CN104882170A - Delay eliminating method for signal of self-powered silver detector based on H2/H-infinity hybrid filtering - Google Patents

Delay eliminating method for signal of self-powered silver detector based on H2/H-infinity hybrid filtering Download PDF

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CN104882170A
CN104882170A CN201510165515.1A CN201510165515A CN104882170A CN 104882170 A CN104882170 A CN 104882170A CN 201510165515 A CN201510165515 A CN 201510165515A CN 104882170 A CN104882170 A CN 104882170A
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彭星杰
李庆
龚禾林
陈长
赵文博
刘启伟
李向阳
于颖锐
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Nuclear Power Institute of China
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Abstract

The invention discloses a delay eliminating method for a signal of a self-powered silver detector based on H2/H-infinity hybrid filtering. The delay eliminating method sequentially comprises the following steps of 1, establishing a nuclear reaction model of silver and thermal neutrons; 2, establishing a discrete state equation corresponding to the nuclear reaction model through decoupling transform; 3, determining the instant response share of the current of the self-powered silver detector; and 4, carrying out delay elimination on a current signal of the self-powered silver detector by using an H2/H-infinity hybrid filter. When the delay eliminating method is applied, a current signal of a self-powered silver neutron detector can be subjected to delay elimination, and noise can also be effectively inhibited, so that the self-powered silver neutron detector can also be normally used under the instantaneous condition of a reactor; in addition, a filtering error variance corresponding to an error measuring channel is only required to have an upper bound in the method, so that the self-powered silver neutron detector can also be normally applied when an input signal is an indeterminable signal with limited energy.

Description

Based on H2Signal delay elimination method for silver self-powered detector based on/H-infinity hybrid filtering
Technical Field
The invention relates to a processing technology of in-core silver self-powered neutron detector signals used by a nuclear reactor power distribution online monitoring system, in particular to a silver self-powered detector signal delay elimination method based on H2/H infinity hybrid filtering.
Background
The silver self-powered neutron detector used as an in-core detector of an advanced reactor core measuring system has the advantages that the sensitive material silver of the silver self-powered neutron detector reacts with secondary nuclides generated by neutrons to generate current, and the current is in direct proportion to the flux of the position in a steady state, so that the neutron flux of the position can be inferred by measuring the silver self-powered neutron detector. Because the main component of the detector current is generated by the beta decay of the secondary nuclide, under the transient condition of the reactor (the condition of neutron flux level change), the detector current cannot reflect the change of the flux level in real time, but has certain delay, and the delay time parameter is consistent with the beta decay of the secondary nuclide. Therefore, in order to ensure the accuracy of neutron flux measurement, the current signal of the silver self-powered neutron detector needs to be subjected to delayed elimination processing in the advanced core measurement system using the silver self-powered neutron detector as a neutron measurement device.
Because the actual measurement process is always accompanied by noise (process noise and measurement noise), the noise of the current signal of the detector can be amplified to 20 times at most by using a direct mathematical inversion method for delay elimination, so that the measurement precision is influenced. Therefore, in the delay eliminating process, amplification of noise needs to be effectively suppressed.
The current elimination applied to the signal delay of the silver self-powered detector is mainly realized based on a Kalman filter, the application of the method must assume that an external disturbance input signal of a system is a white noise signal with known statistical characteristics, and when the input signal is an uncertain signal with limited energy, the statistical characteristics are difficult to obtain, and the method is difficult to apply.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a silver self-powered neutron detector signal delay elimination method based on H2/H infinity hybrid filtering, which can delay and eliminate the current signal of the silver self-powered neutron detector and effectively inhibit noise during application, so that the silver self-powered neutron detector can be normally used under the transient working condition of a reactor, and the method only requires that the filtering error variance corresponding to a measurement error channel has an upper bound, so that the silver self-powered neutron detector can also be normally applied when an input signal is an uncertain signal with limited energy.
