CN104882175A - Delay eliminating method for signal of self-powered rhodium detector based on Luenberger-form H-infinity filtering - Google Patents

Abstract

The invention discloses a delay eliminating method for a signal of a self-powered rhodium detector based on Luenberger-form H-infinity filtering. The delay eliminating method sequentially comprises the following steps of 1, establishing a nuclear reaction model of rhodium 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 rhodium detector; and 4, carrying out delay elimination on a current signal of the self-powered rhodium detector by using a Luenberger-form H-infinity filter. When the delay eliminating method is applied, a current signal of a self-powered rhodium neutron detector can be subjected to delay elimination, and noise can also be effectively inhibited, so that the self-powered rhodium neutron detector can also be normally used under the instantaneous condition of a reactor; in addition, due to the adoption of the Luenberger-form H-infinity filter, the statistical property of an external disturbance input signal is not needed to be known in advance during delay elimination.

Description

Based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering

Technical field

The present invention relates to the treatment technology that nuclear reactor power is distributed in rhodium self-power neutron detector signal in line monitoring system heap used, specifically based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering.

Background technology

As the rhodium self-power neutron detector of detector in advanced reactor core measuring system heap, there is β and to decay generation current in the secondary nucleic that its sensitive material rhodium and neutron reaction produce, under stable situation, this size of current is directly proportional to position flux, therefore can know its position neutron flux by inference by measuring rhodium self-powered detector.Because such detector current principal ingredient is produced by secondary nucleic β decay, in reactor transient state situation (situation of neutron-flux level change), such detector current can not reflect the change of flux level in real time, but having certain delay, delay time parameter decays consistent with the β of secondary nucleic.Therefore, utilizing rhodium self-power neutron detector to make the advanced reactor core measuring system of neutron measurement device, in order to ensure the accuracy of neutron flux measurement, needing the current signal visiting device to rhodium self-sufficiency to do to postpone Processing for removing.

Owing to being always attended by noise (process noise and measurement noises) in the measuring process of reality, utilizing direct mathematical inversion method to do to postpone elimination can amplify detector current signal noise, is maximumly amplified to 20 times, the precision that impact is measured.Therefore, in delay Processing for removing process, the amplification of effective restraint speckle is needed.

The elimination being applied to rhodium self-powered detector signal delay at present mainly realizes based on Kalman filter, must suppose that the external disturbance input signal of system is a white noise signal with known statistical property during its application, when input signal is a neutral signal with finite energy, its statistical property is difficult to obtain, and the method is just difficult to application.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, provide a kind of rhodium self-powered detector signal delay removing method based on Luenberger form H ∞ filtering, delay Processing for removing can be carried out to the current signal of rhodium self-power neutron detector during its application, and can effective restraint speckle, rhodium self-power neutron detector also can normally be used when reactor transient condition, and owing to present invention employs the H ∞ wave filter of Luenberger form, without the need to knowing the statistical property of external disturbance input signal in advance when doing to postpone to eliminate.

The present invention solves the problem and is achieved through the following technical solutions: based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering, it is characterized in that, comprise the following steps:

Based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering, it is characterized in that: comprise the following steps:

Step 1, set up the nuclear reaction model of rhodium and thermal neutron:

Under reactor transient condition, the change of flux causes the change of rhodium self-power neutron detector electric current and asynchronous, and the latter has certain delayed compared with the former, the concrete formula describing above-mentioned reaction is as follows:

$\frac{\∂m_2\left(t\right)}{\∂t}=a_{2}n\left(t\right)-{\mathrm{\λ}}_2{m}_2\left(t\right)---\left(1\right)$

$\frac{\∂m_1\left(t\right)}{\∂t}=a_{1}n\left(t\right)+{\mathrm{\λ}}_2{m}_2\left(t\right)-{\mathrm{\λ}}_1{m}_1\left(t\right)---\left(2\right)$

I(t)＝cn(t)+λ ₁m ₁(t) (3)

Wherein, m ₁(t), m ₂t () represents respectively ¹⁰⁴rh and ^104mthe quantity of electric charge that Rh directly causes, n (t) represents the detector current under the detector equilibrium state that detector place thermal neutron flux is corresponding, λ ₁, λ ₂represent respectively ¹⁰⁴rh and ^104mthe disintegration constant of Rh, c represents the transient response share of detector current, a ₁, a ₂represent respectively ¹⁰⁴rh and ^104mthe electric current share that Rh causes, I (t) represents rhodium self-supporting energy electric current;

