SU1084736A1 - Quantized filter - Google Patents

Abstract

DISCRETE FILTER containing the first correction block and the saf holder block in series, the extrapolation block, the feedback block and the first Comparison element, characterized in that, in order to improve the accuracy of reproduction of the useful signal with measurement errors imposed on it in the absence of disturbing noise , a compensation filter is introduced into it, the second element of the comparison, the first and second adders and the second correction block, the input of which is connected to the output of the first correction block and to the first input the house of the first adder, the second input of the extrapolation unit connected to the output and the first input of the second adder, the second input of which is connected to the output of the second correction unit, the input of the compensation filter is connected to the second input of the first reference element, and the output to the first input of the second comparison element , the second (L input connected to the output of the first element comparison, the output to the input of the first correction unit, and the output of the first adder is connected to the input of the delay unit. X) 4 a

Description

The invention relates to systems of automatic control and control, intended for high-quality separation of the useful signal from the additive mixture of signal and interference.

An optimal discrete filter is known, which makes it possible to improve the quality of automatic control systems when they are subjected to an additive mixture of signal and noise lj.

Closest to the present invention is a discrete filter comprising a first correction block and a serially connected delay block, an extrapolation block, a feedback block and the first element of comparison 2j.

A disadvantage of the known filter is that, when synthesized from the optimality conditions, it does not provide high-quality reproduction of the useful signal with errors imposed on it in the absence of disturbing noise.

The purpose of the invention is to increase the accuracy of reproduction of the useful signal when errors are imposed on it in the measurement in the absence of disturbing noise.

The goal is achieved by introducing a compensation filter into the discrete filter, the second comparison element, the first and second adders and the second correction block, whose input is connected to the output of the first correction block and the first input of the first adder, the second input connected to the output of the extrapolation unit and the first input of the second adder, the second input of which is connected to the output of the second correction block, the input of the compensation filter is connected to the second input of the first comparison element, and the output to the first y input of the second comparison element, a second input connected to the output of the first comparison element, the output - to the input of the first correction unit and the output of the first adder is coupled to the input of the delay unit.

FIG. 1 shows the structural scheme of the proposed discrete filter J ya of FIG. 2 is a block diagram of the compensation filter in FIG. 3 is a block diagram of the input action model; in fig. 4 graphs of the passage of the useful signal in FIG. 5 - graphs of the passage of interference (measurement errors).

The discrete filter contains the first (corrections unit 1, delay unit 2, extrapolation unit 3, feedback unit 4, first comparison element 5, compensation filter 6, second comparison element 7, first 8 and second 9 adders, second correction unit 10. Blocks 1, 3, 4, 10 are described by transfer matrices K, K, K, respectively, and block 2 - by the delay operator E

FIG. 2 shows a matrix structural scheme of a compensation filter synthesized on the basis of the X symmetry properties with respect to

models of the input action shown in FIG. 3. Here, the vector of disturbing noise (oi is assumed to be zero), Xd, x, g, -i, 3. The vectors of the initial state, state, useful effect, Measurement errors and input filter effect, respectively. The compensation filter 6 decomposes the following I blocks: observation blocks 11 and 12 with I and H matrices, respectively, delay blocks 13 and 14, extrapolation blocks 15 and 16 with the transfer matrix F (1), reference element 17, transfer block 18 with a factor

To "0

at time n 0 and

Ch8

at times p 0, adder 19, adder 20, extrapolation unit 21 with transfer matrix F (1), delay unit 22, observation unit 23 with matrix I, adder 24.

From the comparison of the circuits of FIG. 2 and Fig. 3, it follows that the blocks 11, 13, 15 and 17 of the compensation filter are symmetric (with respect to the point n = the vector of measurement error vector i (n + l) to the corresponding blocks 23, 22, 21 and 2 of the input effect model. There is a reversal of mathematical operations in the blocks of the compensation filter with respect to the corresponding blocks of the mathematical model of the input action (summation in block 20 and subtraction in element 17, direct H conversion in block 23 and the inverse transformation in block 11).