The invention mainly solves the problems by the following technical scheme: the method for eliminating the signal delay of the silver self-powered detector based on H2/H infinity hybrid filtering is characterized by comprising the following steps of:
step 1, establishing a nuclear reaction model of silver and thermal neutrons:
under the transient working condition of the reactor, the change of the flux causes the change of the current of the silver self-powered neutron detector to be not synchronous, the current of the silver self-powered neutron detector has a certain lag compared with the current of the silver self-powered neutron detector, and a specific formula for describing the reaction is as follows:
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>108</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>107</mn> <mn>107</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> <mn>108</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>110</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>109</mn> <mn>109</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> <mn>110</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=(109K109σ109Ag+107K107σ107Ag)φ(t)
(3)
+110K110λ110Ag(t)+108K108λ108Ag(t)
wherein,108ag (t) represents108The density of the core of Ag is,110ag (t) represents110The density of the core of Ag is,107ag represents107The density of the core of Ag is,109ag represents109The nuclear density of Ag, phi (t) represents the neutron flux at the detector,107sigma represents107The neutron capture cross-section of Ag,109sigma represents109The neutron capture cross-section of Ag,108lambda denotes108The beta decay constant of Ag is such that,110lambda denotes110The beta decay constant of Ag is such that,107k represents107The probability of current generation after neutron capture by Ag,109k represents109The probability of current generation after neutron capture by Ag,108k represents108The probability of current generation after beta decay of Ag,110k represents110The probability of current generation after beta decay of Ag, and I (t) represents SPND current; the method comprises the steps of deriving a continuous time variable mathematical model corresponding to a physical process of a signal generated by a silver self-powered detector based on a first principle, and deriving a continuous time variable mathematical model corresponding to the physical process of the signal generated by the silver self-powered detector based on the first principle, wherein a nuclear reaction model is a basis of delay elimination based on a filter;
step 2, obtaining a discrete state equation corresponding to the nuclear reaction model by adopting decoupling transformation:
the dynamics were modeled using a Laplace transform as:
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mmultiscripts> <mi>&lambda;q</mi> <mn>110</mn> </mmultiscripts> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mmultiscripts> <mi>&lambda;r</mi> <mn>108</mn> </mmultiscripts> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=p(x1(t)+x2(t)+x3(t)) (6)
wherein p is the instantaneous current contribution and q is110Ag (t) a delayed current contribution corresponding to beta decay, r is108Ag (t) takes a delayed current share corresponding to beta decay.
By performing time discretization on equations (4), (5) and (6) and adding a process noise term and a measurement noise term, a discrete state equation can be obtained as follows:
<math> <mrow> <msub> <mi>x</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <msub> <mi>&lambda;T</mi> <mi>s</mi> </msub> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>w</mi> <mi>k</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
Ik=[p p p]xk+vk (8)
φk=[1 0 0]xk(9)
wherein <math> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>=</mo> <msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mi>k</mi> </msub> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mi>k</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow> </math> wkIs process noise, vkFor measuring noise, TSIs the sampling time.
Initial value is
<math> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mn>0</mn> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Step 3, determining the transient response share of the current of the silver self-powered detector:
in a reactor starting physical experiment stage, a power step is formed by increasing/decreasing reactor power, corresponding measured values of out-of-stack detector signals and measured values of self-silver-supply energy detectors are recorded, the out-of-stack detectors can instantaneously respond to the change of neutron flux, the corresponding measured values can be regarded as real neutron flux, N different predicted values of instantaneous response portions are given by adjusting theoretical values of the instantaneous response portions, then the measured values of the out-of-stack detectors are substituted into a discrete state equation, N groups of theoretical values of self-silver-supply energy detectors can be obtained, the theoretical values are compared with the measured values of the self-silver-supply energy detectors, and the predicted values of the instantaneous response portions corresponding to a certain group of theoretical values with the best conformity are taken as the instantaneous response portions adopted by subsequent delay elimination;
and 4, utilizing an H2/H infinity hybrid filter to delay and eliminate the current signal of the self-powered silver detector:
for a discrete control process system, the system can be described by an equation of state:
x(k+1)=Ax(k)+B1w(k)+B2v(k)
y(k)=Cx(k)+D1w(k)+D2v(k) (9)
z(k)=Lx(k)
wherein x (k) is an n-dimensional state vector of a k-th sampling point, w (k) system process noise, v (k) is system observation white noise, y (k) is a measurement value of the k-th sampling point, z (k) is a L-dimensional vector to be solved, and L is a L x n-dimensional matrix;
