CN108759875B - Sensor dynamic compensation method based on system identification and frequency response correction - Google Patents

Sensor dynamic compensation method based on system identification and frequency response correction Download PDF

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CN108759875B
CN108759875B CN201810564896.4A CN201810564896A CN108759875B CN 108759875 B CN108759875 B CN 108759875B CN 201810564896 A CN201810564896 A CN 201810564896A CN 108759875 B CN108759875 B CN 108759875B
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CN108759875A (en
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杨双龙
杨睿
查富圆
邵春莉
刘厚德
谷恒
徐科军
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Hefei University of Technology
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Abstract

The invention relates to a sensor dynamic compensation method based on system identification and frequency response correction, which combines a time domain identification method and a frequency domain design method and is used for designing a sensor dynamic compensator so as to effectively improve the time-frequency domain dynamic measurement performance of a sensor. Firstly, performing a step response experiment on a sensor to obtain dynamic calibration experiment data of the sensor; secondly, identifying a primary compensator of the sensor by adopting a system identification method, wherein the primary compensator is used for reducing time domain dynamic measurement errors of the sensor; then, according to the frequency response characteristics of the sensor after primary compensation, carrying out error overrun modal analysis and cycle construction of a secondary compensator, and using the error overrun modal analysis and the cycle construction of the secondary compensator for frequency response correction after the primary compensation so as to widen the measurement bandwidth of the sensor; finally, in application, the primary compensator and the secondary compensator are adopted to carry out dynamic compensation on the measurement output of the sensor in sequence, so that the time domain following performance and the frequency domain measurement bandwidth of the dynamic measurement of the sensor are effectively improved.

Description

Sensor dynamic compensation method based on system identification and frequency response correction
Technical Field
The invention relates to a sensor dynamic error correction technology, in particular to a time domain real-time dynamic compensation technology suitable for a sensor dynamic measurement error, which solves the problem that the dynamic measurement bandwidth of a sensor cannot be widened when the existing sensor time domain dynamic compensation technology cannot effectively compensate a low-order error overrun mode.
Background
The dynamic measurement error of the sensor is an important factor for limiting the dynamic measurement bandwidth of the sensor and restricting the dynamic test performance of the sensor. The real-time dynamic compensation of the measurement data of the sensor in the application is an important way for reducing the dynamic measurement error of the sensor and improving the dynamic measurement performance of the sensor. The key to the dynamic compensation of the sensor is the design of the dynamic compensator. Currently, many methods for designing dynamic compensators exist, such as pole-zero placement, system identification, and the like. The pole-zero configuration method is dependent on a dynamic model of a sensor, and mainly comprises the steps of constructing a compensator to enable the pole-zero point of the compensator to be cancelled with unreasonable pole-zero points in the sensor model, and introducing expected pole-zero points of a system, so that the sensor achieves expected dynamic performance after being cascaded with the dynamic compensator. The system identification method is similar to the zero-pole configuration method in nature, but the method does not depend on a sensor dynamic model, and parameters of the sensor dynamic compensator are obtained through identification of actual output and expected output of the sensor, so that a good dynamic compensation effect can be generally obtained. The commonly used system identification methods include a least square method, a prediction error parameter estimation method, a neural network method and the like. Since the dynamic compensation is performed in the time domain, these methods also identify the dynamic compensator for obtaining the sensor based on the criterion of minimizing the time-domain error between the dynamically compensated output of the sensor and the expected output. Although the compensator obtained by the system identification method can generally effectively reduce the step response adjustment time and overshoot of the sensor in the time domain, so as to obtain a relatively good compensation effect, if the error of the high-order modal component in the output signal of the sensor is much larger than the error of the low-order modal component, the compensator obtained by the system identification method often ignores the compensation of the low-order modal with a smaller amplitude component. In this case, if the low-order modal component error exceeds the allowable error band, the compensator may significantly reduce the time-domain dynamic error of the sensor measurement output, but may not effectively widen the dynamic measurement bandwidth of the sensor. For convenience of description, the modal component exceeding the allowable error band is hereinafter referred to as an error over-limit mode. In addition, if the sensor has a non-minimum phase link and a dominant positive zero point is small, the dynamic compensator identified by the system can shorten the step response adjustment time but lengthen the rise time, so that the measurement bandwidth of the sensor is also reduced. For these situations, it is often difficult for the system identification method to obtain a good balance between the time domain response time, the overshoot amount, and the frequency domain measurement bandwidth, thereby affecting the dynamic compensation effect on the sensor measurement output.
Disclosure of Invention
The invention provides a method for designing a primary sensor compensator based on system identification, constructing a secondary sensor compensator based on frequency response correction and dynamically compensating the measurement output of a sensor, aiming at solving the problem that the dynamic measurement bandwidth of the sensor cannot be widened because the existing sensor time domain dynamic compensation technology cannot effectively compensate the low-order error overrun mode.
The technical scheme adopted by the invention is as follows: firstly, performing a dynamic calibration experiment on a sensor by adopting a step response method to obtain step response experiment data of the sensor; secondly, identifying a primary compensator of the sensor by adopting a system identification method, wherein the primary compensator is used for reducing time domain dynamic measurement errors of the sensor; then, analyzing an error overrun mode restricting the measurement bandwidth of the sensor according to the frequency response characteristic of the sensor after primary compensation, and analyzing a cycle structure of a secondary compensator and the error overrun mode after secondary cycle compensation until no error overrun mode exists in the expected measurement bandwidth of the sensor, wherein the obtained secondary compensator is used for correcting the frequency response of each error overrun mode of the sensor after primary compensation so as to widen the measurement bandwidth of the sensor; finally, in application, the measurement output of the sensor is dynamically compensated in sequence by adopting a primary compensator designed by system identification and a secondary compensator constructed, so that the dynamic following performance of time domain measurement is improved, and the frequency domain measurement bandwidth is effectively widened. The transfer function of the quadratic compensator consists of a proportional link, a second order differential link and a second order oscillation link, and the parameters of the transfer function are calculated according to amplitude-frequency curves of various error overrun modes.