FIG. 4 shows graphs of useful signals at the outputs of the model blocks and the compensation filter. from which it can be seen that the useful signal at the output of the comparison element 17 is zero everywhere, except for the initial moment of time L 0. This is explained by the fact that the extrapolator of block 1 is exactly the same as the extrapolator of block 21, and the matrix of blocks 23 and 11 mutually inverse. FIG. Figure 5 shows graphs of measurement errors (interference) at the outputs of the compensation filter blocks, illustrating the order of the passage of measurement errors, 2,. through the blocks of the compensation filter. The device works as follows. . The input signal of the filter U (n + 1), which is an additive mixture of the useful signal (and + 1) and measurement errors (n + 1), is fed to the comparison element 5 and the compensation filter 6. The signal of the AuCn-1 signal is output comparison element 5 and the output signal of the compensation filter 6, which is a vector of measurement errors (n + are subtracted in the comparison element 7, the output signal of which is proportional to the useful signal through the correction unit 1 is fed to the adder 8 and the second correction unit 10. From the output of the adder 8 signal through the sequence The interconnected delay unit 2 and extrapolation unit 3 are fed to the second input of this adder, as well as to the adder 9 and through the feedback unit 4 to the comparison element 5. The output signal of the filter is removed from day 9, the second input of which receives the signal from the output of block 10. We show that the proposed discrete filter actually provides high-quality reproduction of the useful signal with errors imposed on it in the absence of disturbing noise and that the stability of the filter than the prototype. Considering that the beneficial effect and measurement errors are related by an additive operator, one can approach the task of constructing an effective discrete filter from other positions. Based on the symmetry property of a known model of a useful signal, a compensation filter can be synthesized to attenuate the vector of measurement errors. Then it becomes possible to synthesize a full corrective device from the condition of invariance of the error from the useful signal. At the time P 0, the coefficient of block 18 is O and the writing of the useful signal x to block 14 of the delay is not performed. At the moment of time, interference -1 is recorded in block 13 and in block 14 (since the coefficient of block 18 is already equal to 1) and, apart from Toroi-, this interference passes to you-. the course of the compensation filter is unchanged (since it is a single matrix). At the next moment of time, compensation occurs due to a change in the polarity of the noise in the reference element 17, with the noise in passing to the output of the filter without changes, etc. As a result of the operation of the compensation filter at its output, starting from the time moment ri-I, there will be only a measurement error (disturbance), and there is no useful signal. The inclusion of the compensation filter 6 in the discrete filter circuit (Fig.) Allows to completely eliminate the presence of interference in the skewer signal & U, which makes it possible to calculate the second correction block 10 from (INVARIANCE CONDITIONS. To this end, from the block diagram (Fig. 1 ) we find the signal X (and + 1). X, ("40-KVX, (n + 1) EH | S, nx {p44)) G1 .. (1) From X, tnt)., K4K3E-7XHxUM ). (2) Input designation, 1С4цг - ..: for Il- 3 we get the following expressions for the signal X- (n + 1)). NOT-X (pi); (3) Find the signal X (ifj +1) i CDP4) K ,, “LI 1I g, HX (miVk4kirV, (. Kq H, then taking into account (2) Since we get HeM-, OK, K4 1-KgECH-1 P4-dU (4) 51 Folding expressions (3) and (4) we have the following expression for estimating the useful signal taken from the adder 9, X (r and V-X2 (pmNH1, K, o): L4-K okLK41 WE - nx (II). From (5) it follows that the output the filter signal d (n + 1) will be equal to the input useful signal x (n + 1) if the expression in braces is equal to 1. This happens if the matrix k Correction block 10 will have 10, 6) Unlike the optimal Kalman filter, there are no hard restrictions on the choice of matrix elements Cd. Therefore, correction block 1 in Fig. 1 can be chosen from the stability conditions of the closed control loop formed by blocks 1-8 The existing tuning algorithms of the correction block 1 (i.e., devices with variable parameters) are calculated from the filter's optimality conditions and, therefore, do not ensure its stability, as a result of which the actual processes occurring in Information processing systems tend to diverge. The effectiveness of the proposed discrete fi-ttra in front of the known one, which is selected as a discrete filter with constant parameters (memory) (1), will be shown using a specific example. Let the beneficial effect X (t) in discrete time (tc) be described by a polynomial of the first degree) ((nHUxU- T, where T is the discrete period X (n-1) is the rate of change of the beneficial effect. Entering the x / n state variables) - (p),) x (d)) we obtain the following, ie, the equations of extrapolation of the discrete filter X (I, X, (n-1) f) T, XjCn) X (nl). Whence the extrapolation matrix for the mett view 1 t 10 lj Suppose that one condition X is measured (observed) (n), we obtain the observation matrix I l o (8) And therefore the weight matrix K of the discrete filter is D - constant parameters. We show that at the output of the compensation filter 6 (Fig. 1), interference i will be detected. FIG. 5 for the moment of time AND 1 we have U «-HH-4 ,, - ,,. .V,.