assuming that the system is asymptotically stable, for a given constant γ >0, it is desirable to design a full-order linear filter that is asymptotically stable
x ^ ( k + 1 ) = A f x ^ ( k ) + B f y ^ ( k ) z ^ ( k ) = C f x ^ ( k ) - - - ( 10 )
So that
x ~ ( k + 1 ) = A ~ x ~ ( k ) + B ~ 1 w ~ ( k ) + B ~ 2 v ~ ( k ) z ~ ( k ) = C ~ x ~ ( k ) - - - ( 11 )
Is asymptotically stable, and corresponds to a channelHas an upper bound, i.e. the filtering error variance <math> <mrow> <munder> <mi>lim</mi> <mrow> <mi>t</mi> <mo>&RightArrow;</mo> <mo>&infin;</mo> </mrow> </munder> <mi>E</mi> <mo>{</mo> <msup> <mover> <mi>z</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mover> <mi>z</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>&le;</mo> <mi>trace</mi> <mo>,</mo> </mrow> </math> Corresponding to the channel <math> <mrow> <mi>w</mi> <mo>&RightArrow;</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> </mrow> </math> Is satisfied with <math> <mrow> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>&lt;</mo> <mi>&gamma;</mi> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mi>w</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>,</mo> </mrow> </math> Wherein
x ~ ( k ) = x ( k ) x ^ ( k ) , A ~ = A 0 B f C A f , B ~ 1 = B 1 B f D 1 B ~ 2 = B 2 B f D 2 , C ~ = L - C f , z ~ ( k ) = z ( k ) - z ^ ( k ) - - - ( 12 )
For given constants γ >0 and trace >0, the system has an H2/H ∞ hybrid filter, if and only if the following linear matrix inequality holds
<math> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mi>I</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>RA</mi> </mtd> <mtd> <mi>RA</mi> </mtd> <mtd> <mi>R</mi> <msub> <mi>B</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> <mo>+</mo> <mi>S</mi> </mtd> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> </mtd> <mtd> <mi>X</mi> <msub> <mi>B</mi> <mn>2</mn> </msub> <mo>+</mo> <mi>Z</mi> <msub> <mi>D</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>L</mi> <mo>-</mo> <mi>T</mi> </mtd> <mtd> <mi>L</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>I</mi> </mtd> </mtr> </mtable> </mfenced> <mo>></mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>
trace * * RB 1 R * X B 1 + Z D 1 R X > 0 - - - ( 14 )
Where R, X is the symmetric positive definite matrix to be solved and S, Z, T is the general matrix to be solved;
after the matrix is obtained, the correlation matrix of the H2/H ∞ hybrid filter is expressed as follows:
Af=(R-X)-1S,Bf=(R-X)-1Z,Cf=T (15);
for a self-powered silver detector, the corresponding matrix in equation (8) can be known from its discrete state equations as:
<math> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <msub> <mi>&lambda;T</mi> <mi>s</mi> </msub> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
B 1 = 1 0 0
B 2 = 0 0 0
C=[p p p]
D1=[0]
D2=[1]
L=[1 0 0]
by solving the linear matrix inequalities (12) and (13), the H2/H infinity hybrid filter matrix A can be obtainedf、Bf、CfTherefore, the current value of the detector at any time after the elimination delay can be obtained by the following steps:
from initial current measurementsCan obtain the product <math> <mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> </mtd> </mtr> <mtr> <mtd> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> The initial 0 time delay is eliminated to obtain a current value of z ^ ( 0 ) = C f x ^ ( 0 ) ;
For any time k +1(k 0, 1.),and the current value after the delay elimination at the time k +1 is z ^ ( k + 1 ) = C f x ^ ( k + 1 ) .
The invention is applied by using H2the/H infinity filter principle can effectively inhibit the amplification of noise in the delay elimination process, the better the noise inhibition effect is, the delay effect will gradually become worse, therefore, when the invention is applied, the parameters need to be properly adjusted to enable the delay elimination effect and the noise inhibition to reach the optimal balance.
When neutron flux density in a large dynamic range needs to be detected, a current signal in the large dynamic range needs to be detected correspondingly, the problem is concentrated on an analog-to-digital converter, in order to adapt to quantification of current in the large dynamic range, a grading resistor is sampled by the analog-to-digital converter of the silver self-powered detector, when the current signal changes in a large range, the analog-to-digital converter can generate resistor gear conversion, and because all gears are not completely matched, switching among the gears can cause sudden change of an output signal which is approximate to a step.
After entering the delay elimination module, the abrupt change component caused by the gear shifting is amplified seriously, so that the step abrupt change in the time domain is amplified seriously, and the quality of the final signal delay elimination is influenced (the abrupt change part of the signal is distorted seriously). During the shift period, the change in signal is mainly contributed by the shift jump, and the change in current signal due to the neutron flux density change is relatively negligible.
In the case of gear shifting, the method further comprises the following steps of processing the original signal according to a signal processing method: in a gear shifting area, supposing that neutron flux is kept unchanged, then reversely deducing a current signal generated by neutron flux density, and subtracting actual output current of a detector to obtain a gear shifting abrupt change component; and (3) subtracting the gear shifting sudden change component from the output current of the detector outside the gear shifting region to obtain a current signal generated by neutron flux density, and then carrying out delay elimination processing on the current signal.
