CN103166233A - Continuous time state estimation method based on Kalman-Bucy filter - Google Patents

Abstract

The invention provides a continuous time state estimation method based on a Kalman-Bucy filter. The continuous time state estimation method is characterized in that a continuous time state equation of a reactive compensation device under the white noise interfering condition is obtained; a process interfering noise matrix and a measurement noise matrix in the continuous time state equation are substituted into a Riccati equation, and gain coefficients of the Kalman-Bucy filter are obtained through the Riccati equation; and the Kalman-Bucy filter is constructed, and a continuous time state estimation value of the reactive compensation device is obtained. By the method, an unbiased estimation value of the reactive compensation device can be obtained, and process noise and measurement noise interference of the reactive compensation device can be effectively filtered; and the method has a better filtering effect compared with the conventional method in which an observer is used and very suitable for electrical equipment such as the reactive compensation device which is complex in electromagnetic interference.

Description

Method for estimating state continuous time based on Kalman Bush filtering

Technical field

The present invention relates to reactive power compensator Control System Design field in iron and steel metallurgical industry, specifically belong to a kind of reactive power compensator method for estimating state continuous time based on Kalman Bush filtering.

Background technology

TCR type reactive power compensator has important function for voltage fluctuation in the solution iron and steel metallurgical industry, power factor regulation, the reactive power compensator PID control structures that adopt based on the output feedback during engineering is used at present more, generally speaking STATE FEEDBACK CONTROL is exported FEEDBACK CONTROL and can be obtained better sound attitude control performance, and state observer is the basis of state feedback, and the state observer that therefore designs a kind of excellence just becomes the basis of reactive compensation control system.Traditional observer based on imperial Burger method is only suitable for state observation and there is no the effect of filtering, can't eliminate for the process noise that exists in system and measurement noise, filter based on Kalman Bush method can be observed state, therefore the random interfering signal that exists in again can filtering appts is fit to be applied to this power electronic system of reactive power compensator very much.

Summary of the invention

The technical problem to be solved in the present invention is: a kind of method for estimating state continuous time based on Kalman Bush filtering is provided, and the reactive power compensator state under the noise jamming environment of can obtaining is without inclined to one side estimation.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: method for estimating state continuous time based on Kalman Bush filtering is characterized in that:

Obtain state equation continuous time under reactive power compensator white noise disturbed condition; And with the process interference noise matrix in this state equation with measure in noise matrix substitution Riccati equation, obtain the Kalman Bush filter gain coefficient of Kalman Bush filter by finding the solution Riccati equation continuous time; Structure Kalman Bush filter obtains reactive power compensator state estimation continuous time value.

As stated above, it is characterized in that: it comprises the following steps:

Step 1, sampling reactive power compensator thyristor control angle u (t) are as the input data, sampling reactive power compensator reactive power y (t) is as the output data, utilize the Model Distinguish algorithm according to input, output data acquisition reactive power compensator continuous time model, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) is the t moment system state variables value that measures,

The differential of expression x (t), w (t) is 1 * 1 process random noise, A, B, C, B _ωBe coefficient matrix, and A is n * n matrix, B is n * 1 matrix, and C is 1 * n matrix, B _ωBe n * 1 matrix, v (t) is for measuring random noise;

The variance of step 2, computational process random noise w (t) is process interference noise matrix W, and the variance of measuring random noise v (t) namely measures noise matrix V, and its computing formula is as follows:

$W=\frac{1}{L_W}\underset{t=t_{W0}}{\overset{t=t_{\mathrm{We}}}{\mathrm{\Σ}}}{(w\left(t\right)-\stackrel{\‾}{w})}^2,$

Wherein

Be the average of process noise, L _WBe the data length of w (t), t _W0Be the initial time of w (t), t _WeBe the termination moment of w (t);

$V=\frac{1}{L_W}\underset{t=t_{V0}}{\overset{t=t_{\mathrm{Ve}}}{\mathrm{\Σ}}}{(v\left(t\right)-\stackrel{\‾}{v})}^2,$

Wherein

Be the average of process noise, L _WBe the data length of v (t), t _V0Be the initial time of v (t), t _VeBe the termination moment of v (t);

Step 3, the process interference noise matrix W that obtains according to step 2 and measure noise matrix V, and coefficient matrices A, C, B in step 1 _ω, find the solution Riccati equation

Obtain positive definite symmetric matrices P; The wherein transposition computing of symbol " T " representing matrix, symbol " 1 " expression is carried out inversion operation to matrix;

Step 4, the positive definite symmetric matrices P that tries to achieve by step 3, computer card Germania Bush filter gain COEFFICIENT K=P * C ^T* V ^-1

Step 5, utilize u (t), y (t) structure Kalman Bush filter, the continuous time filter structure is following form: $\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=A\hat{x}\left(t\right)+\mathrm{Bu}\left(t\right)+K(y\left(t\right)-C\hat{x}\left(t\right)),$ Wherein Be the estimated value of x (t),

For

Differential.

