequency is ωem；
Above-mentioned MD3 and MD4 classes error transfinites in mode, continuous two wave crests or two trough extreme points and in-between reversed pole
The sum of difference in magnitude of value point E is calculated as follows：
E=| A1-B |+| A2-B |
In above formula, A1, A2 are respectively the extreme point amplitude of continuous two wave crests or two troughs, and B is two wave crests or two waves
The amplitude of reversed extreme point among paddy.
4. a kind of sensor dynamic based on System Discrimination and frequency response correction as described in claim 1 and claim 2 compensates
Method, it is characterised in that：In second compensation device construction in second compensation device looping construct flow, second compensation device G2,i(s) it adopts
The transmission function that is made of proportional component, secondary differential element and order Oscillating link with following one characterizes：
Enable ζ1/ζ2=λ, ωn1/ωn2=β, obtains G2,i(s) amplitude versus frequency characte is as follows：
Second compensation device G2,i(s) calculating divides the following two kinds situation：
Situation one, MD1, MD3, MD4 quasi-representative error in model analysis of transfiniting for the low order error transfinite mode mi,
Second compensation device G2,i(s) calculating step is：
1. taking β=1, ωn2=ωem, enable correction frequency band
2. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency ωk
Place enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating formula,
It is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1,q2,…,qN]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points；
3. solving above-mentioned equation group using least square method obtains λ and ζ2；
4. according to ζ1=λ ζ2、ωn1=ωn2Calculate ζ1、ωn1；
5. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniError is super in (j ω)
Limit mode miSecond compensation device G2,i(s)；
Situation two, the MD2 quasi-representative errors in model analysis of transfiniting for the low order error transfinite mode mi, second compensation
Device G2,i(s) calculating step is：
1. enabling correction frequency band
2. determining the interval B of β：When due to ω →+∞ | G2,i(jω)|→1/β2, to reduce second compensation device to correction frequency
Band [ωlow,ωup] outer sensor Frequency Response influence, ensure in the design of second compensation device | 1/ β2-1|≤etol/ 2, i.e.,If MiMode m in (j ω)iWave crest in preceding, trough rear, that is, require | G2,i(j
ω) | trough in preceding, wave crest rear, the interval of β takes If MiMode m in (j ω)iWave
Gu Qian, wave crest are in rear, i.e. requirement | G2,i(j ω) | wave crest in preceding, trough rear, the interval of β takes
3. unique step takes W β value [β in interval B(1),β(2),β(3),...,β(W)], successively by β(l)Substitution formulaIn β calculate W ωn2ValueWherein, l=1,2,3 ..., W；
4. according to the expected compensation effect of second compensation device, in correction frequency band [ωlow,ωup] in different discrete point in frequency ωk
Place enables | G2,i(jωk) |=1/ | Mi(jωk) | and substitute into aforementioned second compensation device amplitude versus frequency characte | G2,i(j ω) | calculating formula,
It is organized into following systems of linear equations
In above formula,
U=[U1,U2], Q=[q1,q2,…,qn]T
U1=[u11,u12,…,u1N]T, U2=[u21,u22,…,u2N]T
Wherein, k=1,2 ... ..., N, N are correction frequency band [ωlow,ωup] in discrete frequency points；
5. successively by β(l)WithAbove formula is substituted into, corresponding W groups parameter lambda is calculated using least square method(l)WithWherein l
=1,2,3 ..., W；
6. by above-mentioned W groups parameter beta(l)、λ(l)、Second compensation device amplitude versus frequency characte is substituted into successively | G2,i(j ω) | calculating
In formula, W second compensation device amplitude versus frequency characte is obtainedWherein l=1,2,3 ..., W；
7. in correction frequency band [ωlow,ωup] in examine it is eachReservation meets condition
's
8. retaining from previous stepMiddle selection one makesMinimumIts corresponding parameter beta(l)、λ(l)、As error transfinites mode miSecond compensation device optimal solution parameter
β、λ、ζ2、ωn2；
9. according to ζ1=λ ζ2、ωn1=β ωn2Calculate to obtain ζ1、ωn1；
10. by ζ1、ζ2、ωn1、ωn2Substitute into second compensation device G2,i(s) up to M in the expression formula of transmission functioniError is super in (j ω)
Limit mode miSecond compensation device G2,i(s)。
5. a kind of sensor dynamic compensation method based on System Discrimination and frequency response correction as described in claim 1, feature
It is：Sensor time domain dynamic compensates, and is as picking out sensor single compensation device G1(s) and looping construct goes out sensor
Whole p second compensation device G2,i(s) after, the practical measurement for sensor exports, and first uses single compensation device G1(s) right
The output of sensor carries out single compensation, then according to p second compensation device G2,i(s) looping construct sequence is using each secondary
Compensator G2,i(s) the single compensation result of sensor measurement output is compensated successively；Second compensation device G2,1(s) input
For single compensation device G1(s) output, second compensation device G2,i(s) input is second compensation device G2,i-1(s) output, wherein i
=2,3 ..., p；Second compensation device G2,p(s) output is the final dynamic compensation result of sensor measurement output.
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