The design structure of the gear shifting area is as follows:
in the shift region (k)1≤k≤k2) Assuming that the neutron flux density is constant, there are:
n(k+1)=n(k) (16)
<math> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>
the current signals of the silver self-powered detector can be reversely deduced as follows:
I(k+1)=p(n(k+1)+x1(k+1)+x2(k+1)) (19)
-delay cancellation by the steps of claim 1, using the back-pushed current (18) as the actual output current of the detector;
in the shift range time boundary k2The shift induced current offset may be estimated by:
D = I ( k 2 ) - y ^ ( k 2 ) - - - ( 20 )
whereinIs represented at k2The actual output current of the detector at the moment; outside the gear shifting area, the actual output current of the detector needs to be offset and compensated to offset the influence caused by gear shifting, the actual output current of the detector is added with the current offset caused by gear shifting represented by the formula (20) to obtain a current signal generated by neutron flux density, and then the current signal is delayed and eliminated.
In conclusion, the invention has the following beneficial effects:
the method has the advantages that the whole process is simple, the realization is convenient, the current signal of the silver self-powered neutron detector can be delayed and eliminated, the noise can be effectively inhibited, and the silver self-powered neutron detector can be normally used under the transient working condition of a reactor; the invention is based on H2Implementation of a/H-infinity hybrid filter in the inputThe incoming signal can be normally applied when the incoming signal is an uncertain signal with limited energy; when the method is applied, the design of the filter is converted into the calculation of a corresponding linear matrix inequality, the calculation is convenient, and the LMIToolbox of Matlab can be conveniently used for solving;
the invention solves the problem of delayed elimination of the signals of the in-reactor silver self-powered neutron detector used by the nuclear reactor power distribution online monitoring system. The signal of the self-powered silver neutron detector is subjected to delay elimination, smoothing and noise reduction by using the H2/H-infinity hybrid filter, and the optimal balance of the signal delay elimination effect and the noise suppression effect can be well achieved by properly selecting the parameters of the H2/H-infinity hybrid filter. The method can ensure that the current signal of the silver self-powered detector is directly used for the subsequent links of the advanced reactor core measuring system without losing accuracy;
3, carrying out delayed elimination processing on a current signal of the silver self-powered neutron detector, wherein the response time is the time required for the signal to recover to 90% of the steady-state current in 2-5 seconds when the step flux changes;
4, in the process of delaying and eliminating the current signal of the silver self-powered neutron detector, noise reduction processing is carried out on the measured current signal, and the noise amplification factor, namely the ratio of the relative error of the current after the delaying and eliminating processing to the noise is suppressed to be 1-4 times;
the invention can effectively process the influence of the step caused by hardware shifting on the delay elimination effect.
Drawings
FIG. 1 is a block diagram of a silver self-powered neutron detector of the present invention;
FIG. 2 is a process flow diagram of one embodiment of the present invention;
FIG. 3 is a graph of silver reacting with a thermal neutron core.
Reference numbers and corresponding part names in the drawings:
1-emitter, 2-insulating layer, 3-collector, 4-lead, 5-protective shell, 6-insulated cable, 7-current line, 8-background line, 9-sealed tube, and 10-current output end.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
Example (b):
fig. 1 shows a structure diagram of a self-powered silver neutron detector, wherein names of parts with respective serial numbers correspond to: 1-an emitter, 2-an insulating layer, 3-a collector, 4-a lead, 5-a protective shell, 6-an insulating cable, 7-a current line, 8-a background line, 9-a sealing tube, 10-a current output end, wherein the silver self-powered neutron detector has the characteristic parameters as follows: lambda [ alpha ]108=ln2/2.42/60s-1=0.0048s-1,λ110=ln2/24.4s-1=0.0284s-1P is 0.09, q is 0.66, r is 0.25; fig. 3 is a schematic process diagram of a reaction principle of silver and neutron nuclei, and the device of fig. 1 is adopted to measure in the reaction process of fig. 3. As shown in fig. 2, the method for eliminating delay of silver self-powered detector signal based on H2/H ∞ hybrid filtering comprises the following steps in sequence: step 1, establishing a nuclear reaction model of silver and thermal neutrons; step 2, establishing a discrete state equation corresponding to the nuclear reaction model by adopting decoupling transformation; step 3, determining the transient response share of the current of the silver self-powered detector; and 4, utilizing an H2/H infinity hybrid filter to delay and eliminate the current signal of the self-powered silver detector.