The technical process of the invention comprises the following steps: dynamic step response experiment 1 → primary compensator identification 2 → secondary compensator loop construction 3 → sensor time domain dynamic compensation 4, as shown in fig. 1.
The dynamic step response experiment 1 is to perform a dynamic calibration experiment on the sensor by using a step response method to obtain a step input signal x (t) and a response output signal y (t).
The primary compensator identification 2 is the primary compensator G for designing the sensor by adopting a system identification method in the time domain according to the input signal x (t) and the response output signal y (t) of the step response experiment of the sensor1(s)。
And the secondary compensator cyclic structure 3 is an error overrun mode which restricts the measurement bandwidth of the sensor according to the frequency response characteristic analysis of the sensor after primary compensation, and the cyclic structure of the secondary compensator and the cyclic analysis of the error overrun mode after secondary compensation are carried out until no error overrun mode exists in the expected measurement bandwidth of the sensor. The cycle flow of the secondary compensator cycle structure 3 is the pre-compensation frequency response calculation 5 → the error overrun mode judgment 6 → the low-order error overrun mode analysis 7 → the secondary compensator structure 8, and the cycle end condition is that the judgment result of the error overrun mode judgment 6 is the error-free overrun mode.
Front compensation frequency response calculation 5: the step is that the frequency response function of the sensor after being compensated by the primary compensator designed in the front and the secondary compensator constructed in a circulating way is calculated, and the calculation is divided into two conditions of primary pre-compensation frequency response calculation and secondary pre-circulation compensation frequency response calculation. Calculating the primary pre-compensation frequency response, namely calculating the pre-compensation frequency response when entering the first circulation after the circulation structure 3 process of the secondary compensator, and respectively calculating the frequency response function G of the sensor0(j ω) and frequency response function G of primary compensator1(j omega), then multiplying the two to obtain the front compensation frequency response M of the sensor after primary compensation1(j ω) and amplitude-frequency characteristic | M thereof1(jω)|＝|G0(jω)G1(j ω) |; calculating the secondary circulation pre-compensation frequency response, namely calculating the pre-compensation frequency response after the 2 nd circulation after entering the 3 flow of the secondary compensator circulation structure, and calculating the secondary compensator G of the i-1 th circulation structure in the i-th circulation2,i-1Frequency response function G of(s)2,i-1(j ω), and then calculating the pre-compensation frequency response M of the i-1 th cyclei-1(j ω) and G2,i-1Multiplying (j omega) to obtain the pre-compensation frequency response M of the sensor in the ith cyclei(j ω) and amplitude-frequency characteristic | M thereofi(jω)|＝|Mi-1(jω)G2,i-1(jω)|。
And 6, judging an error overrun mode: this step is the desired measurement bandwidth [0, ω ] at the sensorbd]Internal assay Mi(j ω) whether or not there is a band e of an amplitude exceeding the allowable errortolError overrun mode mi. If M isiIf the (j omega) has an error overrun mode, performing subsequent low-order error overrun mode analysis 7 and secondary compensator structure 8, and circulating; if M isiIn the error-free overrun mode (j ω), the quadratic compensator loop configuration 3 ends.
And (3) performing low-order error overrun modal analysis 7: the step is that under the condition that the error overrun mode judgment 6 judges that the error overrun mode exists, the front compensation frequency response M of the secondary compensator circulation structure 3 in the ith circulation is analyzedi(j ω) at the desired measurement bandwidth [0, ω ] of the sensorbd]Inner lowest order error overrun mode miType of (2), error overrun band
Figure BDA0001684282300000033
And an extremum point frequency. The typical error overrun modes are divided into 4 types according to the following judgment rules:
MD1 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolIf only one peak exists or only one trough exists, the frequency band is considered to have an MD1 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000031
miHas an extreme point frequency of ωem。
MD2 type: in a continuous frequency band [ omega ]l,ωh]Inner, | Mi(j ω) | appears as a pair of adjacent peaks and valleys, and | M | except for the transition band between the peaks and valleysi(jω)|-1|＞etolIf so, the frequency band is considered to have an MD2 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000032
miHas an extreme point frequency of omegae1And ωe2And omegae1＜ωe2。
MD3 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd two continuous wave crests or two wave troughs exist, and the sum E of the amplitude differences of the extreme points of the two wave crests or the two wave troughs and the middle reverse extreme point thereof is less than or equal to 3EtolIf there is an error overrun mode of MD3 class in the continuous frequency band; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000041
miThe extreme point frequency of (2) is taken as the average value omega of the extreme point frequencies of two wave crests or two wave troughsem。
MD4 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd two continuous wave crests or two continuous wave troughs exist, and the sum of the amplitude differences of the extreme points of the two wave crests or the two wave troughs and the reverse extreme point in the middle of the two wave crests or the two wave troughs is more than 3EtolThen, it is determined that there are two consecutive MD4 errors in the continuous frequency bandA difference overrun mode; if the low-order mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be miLet m beiIn the continuous frequency band [ omega ]l,ωh]The frequency of the inner intermediate inverse extremum is ωmThen m isiError over-limit band of
Figure BDA0001684282300000042
miHas an extreme point frequency of ωem。
In the MD3 and MD4 error overrun modes, the sum E of the amplitude differences between two consecutive peaks or two valley extreme points and the opposite extreme point therebetween is calculated according to the following formula:
E＝|A1-B|+|A2-B|
in the above formula, a1 and a2 are the amplitudes of the extreme points of two continuous peaks or two troughs, respectively, and B is the amplitude of the opposite extreme point between the two peaks or two troughs.