Step 2, employing decoupling conversion obtain discrete state equations corresponding to nuclear reaction model:

Laplace transform is done to formula (1), formula (2) and formula (3), obtains following equation:

$\frac{I\left(s\right)}{n\left(s\right)}=c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}---\left(4\right)$

During equilibrium state, equation becomes

$\frac{I_0}{n_0}=c+a_1+a_2=1---\left(5\right)$

So formula (4) becomes

$I\left(s\right)=n\left(s\right)\·\frac{I_0}{n_0}(c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2})---\left(6\right)$

Inverse Laplace transformation is carried out to formula (6), obtains following state equation

$\frac{\∂x_1\left(t\right)}{\∂t}=\frac{1}{c}(a_1\·{\mathrm{\λ}}_1-a_2\·g)\·n\left(t\right)-{\mathrm{\λ}}_1{x}_1\left(t\right)---\left(7\right)$

$\frac{\∂x_2\left(t\right)}{\∂t}=\frac{1}{c}{a}_2\·g\·n\left(t\right)-{\mathrm{\λ}}_2{x}_2\left(t\right)---\left(8\right)$

I(t)＝[c,c,c]·X(t) (9)

Wherein

$g=\frac{{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{{\mathrm{\λ}}_1-{\mathrm{\λ}}_2}$

$X\left(t\right)=\left[\begin{array}{c}n\left(t\right)\\ x_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]$

Initial value

$X\left(0\right)=\left[\begin{array}{c}n\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·n\left(0\right)\\ \frac{1}{c}(a_2\·g)\·n\left(0\right)\end{array}\right]---\left(10\right)$

(7), the discrete state equations of (8), (9) correspondence is

$X(k+1)=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_2& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]\·X\left(k\right)+\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]\·W\left(k\right)---\left(11\right)$

I(k)＝[c c c]·X(k)+[1]·V(k) (12)

n(k)＝[1 0 0]·X(k) (13)

Wherein, $X\left(k\right)=\left[\begin{array}{c}n\left(k\right)\\ x_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]$

Initial value is

$X\left(0\right)=\left[\begin{array}{c}I\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·I\left(0\right)\\ \frac{1}{c}(a_2\·g)\·I\left(0\right)\end{array}\right]---\left(14\right);$

Step 3, determine the transient response share of rhodium self-powered detector electric current:

In the reactor start-up Physical Experiment stage, form power step by lifting/lowering reactor capability, record corresponding ex-core detector signal measured value and rhodium self-powered detector signal measured value; Ex-core detector can the change of transient response neutron flux, and corresponding measured value can think real neutron flux; By the given N number of different transient response share predicted value of theoretical value of adjustment transient response share, again ex-core detector signal measured value is substituted into discrete state equations, N group rhodium self-powered detector signal theory value can be obtained, theoretical value and rhodium self-powered detector signal measured value are compared, gets certain best group theoretical value corresponding transient response share predicted value of wherein matching degree for subsequent delay and eliminate the transient response share adopted;

Step 4, utilize the H ∞ wave filter of Luenberger form to rhodium self-powered detector current signal do postpone eliminate:

For a discrete control procedure system, this system can describe with a state equation:

x(k+1)＝Ax(k)+Bw(k)

y(k)＝Cx(k)+Dw(k) (15)

z(k)＝Lx(k)

Wherein, the n dimension state vector that x (k) is kth time sampled point, w (k) contains systematic procedure noise and systematic observation white noise, and y (k) is the measured value of kth time sampled point, z (k) 1 ties up and waits to ask vector, and L is that l*n ties up matrix;

For discrete system (15), design the linear Luenberger wave filter in following asymptotically stable full rank

$\begin{array}{c}{\hat{x}}_{k+1}=A{\hat{x}}_k+K(y_k-C{\hat{x}}_k)\\ {\hat{z}}_k=L{\hat{x}}_k\end{array}---\left(16\right)$

Formula (16) is H ∞ wave filter, and for a given γ, and if only if, and following MATRIX INEQUALITIES has solution:

$\left[\begin{array}{cccc}Y& 0& A^{T}Y-C^T{W}^T& L^T\\ 0& {\mathrm{\γ}}^{2}I& B^{T}Y-D^T{W}^T& 0\\ \mathrm{YA}-\mathrm{WC}& \mathrm{YB}-\mathrm{WD}& Y& 0\\ L& 0& 0& 1\end{array}\right]\≥0---\left(17\right)$