The specific implementation steps for establishing the silver and thermal neutron nuclear reaction model in the embodiment are as follows: as shown in fig. 2, under the transient operating condition of the reactor, the flux change causes the silver self-powered neutron detector current to change asynchronously, and the latter has a certain lag behind the former, and the specific formula describing the reaction is as follows:
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>108</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>107</mn> <mn>107</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> <mn>108</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>110</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>109</mn> <mn>109</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> <mn>110</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=(109K109σ109Ag+107K107σ107Ag)φ(t)
(3)
+110K110λ110Ag(t)+108K108λ108Ag(t)
wherein,108ag (t) represents108The density of the core of Ag is,110ag (t) represents110The density of the core of Ag is,107ag represents107The density of the core of Ag is,109ag represents109The nuclear density of Ag, phi (t) represents the neutron flux at the detector,107sigma represents107The neutron capture cross-section of Ag,109sigma represents109The neutron capture cross-section of Ag,108lambda denotes108The beta decay constant of Ag is such that,110lambda denotes110The beta decay constant of Ag is such that,107k represents107The probability of current generation after neutron capture by Ag,109k represents109The probability of current generation after neutron capture by Ag,108k represents108The probability of current generation after beta decay of Ag,110k represents110The probability of current generation after beta decay of Ag, and I (t) represents SPND current;
step 2, obtaining a discrete state equation corresponding to the nuclear reaction model by adopting decoupling transformation:
the dynamics were modeled using a Laplace transform as:
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mmultiscripts> <mi>&lambda;q</mi> <mn>110</mn> </mmultiscripts> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mmultiscripts> <mi>&lambda;r</mi> <mn>108</mn> </mmultiscripts> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=p(x1(t)+x2(t)+x3(t)) (6)
wherein p is the instantaneous current contribution and q is110Ag (t) a delayed current contribution corresponding to beta decay, r is108Ag (t) takes a delayed current share corresponding to beta decay.
By performing time discretization on equations (4), (5) and (6) and adding a process noise term and a measurement noise term, a discrete state equation can be obtained as follows:
<math> <mrow> <msub> <mi>x</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <msub> <mi>&lambda;T</mi> <mi>s</mi> </msub> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>w</mi> <mi>k</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
Ik=[p p p]xk+vk (8)
φk=[1 0 0]xk (9)
wherein <math> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>=</mo> <msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mi>k</mi> </msub> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mi>k</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow> </math> wkIs process noise, vkFor measuring noise, TSIs the sampling time.
Initial value is
<math> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mn>0</mn> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Step 3, determining the transient response share of the current of the silver self-powered detector:
in a reactor starting physical experiment stage, a power step is formed by increasing/decreasing reactor power, corresponding measured values of out-of-stack detector signals and measured values of self-silver-supply energy detectors are recorded, the out-of-stack detectors can instantaneously respond to the change of neutron flux, the corresponding measured values can be regarded as real neutron flux, N different predicted values of instantaneous response portions are given by adjusting theoretical values of the instantaneous response portions, then the measured values of the out-of-stack detectors are substituted into a discrete state equation, N groups of theoretical values of self-silver-supply energy detectors can be obtained, the theoretical values are compared with the measured values of the self-silver-supply energy detectors, and the predicted values of the instantaneous response portions corresponding to a certain group of theoretical values with the best conformity are taken as the instantaneous response portions adopted by subsequent delay elimination;
and 4, utilizing an H2/H infinity hybrid filter to delay and eliminate the current signal of the self-powered silver detector:
for a discrete control process system, the system can be described by an equation of state:
x(k+1)=Ax(k)+B1w(k)+B2v(k)
y(k)=Cx(k)+D1w(k)+D2v(k) (9)
z(k)=Lx(k)