Secondary compensator structure 8: this step is for Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]Inner lowest order error overrun mode miConstructing a secondary compensator G corresponding thereto2,i(s) for the over-error mode miAnd carrying out frequency response correction. Secondary compensator G2,iAnd(s) is characterized by adopting a transfer function consisting of a proportional element, a second-order differential element and a second-order oscillation element.
Figure BDA0001684282300000043
Let ζ be1/ζ2＝λ、ωn1/ωn2β, get G2,i(s) has the following amplitude-frequency characteristics
Figure BDA0001684282300000044
Above | G2,iThe curve form of (j ω) | has a feature that when β is 1, | G2,i(j ω) | has only one wavePeak or trough, and the frequency of extreme point of peak or trough is omegan2The amplitude of the extreme point is lambda, and when β is not equal to 1, | G2,i(j omega) I has a pair of adjacent wave crest and wave trough, and when β is less than 1, the wave trough is in front and the wave crest is behind, when β is more than 1, the wave crest is in front and the wave trough is behind, and the product of extreme point frequencies of the wave crest and the wave trough
Figure BDA0001684282300000045
When ω → 0, | G2,i(j ω) | → 1, and when ω → + ∞ G2,i(jω)|→1/β2. Accordingly, the invention calculates the secondary compensator G of each type of error overrun mode by adopting the following method under the following two conditions aiming at 4 types of typical error overrun modes in the low-order error overrun mode analysis 72,i(s) is determined.
The first condition is as follows: aiming at typical error overrun modes m of MD1, MD3 and MD4 in the low-order error overrun mode analysis 7iSecondary compensator G thereof2,iThe calculation steps of(s) are:
① takes β ═ 1, ωn2＝ωemLet the correction band
Figure BDA0001684282300000051
② according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Different discrete frequency points omega inkLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure BDA0001684282300000052
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1，q2,…,qN]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure BDA0001684282300000053
Figure BDA0001684282300000054
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in.
③ solving the above equation system by least square method to obtain lambda and zeta2。
④ according to ζ1＝λζ2、ωn1＝ωn2Calculate zeta1、ωn1。
⑤ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)。
Case two: aiming at the typical error overrun mode m of MD2 class in the low-order error overrun mode analysis 7iSecondary compensator G thereof2,iThe calculation steps of(s) are:
① order correction band
Figure BDA0001684282300000055
② determining β value interval B, because omega → + ∞ time | G2,i(jω)|→1/β2To reduce the secondary compensator pair correction band [ omega ]low,ωup]Influence of external sensor frequency response characteristic, ensuring |1/β in secondary compensator design2-1|≤etol/2, i.e.
Figure BDA0001684282300000056
If M isiMode m in (j ω)iWith the wave crest in front and the wave trough in back, i.e. requiring | G2,iThe trough of (j omega) is at the front and the peak is at the frontThen, the value interval of β is taken
Figure BDA00016842823000000511
If M isiMode m in (j ω)iWith the trough in front and the crest in back, i.e. requiring | G2,iThe peak of (j omega) is in front of the trough, the trough is in back, and the value interval of β is taken
Figure BDA0001684282300000058
③ taking W β values [ β ] in equal step length in the value interval B(1),β(2),β(3),...,β(W)]β are sequentially mixed(l)Substituted type
Figure BDA0001684282300000059
β in (1) calculate W ωn2Value of
Figure BDA00016842823000000510
Wherein l is 1,2,3, …, W.
④ according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Different discrete frequency points omega inkLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure BDA0001684282300000061
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1，q2,…,qn]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure BDA0001684282300000062
Figure BDA0001684282300000063
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in.
⑤ in turn will β(l)And
Figure BDA0001684282300000064
substituting the formula into the formula, and calculating corresponding W groups of parameters lambda by adopting a least square method(l)And
Figure BDA0001684282300000065
where l is 1,2,3, …, W.
⑥ grouping the W sets of parameters
Figure BDA0001684282300000066
Substituting the amplitude-frequency characteristic | G of the secondary compensator in sequence2,iIn the calculation formula of (j omega) I, the amplitude-frequency characteristics of W secondary compensators are obtained
Figure BDA0001684282300000067
Where l is 1,2,3, …, W.
⑦ in the correction band [ omega ]low,ωup]Inner inspection of each
Figure BDA0001684282300000068
Reservation of satisfaction condition
Figure BDA0001684282300000069
Is/are as follows
Figure BDA00016842823000000610
⑧ remaining from the previous step
Figure BDA00016842823000000611
In which one is selected to
Figure BDA00016842823000000612
Minimum size
Figure BDA00016842823000000613
Corresponding parameters thereof
Figure BDA00016842823000000614
Figure BDA00016842823000000615
I.e. the error over-limit mode miThe optimal solution parameters β, lambda and zeta of the quadratic compensator2、ωn2。
⑨ according to ζ1＝λζ2、ωn1＝βωn2Calculated zeta1、ωn1。
⑩ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)。
The sensor time domain dynamic compensation 4 is the identification of the primary compensator G in the sensor by the primary compensator identification 21(s) and the second order compensator cycle construction 3 cycle construction of all the p second order compensators G2,i(s) thereafter, for the actual measured output of the sensor, a primary compensator G is first employed1(s) performing a primary compensation of the sensor output, followed by p secondary compensators G2,i(s) the cyclic structure sequence of which uses the secondary compensators G2,i(s) sequentially compensating the primary compensation results output by the sensor; secondary compensator G2,1(s) input to a primary compensator G1(s) output, secondary compensator G2,i(s) input as a quadratic compensator G2,i-1(s), wherein i is 2,3, …, p; secondary compensator G2,pThe output of(s) is the final dynamic compensation result of the sensor measurement output.