Wherein Y=Y ^t∈ R ^{n × n}, W ∈ R ^{n × r}, J=J ^t∈ R ^{m × m}, the gain K=Y of H ∞ wave filter ^-1w;

For rhodium self-powered detector, by the homography in the known equation of its discrete state equations (15) be:

$A=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_2& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]$

$B=\left[\begin{array}{cc}1& 0\\ 0& 0\\ 0& 0\end{array}\right]$

C＝[c c c]

D＝[0 1]

L＝[1 0 0]

By solving LMI (17), H ∞ electric-wave filter matrix K can be obtained, thus can obtain by following steps the detector current value eliminated and postpone rear any time:

By initial current measured value can obtain $\hat{x}\left(0\right)=\left[\begin{array}{c}\hat{y}\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·\hat{y}\left(0\right)\\ \frac{1}{c}(a_2\·g)\·\hat{y}\left(0\right)\end{array}\right],$ Initial 0 moment postpones to eliminate after-current value $\hat{z}0=C_f\hat{x}\left(0\right);$

For any k+1 (k=0,1 ...) and the moment, and the k+1 moment postpone eliminate after current value be $\hat{z}(k+1)=L\hat{x}(k+1).$

The H ∞ Filter Principle of Luenberger form is utilized when the present invention applies, in delay elimination process, can the amplification of restraint speckle effectively, noise suppression effect is better, carryover effects can be deteriorated gradually, therefore, suitable regulating parameter is needed to make delay eradicating efficacy and squelch reach optimum balance when the present invention applies.

In sum, the present invention has following beneficial effect:

The overall operation of 1 the present invention is simple, is convenient to realize, can carries out delay Processing for removing to the current signal of rhodium self-power neutron detector, and can effective restraint speckle, and rhodium self-power neutron detector also can normally be used when reactor transient condition; The H ∞ wave filter that the present invention is based on Luenberger form realizes, input signal be one there is the neutral signal of finite energy time also can normal use; When the present invention applies, design of filter is converted into corresponding linear MATRIX INEQUALITIES to calculate, convenient calculating, can use the LMI Toolbox of Matlab to solve easily.

2 the invention solves the delay elimination problem that nuclear reactor power is distributed in rhodium self-power neutron detector signal in line monitoring system heap used.Delay is eliminated, level and smooth, noise reduction process to utilize H ∞ wave filter to carry out rhodium self-power neutron detector signal, by suitably choosing the H ∞ filter parameter of Luenberger form, can be good at the optimum balance reaching signal delay eradicating efficacy and noise suppression effect.The present invention can ensure that rhodium self-powered detector current signal is directly used in the follow-up link of advanced reactor core measuring system, and does not lose accuracy;

3 the present invention carry out delay Processing for removing to the current signal of rhodium self-power neutron detector, when response time and step variations of flux, signal recuperation to steady-state current 90% needed for time in 2 ~ 10 seconds;

4 the present invention postpone in elimination process to the current signal of rhodium self-power neutron detector, and carry out noise reduction process to measurement current signal, namely noise enlargement factor postpones the electric current relative error after Processing for removing and suppress at 1 ~ 8 times with the ratio of noise;

5 the present invention can effectively process because hardware shifts gears the step caused to the impact postponing eradicating efficacy.

Accompanying drawing explanation

Fig. 1 is rhodium self-power neutron detector structural drawing of the present invention

Fig. 2 is the processing flow chart of the present invention's specific embodiment;

Fig. 3 is rhodium and thermal neutron nuclear reaction figure.

Mark and corresponding parts title in accompanying drawing:

1-emitter, 2-insulation course, 3-collector, 4-wire, 5-containment vessel, 6-insulated cable, 7-current line, 8-tourism background trend line, 9-sealed tube, 10-current output terminal.

Embodiment

Below in conjunction with embodiment and accompanying drawing, detailed description is further done to the present invention, but embodiments of the present invention are not limited thereto.