wherein x (k) is an n-dimensional state vector of a k-th sampling point, w (k) system process noise, v (k) is system observation white noise, y (k) is a measurement value of the k-th sampling point, z (k) is a L-dimensional vector to be solved, and L is a L x n-dimensional matrix;
assuming that the system is asymptotically stable, for a given constant γ >0, it is desirable to design a full-order linear filter that is asymptotically stable
x ^ ( k + 1 ) = A f x ^ ( k ) + B f y ^ ( k ) z ^ ( k ) = C f x ^ ( k ) - - - ( 10 )
So that
x ~ ( k + 1 ) = A ~ x ~ ( k ) + B ~ 1 w ~ ( k ) + B ~ 2 v ~ ( k ) z ~ ( k ) = C ~ x ~ ( k ) - - - ( 11 )
Is asymptotically stable, and corresponds to a channelHas an upper bound, i.e. the filtering error variance <math> <mrow> <munder> <mi>lim</mi> <mrow> <mi>t</mi> <mo>&RightArrow;</mo> <mo>&infin;</mo> </mrow> </munder> <mi>E</mi> <mo>{</mo> <msup> <mover> <mi>z</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mover> <mi>z</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>&le;</mo> <mi>trace</mi> <mo>,</mo> </mrow> </math> Corresponding to the channel <math> <mrow> <mi>w</mi> <mo>&RightArrow;</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> </mrow> </math> Is satisfied with <math> <mrow> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>&lt;</mo> <mi>&gamma;</mi> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mi>w</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>,</mo> </mrow> </math> Wherein
x ~ ( k ) = x ( k ) x ^ ( k ) , A ~ = A 0 B f C A f , B ~ 1 = B 1 B f D 1 B ~ 2 = B 2 B f D 2 , C ~ = L - C f , z ~ ( k ) = z ( k ) - z ^ ( k ) - - - ( 12 )
For given constants γ >0 and trace >0, the system has an H2/H ∞ hybrid filter, if and only if the following linear matrix inequality holds
<math> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mi>I</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>RA</mi> </mtd> <mtd> <mi>RA</mi> </mtd> <mtd> <mi>R</mi> <msub> <mi>B</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> <mo>+</mo> <mi>S</mi> </mtd> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> </mtd> <mtd> <mi>X</mi> <msub> <mi>B</mi> <mn>2</mn> </msub> <mo>+</mo> <mi>Z</mi> <msub> <mi>D</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>L</mi> <mo>-</mo> <mi>T</mi> </mtd> <mtd> <mi>L</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>I</mi> </mtd> </mtr> </mtable> </mfenced> <mo>></mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>
trace * * RB 1 R * X B 1 + Z D 1 R X > 0 - - - ( 14 )
Where R, X is the symmetric positive definite matrix to be solved and S, Z, T is the general matrix to be solved;
after the matrix is obtained, the correlation matrix of the H2/H ∞ hybrid filter is expressed as follows:
Af=(R-X)-1S,Bf=(R-X)-1Z,Cf=T (15);
for a self-powered silver detector, the corresponding matrix in equation (8) can be known from its discrete state equations as:
<math> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <msub> <mi>&lambda;T</mi> <mi>s</mi> </msub> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
B 1 = 1 0 0
B 2 = 0 0 0
C=[p p p]
D1=[0]
D2=[1]
L=[1 0 0]
by solving the linear matrix inequalities (12) and (13), the H2/H infinity hybrid filter matrix A can be obtainedf、Bf、CfTherefore, the current value of the detector at any time after the elimination delay can be obtained by the following steps:
from initial current measurementsCan obtain the product <math> <mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> </mtd> </mtr> <mtr> <mtd> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> The initial 0 time delay is eliminated to obtain a current value of z ^ ( 0 ) = C f x ^ ( 0 ) ;
For any time k +1(k 0, 1.),and the current value after the delay elimination at the time k +1 is z ^ ( k + 1 ) = C f x ^ ( k + 1 ) .
Example 2:
this embodiment is further defined on the basis of embodiment 1 as follows: in the case of a gear shift, the step 4 performs the delay elimination in the following manner:
in the shift region (k)1≤k≤k2) Assuming that the neutron flux density is constant, there are:
n(k+1)=n(k) (16)
<math> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>
the current signals of the silver self-powered detector can be reversely deduced as follows:
I(k+1)=p(n(k+1)+x1(k+1)+x2(k+1)) (19)
-delay cancellation by the steps of claim 1, using the back-pushed current (18) as the actual output current of the detector;
in the shift range time boundary k2The shift induced current offset may be estimated by:
D = I ( k 2 ) - y ^ ( k 2 ) - - - ( 20 )
whereinIs represented at k2The actual output current of the detector at the moment; outside the gear shifting area, the actual output current of the detector needs to be offset and compensated to offset the influence caused by gear shifting, the actual output current of the detector is added with the current offset caused by gear shifting represented by the formula (20) to obtain a current signal generated by neutron flux density, and then the current signal is delayed and eliminated.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications and equivalent variations of the above embodiment according to the present invention are within the scope of the present invention.