The method of the invention has the advantages that: the primary compensator obtained by the time domain system identification method can be used for improving the time domain following performance of dynamic measurement of the sensor, and the secondary compensator constructed based on frequency response correction can be used for correcting the low-order error overrun mode which is not effectively compensated by the primary compensator from the frequency domain, so that the time domain following performance of the dynamic measurement of the sensor and the frequency domain measurement bandwidth are effectively improved.
Drawings
FIG. 1 is a block diagram of the technical process of the method of the present invention, i.e. a flow chart of the sensor dynamic compensation technical scheme based on system identification and frequency response correction;
FIG. 2 is a schematic diagram of the calculation of the pre-compensation frequency response in the ith cycle of the cycle configuration process of the quadratic compensator according to the embodiment of the present invention;
FIG. 3 is a schematic diagram of an exemplary over-error mode of an embodiment of the present invention;
FIG. 4 is a schematic diagram of typical error-overrun modal extremes for MD3 and MD4, in accordance with an embodiment of the present invention;
FIG. 5 shows typical error over-limit modes m of the MD1, MD3 and MD4, in accordance with an embodiment of the present inventioniSecond order compensator G2,i(s) a computational flow diagram;
FIG. 6 shows an exemplary error over-limit mode m of class MD2 according to an embodiment of the present inventioniSecond order compensator G2,i(s) a computational flow diagram;
FIG. 7 is a flow chart of sensor time domain dynamics compensation according to an embodiment of the present invention;
FIG. 8 is a graph of the effect of dynamic compensation of a strain gauge force sensor using the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
the design idea of the invention is as follows: aiming at the problems of large dynamic measurement error and low measurement bandwidth of the sensor, firstly, designing a primary compensator of the sensor by adopting a time domain system identification method based on dynamic step response experimental data of the sensor so as to greatly reduce the time domain dynamic measurement error of the sensor and improve the time domain dynamic following performance measured by the sensor; then, aiming at the error overrun mode which is not effectively compensated by the primary compensator in the expected measurement bandwidth, carrying out secondary compensator circulation construction and circulation analysis of frequency response after secondary compensation until a secondary compensator of all the error overrun modes is constructed, so as to carry out frequency response correction on each error overrun mode, reduce the amplitude error to an allowable error band, and effectively improve the frequency domain measurement bandwidth of the sensor; therefore, in practical application, the actual measurement output signal of the sensor can be dynamically compensated by adopting the primary compensator and then adopting the secondary compensator in sequence, so that the time domain dynamic following performance and the frequency domain measurement bandwidth measured by the sensor are effectively improved.
The technical scheme of the invention is shown in a flow chart in figure 1. Firstly, obtaining dynamic calibration experiment data of a sensor through a dynamic step response experiment 1; secondly, acquiring a primary compensator of the sensor through the primary compensator identification 2; thirdly, a secondary compensator of each error overrun mode of the sensor in the expected measurement bandwidth is analyzed and constructed through a secondary compensator circulating construction 3; and finally, dynamically compensating the output signal measured by the sensor in sequence by adopting the identified primary compensator and the circularly constructed secondary compensator through the sensor time domain dynamic compensation 4.
The dynamic step response experiment 1 is to perform a dynamic calibration experiment on the sensor by using a step response method to obtain dynamic calibration experiment data of the sensor, and the dynamic calibration experiment data is used for subsequent primary compensator identification and secondary compensator construction. In the experiment, step excitation is applied to the sensor, and a step input signal x (t) and a step response output signal y (t) of the sensor are synchronously acquired through the signal acquisition equipment.
The primary compensator identification 2 is the primary compensator G for designing the sensor by adopting a system identification method in the time domain according to the input signal x (t) and the response output signal y (t) of the step response experiment of the sensor1(s)。
And the secondary compensator cyclic structure 3 is an error overrun mode which restricts the measurement bandwidth of the sensor according to the frequency response characteristic analysis of the sensor after primary compensation, and the cyclic structure of the secondary compensator and the cyclic analysis of the error overrun mode after secondary compensation are carried out until no error overrun mode exists in the expected measurement bandwidth of the sensor. The cycle flow of the secondary compensator cycle structure 3 is the pre-compensation frequency response calculation 5 → the error overrun mode judgment 6 → the low-order error overrun mode analysis 7 → the secondary compensator structure 8, and the cycle end condition is that the judgment result of the error overrun mode judgment 6 is the error-free overrun mode.
The calculation schematic diagram of the pre-compensation frequency response calculation 5 is shown in fig. 2, that is, the frequency response function of the calculation sensor after being compensated by the primary compensator and the secondary compensator with a cyclic structure in the foregoing design is divided into two cases of the primary pre-compensation frequency response calculation and the secondary pre-cyclic compensation frequency response calculation. Calculating the primary pre-compensation frequency response, namely calculating the pre-compensation frequency response when entering the first circulation after the circulation structure 3 process of the secondary compensator, and respectively calculating the frequency response function G of the sensor0(j ω) and frequency response function G of primary compensator1(j omega), then multiplying the two to obtain the front compensation frequency response M of the sensor after primary compensation1(j ω) and amplitude-frequency characteristic | M thereof1(jω)|＝|G0(jω)G1(j ω) |; calculating the secondary circulation pre-compensation frequency response, namely calculating the pre-compensation frequency response after the 2 nd circulation after entering the 3 flow of the secondary compensator circulation structure, and calculating the secondary compensator G of the i-1 th circulation structure in the i-th circulation2,i-1Frequency response function G of(s)2,i-1(j ω), and then calculating the pre-compensation frequency response M of the i-1 th cyclei-1(j ω) and G2,i-1Multiplying (j omega) to obtain the pre-compensation frequency response M of the sensor in the ith cyclei(j ω) and amplitude-frequency characteristic | M thereofi(jω)|＝|Mi-1(jω)G2,i-1(jω)|。
An over-error mode decision 6, i.e., the expected measurement bandwidth [0, ω ] at the sensorbd]Internal assay Mi(j ω) whether or not there is a band e of an amplitude exceeding the allowable errortolError overrun mode mi. If M isiIf the (j omega) has an error overrun mode, performing subsequent low-order error overrun mode analysis 7 and secondary compensator structure 8, and circulating; if M isiIn the error-free overrun mode (j ω), the quadratic compensator loop configuration 3 ends.