Embodiment:

Rhodium self-power neutron detector structural drawing as shown in Figure 1, wherein the parts title of each sequence number corresponds to: 1-emitter, 2-insulation course; 3-collector; 4-wire, 5-containment vessel, 6-insulated cable; 7-current line; 8-tourism background trend line, 9-sealed tube, 10-current output terminal; this rhodium self-power neutron detector, its characterisitic parameter is: λ ₁=ln2/42.3s ^-1=0.016386s ^-1, λ ₂=ln2/4.34/60s ^-1=0.00266186s ^-1, c=0.06, a ₁=0.879, a ₂=0.061; Fig. 3 is rhodium and neutron nuclear reaction principle procedure chart, in the course of reaction of Fig. 3, adopts the device of Fig. 1 to measure.As shown in Figure 2, based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering, the following steps of carrying out successively are comprised: step 1, set up the nuclear reaction model of rhodium and thermal neutron; Step 2, employing decoupling conversion set up discrete state equations corresponding to nuclear reaction model; Step 3, determine the transient response share of rhodium self-powered detector electric current; Step 4, utilize the H ∞ wave filter of Luenberger form to rhodium self-powered detector current signal do postpone eliminate.

The concrete implementation step that the present embodiment sets up the nuclear reaction model of rhodium and thermal neutron is as follows: as shown in Figure 2, based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering, it is characterized in that: comprise the following steps:

Step 1, set up the nuclear reaction model of rhodium and thermal neutron:

Under reactor transient condition, the change of flux causes the change of rhodium self-power neutron detector electric current and asynchronous, and the latter has certain delayed compared with the former, the concrete formula describing above-mentioned reaction is as follows:

$\frac{\∂m_2\left(t\right)}{\∂t}=a_{2}n\left(t\right)-{\mathrm{\λ}}_2{m}_2\left(t\right)---\left(1\right)$

$\frac{\∂m_1\left(t\right)}{\∂t}=a_{1}n\left(t\right)+{\mathrm{\λ}}_2{m}_2\left(t\right)-{\mathrm{\λ}}_1{m}_1\left(t\right)---\left(2\right)$

I(t)＝cn(t)+λ ₁m ₁(t) (3)

Wherein, m ₁(t), m ₂t () represents respectively ¹⁰⁴rh and ^104mthe quantity of electric charge that Rh directly causes, n (t) represents the detector current under the detector equilibrium state that detector place thermal neutron flux is corresponding, λ ₁, λ ₂represent respectively ¹⁰⁴rh and ^104mthe disintegration constant of Rh, c represents the transient response share of detector current, a ₁, a ₂represent respectively ¹⁰⁴rh and ^104mthe electric current share that Rh causes, I (t) represents rhodium self-supporting energy electric current;

Step 2, employing decoupling conversion obtain discrete state equations corresponding to nuclear reaction model:

Laplace transform is done to formula (1), formula (2) and formula (3), obtains following equation:

$\frac{I\left(s\right)}{n\left(s\right)}=c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}---\left(4\right)$

During equilibrium state, equation becomes

$\frac{I_0}{n_0}=c+a_1+a_2=1---\left(5\right)$

So formula (4) becomes

$I\left(s\right)=n\left(s\right)\·\frac{I_0}{n_0}(c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2})---\left(6\right)$

Inverse Laplace transformation is carried out to formula (6), obtains following state equation

$\frac{\∂x_1\left(t\right)}{\∂t}=\frac{1}{c}(a_1\·{\mathrm{\λ}}_1-a_2\·g)\·n\left(t\right)-{\mathrm{\λ}}_1{x}_1\left(t\right)---\left(7\right)$

$\frac{\∂x_2\left(t\right)}{\∂t}=\frac{1}{c}{a}_2\·g\·n\left(t\right)-{\mathrm{\λ}}_2{x}_2\left(t\right)---\left(8\right)$

I(t)＝[c,c,c]·X(t) (9)

Wherein

$g=\frac{{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{{\mathrm{\λ}}_1-{\mathrm{\λ}}_2}$

$X\left(t\right)=\left[\begin{array}{c}n\left(t\right)\\ x_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]$

Initial value

$X\left(0\right)=\left[\begin{array}{c}n\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·n\left(0\right)\\ \frac{1}{c}(a_2\·g)\·n\left(0\right)\end{array}\right]---\left(10\right)$

(7), the discrete state equations of (8), (9) correspondence is

$X(k+1)=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_2& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]\·X\left(k\right)+\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]\·W\left(k\right)---\left(11\right)$

I(k)＝[c c c]·X(k)+[1]·V(k) (12)

n(k)＝[1 0 0]·X(k) (13)

Wherein, $X\left(k\right)=\left[\begin{array}{c}n\left(k\right)\\ x_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]$