Claims (3)

1. Based on H2The method for eliminating the signal delay of the silver self-powered detector of the/H infinity hybrid filtering is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing a nuclear reaction model of silver and thermal neutrons:
under the transient working condition of the reactor, the change of the flux causes the change of the current of the silver self-powered neutron detector to be not synchronous, the current of the silver self-powered neutron detector has a certain lag compared with the current of the silver self-powered neutron detector, and a specific formula for describing the reaction is as follows:
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>108</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>107</mn> <mn>107</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> <mn>108</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msup> <mi>d</mi> <mn>110</mn> </msup> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mmultiscripts> <mi>&sigma;</mi> <mn>109</mn> <mn>109</mn> </mmultiscripts> <mi>Ag&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> <mn>110</mn> </mmultiscripts> <mi>Ag</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=(109K109σ109Ag+107K107σ107Ag)φ(t)
(3)
+110K110λ110Ag(t)+108K108λ108Ag(t)
wherein,108ag (t) represents108The density of the core of Ag is,110ag (t) represents110The density of the core of Ag is,107ag represents107The density of the core of Ag is,109ag represents109The nuclear density of Ag, phi (t) represents the neutron flux at the detector,107sigma represents107The neutron capture cross-section of Ag,109sigma represents109The neutron capture cross-section of Ag,108lambda denotes108The beta decay constant of Ag is such that,110lambda denotes110The beta decay constant of Ag is such that,107k represents107The probability of current generation after neutron capture by Ag,109k represents109The probability of current generation after neutron capture by Ag,108k represents108The probability of current generation after beta decay of Ag,110k represents110The probability of current generation after beta decay of Ag, and I (t) represents SPND current;
step 2, obtaining a discrete state equation corresponding to the nuclear reaction model by adopting decoupling transformation:
the dynamics were modeled using a Laplace transform as:
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <mi>q</mi> </mrow> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mi>dt</mi> </mfrac> <mo>=</mo> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <mi>r</mi> </mrow> <mi>p</mi> </mfrac> <msub> <mi>x</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
I(t)=p(x1(t)+x2(t)+x3(t)) (6)
wherein p is the instantaneous current contribution and q is110Ag (t) a delayed current contribution corresponding to beta decay, r is108Ag (t) takes a delayed current share corresponding to beta decay.
By performing time discretization on equations (4), (5) and (6) and adding a process noise term and a measurement noise term, a discrete state equation can be obtained as follows:
<math> <mrow> <msub> <mi>x</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CenterDot;</mo> <msub> <mi>w</mi> <mi>k</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
Ik=[p p p]xk+vk (8)
φk=[1 0 0]xk (9)
wherein <math> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>=</mo> <msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mi>k</mi> </msub> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mi>k</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow> </math> wkIs process noise, vkFor measuring noise, TSIs the sampling time. Initial value is
<math> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&phi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mn>0</mn> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Step 3, determining the transient response share of the current of the silver self-powered detector:
in a reactor starting physical experiment stage, a power step is formed by increasing/decreasing reactor power, corresponding measured values of out-of-stack detector signals and measured values of self-silver-supply energy detectors are recorded, the out-of-stack detectors can instantaneously respond to the change of neutron flux, the corresponding measured values can be regarded as real neutron flux, N different predicted values of instantaneous response portions are given by adjusting theoretical values of the instantaneous response portions, then the measured values of the out-of-stack detectors are substituted into a discrete state equation, N groups of theoretical values of self-silver-supply energy detectors can be obtained, the theoretical values are compared with the measured values of the self-silver-supply energy detectors, and the predicted values of the instantaneous response portions corresponding to a certain group of theoretical values with the best conformity are taken as the instantaneous response portions adopted by subsequent delay elimination;
and 4, utilizing an H2/H infinity hybrid filter to delay and eliminate the current signal of the self-powered silver detector:
for a discrete control process system, the system can be described by an equation of state:
x(k+1)=Ax(k)+B1w(k)+B2v(k)
y(k)=Cx(k)+D1w(k)+D2v(k) (9)
z(k)=Lx(k)
wherein x (k) is an n-dimensional state vector of a k-th sampling point, w (k) system process noise, v (k) is system observation white noise, y (k) is a measurement value of the k-th sampling point, z (k) is a L-dimensional vector to be solved, and L is a L x n-dimensional matrix;
assuming that the system is asymptotically stable, for a given constant γ >0, it is required to design a full-order linear filter that is asymptotically stable
x ^ ( k + 1 ) = A f x ^ ( k ) + B f y ^ ( k ) z ^ ( k ) = C f x ^ ( k ) - - - ( 10 )
So that
x ~ ( k + 1 ) = A ~ x ~ ( k ) + B ~ 1 w ~ ( k ) + B ~ 2 v ~ ( k ) z ~ ( k ) = C ~ x ~ ( k ) - - - ( 11 )