« -.,. ,, ibiol o ii - ™ ... f ,. Since the value of the noise at the output of blocks 16 and 17 is the same and opposite in sign, their sum is zero, and at time point C 2 at the output of the compensation filter, the value of the noise is i. Thus, the compensation filter 6 produces interference i () when And 1, 2, On the other hand, according to the graphs of FIG. 4, the useful signal 5 (at the outputs of blocks 11 and 15 at time t1, respectively, will accept id -., Where XQ and X02 are the magnitudes of the useful effect and its speed at the initial moment of time. This shows that undercompensation of the useful signal at the output of the comparison element 17 equal to vector IX T1 0,2. It is easy to see that all the amount of undercompensation remains the same with p 1. Passing blocks I9, 16, 14 and 12 this undercompensation becomes a scalar value where n 1 ,, ,, equal to virXo2 Since, in element 7 of the comparison, its insertion from the signal does not occur, the purpose of preserving the formation of the useful signal (useful information at the output of element 7, comparison) is necessary to choose the matrix of block 4 equal to 4, where P 1,2, .... Then, along the compensating feedback circuit, additional signals will be sent to the comparison element 5 equal to the PTX, which will lead to the elimination of undercompensation. Consequently, the signal of the LU unresolved signal at the output of the comparison element 7 will be cleared of interference, i.e. iiU - X, - -5, where Xj is the true value of the useful signal; - extrapolated value of the useful signal, (the value of the signal at the output of block 4 without an additional signal TX02) J 6g extrapolation error. According to condition (6), the elements of the matrix K must be inverse to the elements of the matrix. Therefore, with n which approximation we choose Ilk about 1 about 1 ((JE) (9) and (10), we find the X signal at the output of block 1, we have. "С iUl Г ot, ЕэТ р / т J Taking into account (11) we get signal X, at the output of the 10 th unit {about aHPG ee G ee o From the scheme of Fig. 1, we obtain the vector of estimated parameters X as the sum of the vectors X2 and X2, i.e., e --. - Xx-l Replace E with (according to ( 10 we get (14 ,, T G x, -x, e 1 -.Gh. LXzJ ZjU23J4l | TCX, -X ,,) j Hl X ,, M | T (X, -X ,,) J. (.15 ) It can be seen from expression (15) that the estimate X of the useful signal is equal to the true value X of the most useful signal. Consider the estimate J, the speed of measurement of the useful effect. 2 X "RON, -X,). (16) We perform the analysis of expression (16) for the moment of evaluation I 1, according to known initial value Q of the beneficial effect and X. its rate of change, then .1 ..; .., T . S ° -i t So. As the estimate of the useful signal is equal to the true value of the most useful signal, i.e. X X (0), then. XK ,, iX, W. (.7, From (17) it is clear that X2 of the rate of change of the useful signal is equal to the true value of X2 of the net of the useful signal. The delay in time for the period of discreteness T when estimating the speed is due to the incomplete observability of all components of the useful signal X (i) and is inherent in both the prototype and the base object. Consequently, the error in reproducing the useful signal and its rate of change in the proposed discrete filter is zero (i.e., x x, l, whereas in the prototype, these errors are not zero and are determined by the diagonal elements of the filter error matrix. The advantage is offered by the south discrete filter Before known, it is disclosed in the analysis of estimation errors for the conditions of the considered example. Thus, in the proposed discrete filter in the absence of disturbing noise (0, Fig. 3), complete compensation of the measurement error is provided It is possible to realize the conditions of the invariant, anti-error, reproduction errors of the useful signal, while the filter stability is higher than that of the prototype and the base object.

f (n4t}

Jfn) ± i

ff ()

Phag.Z ftHft)

Claims (1)

A DISCRETE FILTER comprising a first correction unit and a sequentially connected delay unit, an extrapolation unit, a feedback unit and a first comparison element, characterized in that, in order to increase the accuracy of reproducing a useful signal when measurement errors are superimposed on it in the absence of disturbing noise, a compensation filter, a second comparison element, the first and second adders and the second correction block, the input of which is connected to the output of the first correction block and to the first input, are introduced into it the first adder, the second input connected to the output of the extrapolation unit and the first input of the second adder, the second input of which is connected to the output of the second correction unit, the input of the compensation filter is connected to the second input of the first comparison element, and the output to the first input of the second comparison element, the second input connected to the output of the first comparison element, the output to the input of the first correction unit, and the output of the first adder is connected to the input of the delay unit. ~ .SU „„ 1684736