Initial value is

$X\left(0\right)=\left[\begin{array}{c}I\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·I\left(0\right)\\ \frac{1}{c}(a_2\·g)\·I\left(0\right)\end{array}\right]---\left(14\right);$

Step 3, determine the transient response share of rhodium self-powered detector electric current:

In the reactor start-up Physical Experiment stage, form power step by lifting/lowering reactor capability, record corresponding ex-core detector signal measured value and rhodium self-powered detector signal measured value; Ex-core detector can the change of transient response neutron flux, and corresponding measured value can think real neutron flux; By the given N number of different transient response share predicted value of theoretical value of adjustment transient response share, again ex-core detector signal measured value is substituted into discrete state equations, N group rhodium self-powered detector signal theory value can be obtained, theoretical value and rhodium self-powered detector signal measured value are compared, gets certain best group theoretical value corresponding transient response share predicted value of wherein matching degree for subsequent delay and eliminate the transient response share adopted;

Step 4, utilize the H ∞ wave filter of Luenberger form to rhodium self-powered detector current signal do postpone eliminate:

For a discrete control procedure system, this system can describe with a state equation:

x(k+1)＝Ax(k)+Bw(k)

y(k)＝Cx(k)+Dw(k) (15)

z(k)＝Lx(k)

Wherein, the n dimension state vector that x (k) is kth time sampled point, w (k) contains systematic procedure noise and systematic observation white noise, and y (k) is the measured value of kth time sampled point, z (k) 1 ties up and waits to ask vector, and L is that l*n ties up matrix;

For discrete system (15), design the linear Luenberger wave filter in following asymptotically stable full rank

$\begin{array}{c}{\hat{x}}_{k+1}=A{\hat{x}}_k+K(y_k-C{\hat{x}}_k)\\ {\hat{z}}_k=L{\hat{x}}_k\end{array}---\left(16\right)$

Formula (16) is H ∞ wave filter, and for a given γ, and if only if, and following MATRIX INEQUALITIES has solution:

$\left[\begin{array}{cccc}Y& 0& A^{T}Y-C^T{W}^T& L^T\\ 0& {\mathrm{\γ}}^{2}I& B^{T}Y-D^T{W}^T& 0\\ \mathrm{YA}-\mathrm{WC}& \mathrm{YB}-\mathrm{WD}& Y& 0\\ L& 0& 0& 1\end{array}\right]\≥0---\left(17\right)$

Wherein Y=Y ^t∈ R ^{n × n}, W ∈ R ^{n × r}, J=J ^t∈ R ^{m × m}, the gain K=Y of H ∞ wave filter ^-1w;

For rhodium self-powered detector, by the homography in the known equation of its discrete state equations (15) be:

$A=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_2& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]$

$B=\left[\begin{array}{cc}1& 0\\ 0& 0\\ 0& 0\end{array}\right]$

C＝[c c c]

D＝[0 1]

L＝[1 0 0]

By solving LMI (17), H ∞ electric-wave filter matrix K can be obtained, thus can obtain by following steps the detector current value eliminated and postpone rear any time:

By initial current measured value can obtain $\hat{x}\left(0\right)=\left[\begin{array}{c}\hat{y}\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·\hat{y}\left(0\right)\\ \frac{1}{c}(a_2\·g)\·\hat{y}\left(0\right)\end{array}\right],$ Initial 0 moment postpones to eliminate after-current value $\hat{z}0=C_f\hat{x}\left(0\right);$

For any k+1 (k=0,1 ...) and the moment, and the k+1 moment postpone eliminate after current value be $\hat{z}(k+1)=L\hat{x}(k+1).$

Embodiment 2:

The present embodiment has made following restriction further on the basis of embodiment 1: when there being gearshift, described step 4 is carried out delay in the following ways and eliminated:

(k in gear shift region ₁≤ k≤k ₂), suppose that neutron-flux density is constant, then have:

n(k+1)＝n(k) (18)

$x_1(k+1)=\frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})n\left(k\right)+e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}{x}_1\left(k\right)---\left(19\right)$

$x_2(k+1)=\frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_{2}n\left(k\right)+e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}{x}_2\left(k\right)---\left(20\right)$

Instead can release rhodium self-powered detector current signal is:

I(k+1)＝c(n(k+1)+x ₁(k+1)+x ₂(k+1)) (21)

By the anti-electric current (21) that pushes away as detector actual output current, carry out delay by step described in claim 1 and eliminate;

At gear shift border zone time k ₂place, the current offset amount that gear shift causes can be estimated by following formula:

$D=I\left(k_2\right)-\hat{y}\left(k_2\right)---\left(22\right)$

Wherein represent at k ₂the detector actual output current in moment;

Outside gear shift region, need to carry out on detector actual output current the impact that bias compensation brings to offset gear shift, detector actual output current is added the current offset amount that gear shift that above formula (22) represents causes, obtain the current signal that neutron-flux density produces, and then delay elimination is carried out to this current signal.