Is asymptotically stable, and corresponds to a channelHas an upper bound, i.e. the filtering error variance <math> <mrow> <munder> <mi>lim</mi> <mrow> <mi>t</mi> <mo>&RightArrow;</mo> <mo>&infin;</mo> </mrow> </munder> <mi>E</mi> <mo>{</mo> <msup> <mover> <mi>z</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mover> <mi>z</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>&le;</mo> <mi>trace</mi> <mo>,</mo> </mrow> </math> Corresponding to the channel <math> <mrow> <mi>w</mi> <mo>&RightArrow;</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> </mrow> </math> Is satisfied with <math> <mrow> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>&lt;</mo> <mi>&gamma;</mi> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mi>w</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msub> <mo>,</mo> </mrow> </math> Wherein
x ~ ( k ) = x ( k ) x ^ ( k ) , A ~ = A 0 B f C A f , B ~ 1 = B 1 B f D 1 B ~ 2 B 2 B f D 2 , C ~ = L - C f , z ~ ( k ) = z ( k ) - z ~ ( k ) - - - ( 12 )
For given constants γ >0 and trace >0, the system has an H2/H ∞ hybrid filter, if and only if the following linear matrix inequality holds
<math> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> <mi>I</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>RA</mi> </mtd> <mtd> <mi>RA</mi> </mtd> <mtd> <msub> <mi>RB</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mo>*</mo> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> <mo>+</mo> <mi>S</mi> </mtd> <mtd> <mi>XA</mi> <mo>+</mo> <mi>ZC</mi> </mtd> <mtd> <msub> <mi>XB</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>ZD</mi> <mn>2</mn> </msub> </mtd> <mtd> <mi>R</mi> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo>*</mo> </mtd> </mtr> <mtr> <mtd> <mi>L</mi> <mo>-</mo> <mi>T</mi> </mtd> <mtd> <mi>L</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>I</mi> </mtd> </mtr> </mtable> </mfenced> <mo>></mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>
trace * * R B 1 R * X B 1 + Z D 1 R X > 0 - - - ( 14 )
Where R, X is the symmetric positive definite matrix to be solved and S, Z, T is the general matrix to be solved;
after the matrix is obtained, the correlation matrix of the H2/H ∞ hybrid filter is expressed as follows:
Af=(R-X)-1S,Bf=(R-X)-1Z,Cf=T (15);
for a self-powered silver detector, the corresponding matrix in equation (8) can be known from its discrete state equations as:
<math> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
B 1 = 1 0 0
B 2 = 0 0 0
C=[p p p]
D1=[0]
D2=[1]
L=[1 0 0]
by solving the linear matrix inequalities (12) and (13), the H2/H infinity hybrid filter matrix A can be obtainedf、Bf、CfTherefore, the current value of the detector at any time after the elimination delay can be obtained by the following steps:
from initial current measurementsCan obtain the product <math> <mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>p</mi> <mi>r</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mi>rq</mi> </mfrac> <mo>&CenterDot;</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> The initial 0 time delay is eliminated to obtain a current value of z ^ ( 0 ) = C f x ^ ( 0 ) ;
For any time k +1(k 0, 1.),and the current value after the delay elimination at the time k +1 is z ^ ( k + 1 ) = C f x ^ ( k + 1 ) .
2. The H-based according to claim 12The method for eliminating the signal delay of the silver self-powered detector of the/H infinity hybrid filtering is characterized by further comprising the following signal processing method for processing the original signal under the condition of gear shifting: in a gear shifting area, supposing that neutron flux is kept unchanged, then reversely deducing a current signal generated by neutron flux density, and subtracting actual output current of a detector to obtain a gear shifting abrupt change component; and (3) subtracting the gear shifting sudden change component from the output current of the detector outside the gear shifting region to obtain a current signal generated by neutron flux density, and then carrying out delay elimination processing on the current signal.
3. The H-based according to claim 12The signal delay elimination method of the silver self-powered detector of the/H infinity hybrid filtering is characterized in that the design structure of the gear shifting region is as follows:
in the shift region (k)1≤k≤k2) Assuming that the neutron flux density is constant, there are:
n(k+1)=n(k) (16)
<math> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>108</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>q</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>108</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mi>&lambda;</mi> <mn>110</mn> </mmultiscripts> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </msup> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>r</mi> <mi>p</mi> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mmultiscripts> <mrow> <mi>&lambda;</mi> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <mn>110</mn> </mmultiscripts> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>
the current signals of the silver self-powered detector can be reversely deduced as follows:
I(k+1)=p(n(k+1)+x1(k+1)+x2(k+1)) (19)
-delay cancellation by the steps of claim 1, using the back-pushed current (18) as the actual output current of the detector;
in the shift range time boundary k2The shift induced current offset may be estimated by:
D = I ( k 2 ) - y ^ ( k 2 ) - - - ( 20 )
whereinIs represented at k2The actual output current of the detector at the moment; outside the gear shifting area, the actual output current of the detector needs to be offset and compensated to offset the influence caused by gear shifting, the actual output current of the detector is added with the current offset caused by gear shifting represented by the formula (20) to obtain a current signal generated by neutron flux density, and then the current signal is delayed and eliminated.
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