Beneficial effect of the present invention is: this method not only can obtain the reactive power compensator state without inclined to one side estimation, but also can and measure noise jamming and carry out effective filtering the reactive power compensator process noise, more traditional state observer has better filter effect, is fit to very much be applied to the power equipment of this electromagnetic interference complexity of reactive power compensator.

Description of drawings

Fig. 1 is the flow chart of one embodiment of the invention.

Fig. 2 is reactive power compensator the first state estimation value curve.

Fig. 3 is reactive power compensator the second state estimation value curve.

Fig. 4 is that the actual output reactive power curve of reactive power compensator is estimated curve of output contrast effect figure with adopting this method.

Embodiment

Based on reactive power compensator method for estimating state continuous time of Kalman Bush filtering, obtain state equation continuous time under reactive power compensator white noise disturbed condition; And with the process interference noise matrix W in this state equation with measure in noise matrix V substitution Riccati equation, obtain the Kalman Bush filter gain coefficient of Kalman Bush filter by finding the solution Riccati equation continuous time; Structure Kalman Bush filter obtains reactive power compensator state estimation continuous time value.

Fig. 1 is the flow chart of one embodiment of the invention, and it specifically comprises the following steps:

Step 1, sampling reactive power compensator thyristor control angle u (t) are as the input data, sampling reactive power compensator reactive power y (t) is as the output data, utilize the Model Distinguish algorithm according to input, output data acquisition reactive power compensator continuous time model, concrete model is described as $\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B_{\mathrm{\ω}}w\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+v\left(t\right)\end{array}\right.,$ Wherein x (t) is the t moment system state variables value that measures,

The differential of expression x (t), w (t) is 1 * 1 process random noise, A, B, C, B _ωBe coefficient matrix, and A is n * n matrix, B is n * 1 matrix, and C is 1 * n matrix, B _ωBe n * 1 matrix, v (t) is for measuring random noise;

The variance of step 2, computational process random noise w (t) is process interference noise matrix W, and the variance of measuring random noise v (t) namely measures noise matrix V, and its computing formula is as follows:

$W=\frac{1}{L_W}\underset{t=t_{W0}}{\overset{t=t_{\mathrm{We}}}{\mathrm{\Σ}}}{(w\left(t\right)-\stackrel{\‾}{w})}^2,$

Wherein

Be the average of process noise, L _WBe the data length of w (t), t _W0Be the initial time of w (t), t _WeBe the termination moment of w (t);

$V=\frac{1}{L_W}\underset{t=t_{V0}}{\overset{t=t_{\mathrm{Ve}}}{\mathrm{\Σ}}}{(v\left(t\right)-\stackrel{\‾}{v})}^2,$

Wherein

Be the average of process noise, L _WBe the data length of v (t), t _V0Be the initial time of v (t), t _VeBe the termination moment of v (t);

Step 3, the process interference noise matrix W that obtains according to step 2 and measure noise matrix V, and coefficient matrices A, C, B in step 1 _ω, find the solution Riccati equation

Obtain positive definite symmetric matrices P; The wherein transposition computing of symbol " T " representing matrix, symbol " 1 " expression is carried out inversion operation to matrix;

Step 4, the positive definite symmetric matrices P that tries to achieve by step 3, computer card Germania Bush filter gain COEFFICIENT K=P * C ^T* V ^-1

Step 5, utilize u (t), y (t) structure Kalman Bush filter, the continuous time filter structure is following form: $\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=A\hat{x}\left(t\right)+\mathrm{Bu}\left(t\right)+K(y\left(t\right)-C\hat{x}\left(t\right)),$ Wherein Be the estimated value of x (t),

For

Differential.

Be connected to a TCR type reactive power compensator on certain 6.5kV of steel mill bus, every phase reactance inductance value L=18.7mH, utilize open loop to control compensation arrangement is carried out the Model Distinguish experiment, the sample reactive power y (t) of thyristor control angle u (t) and system's output in 1 second, utilize Model Distinguish algorithm acquisition reactive power compensator system model to be:

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=\left[\begin{array}{cc}-10.9025531534668& -188.779022142286\\ 148.7801599579912& 2.4037216595325\end{array}\right]x\left(t\right)+\left[\begin{array}{c}-1856.51\\ -115.25\end{array}\right]u\left(t\right)+\left[\begin{array}{c}-0.0017876\\ -0.0117144\end{array}\right]w\left(t\right)\\ y\left(t\right)=\left[\begin{array}{cc}21765000& -4458700\end{array}\right]x\left(t\right)+v\left(t\right)\end{array}\right.,$

Calculate by step 2 and obtain the variance W=1 that process noise disturbs w (t), measure the variance V=1 of noise jamming v (t).

Separate Riccati equation by step 3, can get positive definite symmetric matrices P and be:

$P={10}^{-8}\×\left[\begin{array}{cc}0.019908481942324& 0.133937002203074\\ 0.133937002203074& 0.916964105134374\end{array}\right].$

According to step 4 computer card Germania Bush filter gain COEFFICIENT K be:

$K=\left[\begin{array}{c}-0.001638768022482\\ -0.011733290026127\end{array}\right],$ K is also a matrix.