A low-order error overrun mode analysis 7, namely, a secondary compensator circulation structure is analyzed under the condition that the error overrun mode judgment 6 judges that an error overrun mode existsMake 3 a pre-compensation frequency response M in the i-th cyclei(j ω) at the desired measurement bandwidth [0, ω ] of the sensorbd]Inner lowest order error overrun mode miType of (2), error overrun band
Figure BDA0001684282300000091
And an extremum point frequency. The typical error overrun modes are classified into 4 types according to the following judgment rules, and the schematic diagram is shown in fig. 3:
MD1 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolIf only one peak exists or only one trough exists, the frequency band is considered to have an MD1 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000092
miHas an extreme point frequency of ωem。
MD2 type: in a continuous frequency band [ omega ]l,ωh]Inner, | Mi(j ω) | appears as a pair of adjacent peaks and valleys, and | M | except for the transition band between the peaks and valleysi(jω)|-1|＞etolIf so, the frequency band is considered to have an MD2 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000093
miHas an extreme point frequency of omegae1And ωe2And omegae1＜ωe2。
MD3 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd having two successive peaks or two troughs, two peaks or two troughs having extreme points with opposite extreme points therebetweenThe sum of amplitude differences E is less than or equal to 3EtolIf there is an error overrun mode of MD3 class in the continuous frequency band; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure BDA0001684282300000094
miThe extreme point frequency of (2) is taken as the average value omega of the extreme point frequencies of two wave crests or two wave troughsem。
MD4 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd two continuous wave crests or two continuous wave troughs exist, and the sum of the amplitude differences of the extreme points of the two wave crests or the two wave troughs and the reverse extreme point in the middle of the two wave crests or the two wave troughs is more than 3EtolIf two continuous MD4 error overrun modes exist in the continuous frequency band; if the low-order mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be miLet m beiIn the continuous frequency band [ omega ]l,ωh]The frequency of the inner intermediate inverse extremum is ωmThen m isiError over-limit band of
Figure BDA0001684282300000095
miHas an extreme point frequency of ωem。
In the MD3 and MD4 error overrun modes, the sum E of the amplitude differences between two consecutive peaks or two valley extreme points and the opposite extreme point therebetween is calculated according to the following formula:
E＝|A1-B|+|A2-B|
in the above formula, a1 and a2 are the amplitudes of the extreme points of two continuous peaks or two continuous valleys, respectively, and B is the amplitude of the opposite extreme point between the two peaks or two continuous valleys, as shown in fig. 4.
The secondary compensator configuration 8 being for Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]Inner lowest order error overrun mode miConstructing a secondary complement corresponding theretoPayment device G2,i(s) for the over-error mode miAnd carrying out frequency response correction. Secondary compensator G2,i(s) is characterized by a transfer function consisting of a proportional element, a second order differential element and a second order oscillation element as follows:
Figure BDA0001684282300000101
let ζ be1/ζ2＝λ、ωn1/ωn2β, get G2,i(s) has the following amplitude-frequency characteristics
Figure BDA0001684282300000102
Above | G2,iThe curve form of (j ω) | has a feature that when β is 1, | G2,i(j ω) | has only one peak or trough, and the frequency of the extreme point of the peak or trough is ωn2The amplitude of the extreme point is lambda, and when β is not equal to 1, | G2,i(j omega) I has a pair of adjacent wave crest and wave trough, and when β is less than 1, the wave trough is in front and the wave crest is behind, when β is more than 1, the wave crest is in front and the wave trough is behind, the product of extreme point frequencies of the wave crest and the wave trough is
Figure BDA0001684282300000103
When ω → 0, | G2,i(j ω) | → 1, and when ω → + ∞ G2,i(jω)|→1/β2. Accordingly, the invention calculates the secondary compensator G of each type of error overrun mode by adopting the following method under the following two conditions aiming at 4 types of typical error overrun modes in the low-order error overrun mode analysis 72,i(s) is determined.
The first condition is as follows: aiming at typical error overrun modes m of MD1, MD3 and MD4 in the low-order error overrun mode analysis 7iSecondary compensator G thereof2,iThe calculation flow of(s) is shown in fig. 5, and the specific calculation steps are as follows:
① takes β ═ 1, ωn2＝ωemLet the correction band
Figure BDA0001684282300000104
② according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Different discrete frequency points omega inkLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure BDA0001684282300000105
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1,q2,…,qN]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure BDA0001684282300000106
Figure BDA0001684282300000111
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in.
③ solving the above equation system by least square method to obtain lambda and zeta2。
④ according to ζ1＝λζ2、ωn1＝ωn2Calculate zeta1、ωn1。
⑤ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)。
Case two: for the low orderTypical error overrun mode m of class MD2 in error overrun mode analysis 7iSecondary compensator G thereof2,iThe calculation flow of(s) is shown in fig. 6, and the specific calculation steps are as follows:
① order correction band
Figure BDA0001684282300000112
② determining β value interval B, because omega → + ∞ time | G2,i(jω)|→1/β2To reduce the secondary compensator pair correction band [ omega ]low,ωup]Influence of external sensor frequency response characteristic, ensuring |1/β in secondary compensator design2-1|≤etol/2, i.e.