The above is only preferred embodiment of the present invention, not does any pro forma restriction to the present invention, every according in technical spirit of the present invention to any simple modification, equivalent variations that above embodiment is done, all fall within protection scope of the present invention.

Claims (1)

1., based on the rhodium self-powered detector signal delay removing method of Luenberger form H ∞ filtering, it is characterized in that: comprise the following steps:

Step 1, set up the nuclear reaction model of rhodium and thermal neutron:

Under reactor transient condition, the change of flux causes the change of rhodium self-power neutron detector electric current and asynchronous, and the latter has certain delayed compared with the former, the concrete formula describing above-mentioned reaction is as follows:

$\frac{{\∂m}_2\left(t\right)}{\∂t}=a_{2}n\left(t\right)-{\mathrm{\λ}}_2{m}_2\left(t\right)---\left(1\right)$

$\frac{\∂m_1\left(t\right)}{\∂t}=a_{1}n\left(t\right)+{\mathrm{\λ}}_2{m}_2\left(t\right)-{\mathrm{\λ}}_1{m}_1\left(t\right)---\left(2\right)$

I(t)＝cn(t)+λ ₁m ₁(t) (3)

Wherein, m ₁(t), m ₂t () represents respectively ¹⁰⁴rh and ^104mthe quantity of electric charge that Rh directly causes, n (t) represents the detector current under the detector equilibrium state that detector place thermal neutron flux is corresponding, λ ₁, λ ₂represent respectively ¹⁰⁴rh and ^104mthe disintegration constant of Rh, c represents the transient response share of detector current, a ₁, a ₂represent respectively ¹⁰⁴rh and ^104mthe electric current share that Rh causes, I (t) represents rhodium self-supporting energy electric current;

Step 2, employing decoupling conversion obtain discrete state equations corresponding to nuclear reaction model:

Laplace transform is done to formula (1), formula (2) and formula (3), obtains following equation:

$\frac{I\left(s\right)}{n\left(s\right)}=c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}---\left(4\right)$

During equilibrium state, equation becomes

$\frac{I_0}{n_0}=c+a_1+a_2=1---\left(5\right)$

So formula (4) becomes

$I\left(s\right)=n\left(s\right)\·\frac{I_0}{n_0}(c+\frac{a_1\·{\mathrm{\λ}}_1}{s+{\mathrm{\λ}}_1}+\frac{a_2\·{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{s^2+({\mathrm{\λ}}_1+{\mathrm{\λ}}_2)\·s+{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2})---\left(6\right)$

Inverse Laplace transformation is carried out to formula (6), obtains following state equation

$\frac{\∂x_1\left(t\right)}{\∂t}=\frac{1}{c}(a_1\·{\mathrm{\λ}}_1-a_2\·g)\·n\left(t\right)-{\mathrm{\λ}}_1{x}_1\left(t\right)---\left(7\right)$

$\frac{\∂x_2\left(t\right)}{\∂t}=\frac{1}{c}{a}_2\·g\·n\left(t\right)-{\mathrm{\λ}}_2{x}_2\left(t\right)---\left(8\right)$

I(t)＝[c,c,c]·X(t) (9)

Wherein

$g=\frac{{\mathrm{\λ}}_1\·{\mathrm{\λ}}_2}{{\mathrm{\λ}}_1-{\mathrm{\λ}}_2}$

$X\left(t\right)=\left[\begin{array}{c}n\left(t\right)\\ x_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]$

Initial value

$X\left(0\right)=\left[\begin{array}{c}m\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·n\left(0\right)\\ \frac{1}{c}(a_2\·g)\·n\left(0\right)\end{array}\right]---\left(10\right)$

(7), the discrete state equations of (8), (9) correspondence is

$X(k+1)=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]\·X\left(k\right)+\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]\·W\left(k\right)---\left(11\right)$