According to step 5 structure Kalman Bush filter, its expression formula is:

$\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=\left[\begin{array}{cc}-10.9025531534668& -188.7790221402286\\ 148.7801599579912& 2.4037216595325\end{array}\right]\hat{x}\left(t\right)+\left[\begin{array}{c}-1856.51\\ -115.25\end{array}\right]u\left(t\right)$

$+\left[\begin{array}{c}-0.001638768022482\\ -0.011733290026127\end{array}\right]\left(y\left(t\right)-\left[\begin{array}{cc}21765000& -4458700\end{array}\right]\hat{x}\left(t\right)\right).$

Above-mentioned Kalman Bush filter abbreviation can be got

$\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=\left[\begin{array}{cc}35656.9& -7495.6\\ 255524.1& -52312.9\end{array}\right]\hat{x}\left(t\right)+\left[\begin{array}{c}-1856.51\\ -115.25\end{array}\right]u\left(t\right)+\left[\begin{array}{c}-0.001638768022482\\ -0.011733290026127\end{array}\right]y\left(t\right)$

According to the Kalman Bush filter after abbreviation, with actual reactive-load compensator input u (t), output data y (t) substitution state estimation formula, (state determines according to the model that identification obtains can to get 2 kinds of states of the reactive power compensator shown in accompanying drawing 2 and accompanying drawing 3, model parameter is different, and state is just different) estimation curve.Can find from accompanying drawing 2 and 3, can follow the tracks of rapidly the variation of virtual condition when estimated state changes in system, show that Kalman Bush filter has status tracking ability fast.But significantly fluctuation has appearred in the estimated state instantaneous value when virtual condition changes, although fluctuation disappears very soon, can cause shake for control system, and this point needs to continue research to eliminate this phenomenon.

2 kinds of states of reactive power compensator that above-mentioned estimation is obtained utilize computing formula The idle output of estimating system, its curve as shown in Figure 4, relatively the similarity degree between output estimation curve and actual curve can be found, except estimating that when larger variation occurs system's virtual condition output valve has very large momentary fluctuation, all the other can both be consistent with real output value constantly, show that the present invention designs the Kalman Bush filter that obtains and has filtering preferably and state estimation ability.

Claims (2)

1. based on method for estimating state continuous time of Kalman Bush filtering, it is characterized in that:

Obtain state equation continuous time under reactive power compensator white noise disturbed condition; And with the process interference noise matrix in this state equation with measure in noise matrix substitution Riccati equation, obtain the Kalman Bush filter gain coefficient of Kalman Bush filter by finding the solution Riccati equation continuous time; Structure Kalman Bush filter obtains reactive power compensator state estimation continuous time value.

2. method for estimating state continuous time based on Kalman Bush filtering according to claim 1, it is characterized in that: it specifically comprises the following steps:

Step 1, sampling reactive power compensator thyristor control angle u (t) are as the input data, sampling reactive power compensator reactive power y (t) is as the output data, utilize the Model Distinguish algorithm according to input, output data acquisition reactive power compensator continuous time model, concrete model is described as

Wherein x (t) is the t moment system state variables value that measures,

The differential of expression x (t), w (t) is 1 * 1 process random noise, A, B, C, B _ωBe coefficient matrix, and A is n * n matrix, B is n * 1 matrix, and C is 1 * n matrix, B _ωBe n * 1 matrix, v (t) is for measuring random noise;

The variance of step 2, computational process random noise w (t) is process interference noise matrix W, and the variance of measuring random noise v (t) namely measures noise matrix V, and its computing formula is as follows:

$W=\frac{1}{L_W}\underset{t=t_{W0}}{\overset{t=t_{\mathrm{We}}}{\mathrm{\Σ}}}{(w\left(t\right)-\stackrel{\‾}{w})}^2,$

Wherein

Be the average of process noise, L _WBe the data length of w (t), t _W0Be the initial time of w (t), t _WeBe the termination moment of w (t);

$V=\frac{1}{L_W}\underset{t=t_{V0}}{\overset{t=t_{\mathrm{Ve}}}{\mathrm{\Σ}}}{(v\left(t\right)-\stackrel{\‾}{v})}^2,$

Wherein Be the average of process noise, L _WBe the data length of v (t), t _V0Be the initial time of v (t), t _VeBe the termination moment of v (t);

Step 3, the W and the V that obtain according to step 2, and coefficient matrices A, C, B in step 1 _ω, find the solution Riccati equation

Obtain positive definite symmetric matrices P; The wherein transposition computing of symbol " T " representing matrix, symbol " 1 " expression is carried out inversion operation to matrix;

Step 4, the positive definite symmetric matrices P that tries to achieve by step 3, computer card Germania Bush filter gain COEFFICIENT K=P * C ^T* V ^-1

Step 5, utilize u (t), y (t) structure Kalman Bush filter, the continuous time filter structure is following form: $\stackrel{\stackrel{\·}{^}}{x}\left(t\right)=A\hat{x}\left(t\right)+\mathrm{Bu}\left(t\right)+K(y\left(t\right)-C\hat{x}\left(t\right)),$ Wherein

Be the estimated value of x (t), For Differential.

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