Figure BDA0001684282300000113
If M isiMode m in (j ω)iWith the wave crest in front and the wave trough in back, i.e. requiring | G2,iThe trough of (j omega) is in front of the crest of the wave, and the value interval of β is taken
Figure BDA0001684282300000114
If M isiMode m in (j ω)iWith the trough in front and the crest in back, i.e. requiring | G2,iThe peak of (j omega) is in front of the trough, the trough is in back, and the value interval of β is taken
Figure BDA0001684282300000115
③ taking W β values [ β ] in equal step length in the value interval B(1),β(2),β(3),...,β(W)]β are sequentially mixed(l)Substituted type
Figure BDA0001684282300000116
β in (1) calculate W ωn2Value of
Figure BDA0001684282300000117
Wherein l is 1,2,3, …, W.
④ according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Inside ofDifferent discrete frequency points omegakLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure BDA0001684282300000118
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1,q2,…,qn]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure BDA0001684282300000119
Figure BDA00016842823000001110
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in.
⑤ in turn will β(l)And
Figure BDA00016842823000001111
substituting the formula into the formula, and calculating corresponding W groups of parameters lambda by adopting a least square method(l)And
Figure BDA0001684282300000121
where l is 1,2,3, …, W.
⑥ grouping the W sets of parameters
Figure BDA0001684282300000122
Substituting the amplitude-frequency characteristic | G of the secondary compensator in sequence2,iIn the calculation formula of (j omega) I, the amplitude-frequency characteristics of W secondary compensators are obtained
Figure BDA0001684282300000123
Where l is 1,2,3, …, W.
⑦ in the correction band [ omega ]low,ωup]Inner inspection of each
Figure BDA0001684282300000124
Reservation of satisfaction condition
Figure BDA0001684282300000125
Is/are as follows
Figure BDA0001684282300000126
⑧ remaining from the previous step
Figure BDA0001684282300000127
In which one is selected to
Figure BDA0001684282300000128
Minimum size
Figure BDA0001684282300000129
Corresponding parameters thereof
Figure BDA00016842823000001210
Figure BDA00016842823000001211
I.e. the error over-limit mode miThe optimal solution parameters β, lambda and zeta of the quadratic compensator2、ωn2。
⑨ according to ζ1＝λζ2、ωn1＝βωn2Calculated zeta1、ωn1。
⑩ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)。
The flow of the sensor time domain dynamic compensation 4 is shown in fig. 7, namely, the sensor is located at the sensor stationThe primary compensator identification 2 identifies the primary compensator G1(s) and the second order compensator cycle construction 3 cycle construction of all the p second order compensators G2,i(s) thereafter, for the actual measured output of the sensor, a primary compensator G is first employed1(s) performing a primary compensation of the sensor output, followed by p secondary compensators G2,i(s) the cyclic structure sequence of which uses the secondary compensators G2,i(s) sequentially compensating the primary compensation results output by the sensor; secondary compensator G2,1(s) input to a primary compensator G1(s) output, secondary compensator G2,i(s) input as a quadratic compensator G2,i-1(s), wherein i is 2,3, …, p; secondary compensator G2,pThe output of(s) is the final dynamic compensation result of the sensor measurement output.
Fig. 8 is a diagram showing the effect of dynamic compensation of a strain gauge force sensor using the method of the present invention. The allowable error band for the dynamic measurement of the sensor is + -5%, and the expected measurement bandwidth is 100 Hz. Firstly, carrying out a dynamic calibration experiment on the sensor by adopting the dynamic step response experiment 1; and identifying and obtaining a primary compensator G by adopting the primary compensator identification 2 according to the step response dynamic calibration experimental data of the sensor1(s); then, a secondary compensator G for obtaining a MD2 error overrun mode of the sensor is constructed by the secondary compensator loop construction 32,1(s) and a quadratic compensator G of the MD1 class error overrun mode2,2(s); finally, using G1(s)、G2,1(s)、G2,2(s) sequentially compensating for sensor step response measurement outputs. FIG. 8(a) shows an amplitude-frequency characteristic curve s0 of the sensor and a primary compensator G1Amplitude-frequency characteristic curve s1 of(s) and sensor through primary compensator G1(s) amplitude-frequency characteristic curve s2 after compensation; in FIG. 8(b), the sensors are respectively passed through a primary compensator G1Amplitude-frequency characteristic curve s2 after(s) compensation, quadratic compensator G2,1Amplitude-frequency characteristic curve s3 of(s) and sensor G1(s)、G2,1(s) amplitude-frequency characteristic curve s4 after compensation in turn; in FIG. 8(c), the sensor passes G1(s)、G2,1(s) isAmplitude-frequency characteristic curve s4 after secondary compensation, and secondary compensator G2,2Amplitude-frequency characteristic curve s5 of(s) and sensor G1(s)、G2,1(s)、G2,2(s) amplitude-frequency characteristic curve s6 after compensation in turn; fig. 8(d) shows the sensor step response curve c0 and the dynamically compensated step response curve c 1. As can be seen from fig. 8, after the sensor is subjected to the primary compensation and the secondary compensation, the time domain dynamic error is greatly reduced, and the frequency domain measurement bandwidth is also greatly increased.

Claims (5)

1. A sensor dynamic compensation method based on system identification and frequency response correction is used for designing a dynamic compensator of a sensor according to dynamic calibration experiment data of the sensor, and dynamically compensating actual measurement output of the sensor so as to improve time domain following performance and frequency domain measurement bandwidth of dynamic measurement of the sensor, and comprises the following technical processes: dynamic step response experiment, primary compensator discernment, secondary compensator loop structure, sensor time domain dynamic compensation, its characterized in that:
firstly, acquiring dynamic calibration experiment data of the sensor through a dynamic step response experiment; then, identifying a primary compensator of the sensor by adopting a system identification method; then, carrying out error overrun modal analysis and cycle construction of a secondary compensator according to the frequency response characteristic of the sensor after primary compensation to obtain the secondary compensator of the sensor; in practical measurement application, a primary compensator and a secondary compensator are adopted to dynamically compensate the measurement output of the sensor in sequence.