I(k)＝[c c c]·X(k)+[1]·V(k) (12)

n(k)＝[1 0 0]·X(k) (13)

Wherein, $X\left(k\right)=\left[\begin{array}{c}n\left(k\right)\\ x_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]$

Initial value is

$X\left(0\right)=\left[\begin{array}{c}I\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·I\left(0\right)\\ \frac{1}{c}(a_2\·g)\·I\left(0\right)\end{array}\right]---\left(14\right);$

Step 3, determine the transient response share of rhodium self-powered detector electric current:

In the reactor start-up Physical Experiment stage, form power step by lifting/lowering reactor capability, record corresponding ex-core detector signal measured value and rhodium self-powered detector signal measured value; Ex-core detector can the change of transient response neutron flux, and corresponding measured value can think real neutron flux; By the given N number of different transient response share predicted value of theoretical value of adjustment transient response share, again ex-core detector signal measured value is substituted into discrete state equations, N group rhodium self-powered detector signal theory value can be obtained, theoretical value and rhodium self-powered detector signal measured value are compared, gets certain best group theoretical value corresponding transient response share predicted value of wherein matching degree for subsequent delay and eliminate the transient response share adopted;

Step 4, utilize the H ∞ wave filter of Luenberger form to rhodium self-powered detector current signal do postpone eliminate:

For a discrete control procedure system, this system can describe with a state equation:

x(k+1)＝Ax(k)+Bw(k)

y(k)＝Cx(k)+Dw(k) (15)

z(k)＝Lx(k)

Wherein, the n dimension state vector that x (k) is kth time sampled point, w (k) contains systematic procedure noise and systematic observation white noise, and y (k) is the measured value of kth time sampled point, z (k) 1 ties up and waits to ask vector, and L is that l*n ties up matrix;

For discrete system (15), design the linear Luenberger wave filter in following asymptotically stable full rank

$\begin{array}{c}{\hat{x}}_{k+1}=A{\hat{x}}_k+K(y_k-C{\hat{x}}_k)\\ {\hat{z}}_k=L{\hat{x}}_k\end{array}----\left(16\right)$

Formula (16) is H ∞ wave filter, and for a given γ, and if only if, and following MATRIX INEQUALITIES has solution:

$\left[\begin{array}{cccc}Y& 0& A^{T}Y-C^T{W}^T& L^T\\ 0& {\mathrm{\γ}}^{2}I& B^{T}Y-D^T{W}^T& 0\\ \mathrm{YA}-\mathrm{WC}& \mathrm{YB}-\mathrm{WD}& Y& 0\\ L& 0& 0& I\end{array}\right]\≥0---\left(17\right)$

Wherein Y=Y ^t∈ R ^{n × n}, W ∈ R ^{n × r}, J=J ^t∈ R ^{m × m}, the gain K=Y of H ∞ wave filter ^-1w;

For rhodium self-powered detector, by the homography in the known equation of its discrete state equations (15) be:

$A=\left[\begin{array}{ccc}1& 0& 0\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·(1-e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}})& e^{-{\mathrm{\λ}}_1\·\mathrm{Ts}}& 0\\ \frac{1}{c}{a}_2\·g\·(1-e^{-\mathrm{\λ}2\·\mathrm{Ts}})/{\mathrm{\λ}}_2& 0& e^{-{\mathrm{\λ}}_2\·\mathrm{Ts}}\end{array}\right]$

$B=\left[\begin{array}{cc}1& 0\\ 0& 0\\ 0& 0\end{array}\right]$

C＝[c c c]

D＝[0 1]

L＝[1 0 0]

By solving LMI (17), H ∞ electric-wave filter matrix K can be obtained, thus can obtain by following steps the detector current value eliminated and postpone rear any time:

By initial current measured value can obtain $\hat{x}\left(0\right)=\left[\begin{array}{c}\hat{y}\left(0\right)\\ \frac{1}{c}(a_1-a_2\·g/{\mathrm{\λ}}_1)\·\hat{y}\left(0\right)\\ \frac{1}{c}(a_2\·g)\·\hat{y}\left(0\right)\end{array}\right],$ Initial 0 moment postpones to eliminate after-current value $\hat{z}\left(0\right)=C_f\hat{x}\left(0\right);$

For any k+1 (k=0,1 ...) and the moment, and the k+1 moment postpone eliminate after current value be