2. The method of claim 1, wherein the sensor dynamic compensation method based on system identification and frequency response correction comprises: the secondary compensator is in a circulating structure, namely an error overrun mode which restricts the measurement bandwidth of the sensor according to the frequency response characteristic analysis of the sensor after primary compensation, and the circulating structure of the secondary compensator and the circulating analysis of the error overrun mode after secondary compensation are carried out until no error overrun mode exists in the expected measurement bandwidth of the sensor; the circulating steps of the circulating structure of the secondary compensator are as follows: calculating front compensation frequency response → judging error overrun mode → analyzing low-order error overrun mode → constructing secondary compensator, the condition of cycle ending is that the result of judging error overrun mode is error-free overrun mode;
the front compensation frequency response calculation is divided into two conditions of primary front compensation frequency response calculation and secondary circulation front compensation frequency response calculation for calculating a frequency response function of the sensor after the sensor is compensated by the primary compensator designed in the front and the secondary compensator constructed in a circulation manner; calculating the primary pre-compensation frequency response, namely calculating the pre-compensation frequency response when entering the first circulation after the circulation construction process of the secondary compensator, and respectively calculating the frequency response function G of the sensor0(j ω) and frequency response function G of primary compensator1(j omega), then multiplying the two to obtain the front compensation frequency response M of the sensor after primary compensation1(j ω) and amplitude-frequency characteristic | M thereof1(jω)|＝|G0(jω)G1(j ω) |; calculating the compensation frequency response before the second cycle, namely calculating the compensation frequency response before the 2 nd cycle after entering the cycle construction process of the secondary compensator, and calculating the secondary compensator G with the i-1 st cycle construction in the i-th cycle2,i-1Frequency response function G of(s)2,i-1(j ω), and then calculating the pre-compensation frequency response M of the i-1 th cyclei-1(j ω) and G2,i-1Multiplying (j omega) to obtain the pre-compensation frequency response M of the sensor in the ith cyclei(j ω) and amplitude-frequency characteristic | M thereofi(jω)|＝|Mi-1(jω)G2,i-1(jω)|；
The error overrun mode judgment is the expected measurement bandwidth [0, omega ] of the sensorbd]Internal assay Mi(j ω) whether or not there is a band e of an amplitude exceeding the allowable errortolError overrun mode mi(ii) a If M isi(j omega) if an error overrun mode exists, performing subsequent low-order error overrun mode analysis and secondary compensator construction, and circulating; if M isi(j ω) in the error-free overrun mode, the secondary compensator loop construction process is ended;
the low-order error overrun mode analysis is to analyze the pre-compensation frequency response M of the circulation construction process of the secondary compensator in the ith circulation under the condition that the error overrun mode is judged in the error overrun mode judgment stepi(j ω) expectation at sensorMeasuring bandwidth 0, omegabd]Inner lowest order error overrun mode miType of (2), error overrun band
Figure FDA0002407037520000021
And an extreme point frequency;
the secondary compensator is constructed as for Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]Inner lowest order error overrun mode miConstructing a secondary compensator G corresponding thereto2,i(s) for the over-error mode miAnd carrying out frequency response correction.
3. The method of claim 2, wherein the sensor dynamic compensation method based on system identification and frequency response correction comprises: the low-order error overrun modal analysis in the secondary compensator circulation construction process divides typical error overrun modes into four types of MD1, MD2, MD3 and MD 4; type of typical error overrun mode, front compensation frequency response Mi(j ω) at the desired measurement bandwidth [0, ω ] of the sensorbd]Inner lowest order error overrun mode mi、miError over-limit band of
Figure FDA0002407037520000022
And miThe judgment rule of the extreme point frequency is as follows:
MD1 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolIf only one peak exists or only one trough exists, the frequency band is considered to have an MD1 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure FDA0002407037520000023
miHas an extreme point frequency of ωem；
MD2 type: in a continuous frequency band [ omega ]l,ωh]Inner, | Mi(j ω) | appears as a pair of adjacent peaks and valleys, and | M | except for the transition band between the peaks and valleysi(jω)|-1|＞etolIf so, the frequency band is considered to have an MD2 type error overrun mode; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure FDA0002407037520000024
miHas an extreme point frequency of omegae1And ωe2And omegae1＜ωe2；
MD3 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd two continuous wave crests or two wave troughs exist, and the sum E of the amplitude differences of the extreme points of the two wave crests or the two wave troughs and the middle reverse extreme point thereof is less than or equal to 3EtolIf there is an error overrun mode of MD3 class in the continuous frequency band; if the mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be mi，miError over-limit band of
Figure FDA0002407037520000025
miThe extreme point frequency of (2) is taken as the average value omega of the extreme point frequencies of two wave crests or two wave troughsem；
MD4 type: in a continuous frequency band [ omega ]l,ωh]Inner, | | Mi(jω)|-1|＞etolAnd two continuous wave crests or two continuous wave troughs exist, and the sum of the amplitude differences of the extreme points of the two wave crests or the two wave troughs and the reverse extreme point in the middle of the two wave crests or the two wave troughs is more than 3EtolIf two continuous MD4 error overrun modes exist in the continuous frequency band; if the low-order mode is Mi(j ω) at the desired measurement bandwidth [0, ω [ ]bd]The lowest order error over-limit mode in the interior is made to be miLet m beiIn the continuous frequency band [ omega ]l,ωh]The frequency of the inner intermediate inverse extremum is ωmThen m isiError over-limit band of
Figure FDA0002407037520000031
miHas an extreme point frequency of ωem；
In the MD3 and MD4 error overrun modes, the sum E of the amplitude differences between two consecutive peaks or two valley extreme points and the opposite extreme point therebetween is calculated according to the following formula:
E＝|A1-B|+|A2-B|
in the above formula, a1 and a2 are the amplitudes of the extreme points of two continuous peaks or two troughs, respectively, and B is the amplitude of the opposite extreme point between the two peaks or two troughs.
4. The method of claim 2, wherein the sensor dynamic compensation method based on system identification and frequency response correction comprises: in the secondary compensator structure in the secondary compensator circulation structure flow, the secondary compensator G2,i(s) is characterized by a transfer function consisting of a proportional element, a second order differential element and a second order oscillation element as follows:
Figure FDA0002407037520000032
let ζ be1/ζ2＝λ、ωn1/ωn2β, get G2,iThe amplitude-frequency characteristics of(s) are as follows:
Figure FDA0002407037520000033
secondary compensator G2,iThe calculation of(s) is divided into the following two cases:
case one, aiming at typical error overrun mode m of MD1, MD3 and MD4 in the low-order error overrun mode analysisiSecondary compensator G thereof2,iThe calculation steps of(s) are:
① takes β ═ 1, ωn2＝ωemLet the correction band
Figure FDA0002407037520000034
② according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Different discrete frequency points omega inkLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure FDA0002407037520000035
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1,q2,…,qN]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure FDA0002407037520000036
Figure FDA0002407037520000041
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in;
③ solving the above equation system by least square method to obtain lambda and zeta2；
④ according to ζ1＝λζ2、ωn1＝ωn2Calculate zeta1、ωn1；
⑤ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)；
Case two, aiming at the typical error overrun mode m of MD2 type in the low-order error overrun mode analysisiSecondary compensator G thereof2,iThe calculation steps of(s) are:
① order correction band
Figure FDA0002407037520000042
② determining β value interval B, because omega → + ∞ time | G2,i(jω)|→1/β2To reduce the secondary compensator pair correction band [ omega ]low,ωup]Influence of external sensor frequency response characteristic, ensuring |1/β in secondary compensator design2-1|≤etol/2, i.e.
Figure FDA0002407037520000043
If M isiMode m in (j ω)iWith the wave crest in front and the wave trough in back, i.e. requiring | G2,iThe trough of (j omega) is in front of the crest of the wave, and the value interval of β is taken
Figure FDA0002407037520000044
Figure FDA0002407037520000045
If M isiMode m in (j ω)iWith the trough in front and the crest in back, i.e. requiring | G2,iThe peak of (j omega) is in front of the trough, the trough is in back, and the value interval of β is taken
Figure FDA0002407037520000046
③ taking W β values [ β ] in equal step length in the value interval B(1),β(2),β(3),...,β(W)]β are sequentially mixed(l)Substituted type
Figure FDA0002407037520000047
β in (1) calculate W ωn2Value of
Figure FDA0002407037520000048
Wherein, l is 1,2,3, …, W;
④ according to the desired compensation effect of the quadratic compensator, in the correction band [ omega ]low,ωup]Different discrete frequency points omega inkLet | G2,i(jωk)|＝1/|Mi(jωk) And substituting the amplitude-frequency characteristic | G of the secondary compensator2,i(j ω) | and the formula is then compiled into the following linear system of equations
Figure FDA0002407037520000049
In the above formula, the first and second carbon atoms are,
U＝[U1,U2]，Q＝[q1,q2,…,qn]T
U1＝[u11,u12,…,u1N]T，U2＝[u21,u22,…,u2N]T
Figure FDA00024070375200000410
Figure FDA00024070375200000411
where k is 1,2, … …, and N is the correction band [ ω [ N ] ]low,ωup]The number of discrete frequency points in;
⑤ in turn will β(l)And
Figure FDA00024070375200000412
substituting the formula into the formula, and calculating corresponding W groups of parameters lambda by adopting a least square method(l)And
Figure FDA0002407037520000051
wherein l is 1,2,3, …, W;
⑥ grouping the W sets of parametersβ(l)、λ(l)、
Figure FDA0002407037520000052
Substituting the amplitude-frequency characteristic | G of the secondary compensator in sequence2,iIn the calculation formula of (j omega) I, the amplitude-frequency characteristics of W secondary compensators are obtained
Figure FDA0002407037520000053
Wherein l is 1,2,3, …, W;
⑦ in the correction band
Figure FDA0002407037520000054
Inner inspection of each
Figure FDA0002407037520000055
Reservation of satisfaction condition
Figure FDA0002407037520000056
Is/are as follows
Figure FDA0002407037520000057
⑧ remaining from the previous step
Figure FDA0002407037520000058
In which one is selected to
Figure FDA0002407037520000059
Minimum size
Figure FDA00024070375200000510
Its corresponding parameter β(l)、λ(l)、
Figure FDA00024070375200000511
I.e. the error over-limit mode miThe optimal solution parameters β, lambda and zeta of the quadratic compensator2、ωn2；
⑨ according to ζ1＝λζ2、ωn1＝βωn2Calculated zeta1、ωn1；
⑩ will ζ1、ζ2、ωn1、ωn2Substituted into a secondary compensator G2,i(s) obtaining M from the expression of the transfer functioniError overrun mode m in (j omega)iSecond order compensator G2,i(s)。
5. The method of claim 1, wherein the sensor dynamic compensation method based on system identification and frequency response correction comprises: dynamic compensation of sensor time domain, i.e. primary compensator G in the process of identifying sensor1(s) and all p secondary compensators G cyclically constructing the sensor2,i(s) thereafter, for the actual measured output of the sensor, a primary compensator G is first employed1(s) performing a primary compensation of the sensor output, followed by p secondary compensators G2,i(s) the cyclic structure sequence of which uses the secondary compensators G2,i(s) sequentially compensating the primary compensation results output by the sensor; secondary compensator G2,1(s) input to a primary compensator G1(s) output, secondary compensator G2,i(s) input as a quadratic compensator G2,i-1(s), wherein i is 2,3, …, p; secondary compensator G2,pThe output of(s) is the final dynamic compensation result of the sensor measurement output.
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