SU1322329A1 - Device for determining coefficients of statistical linearization of non-linear dynamic systems - Google Patents

Abstract

The invention relates to the field of computer technology and can be used in modeling to determine the characteristics of nonlinear dynamic systems. The purpose of the invention is to improve the accuracy of the device. Yci poftcTBo contains adder 1 ,. 2.1-2.3 blocks of averaging, inverter 3, switches 4.1-4.3, quad 5, blocks 6.1 and 6.2 multiplying by the sign, voltage amplifiers 7.1 and 7.2, multiplication block 8, amplifiers 9.1 and 9.2 with adjustable gain, 11 clock pulses. The accuracy of determining the coefficients of statistical linearization according to two criteria of statistical equivalence is improved. 2 Il. 00 to to with N) CO (Rich.1

Description

The invention relates to computing and can be used in modeling to determine the characteristics of nonlinear dynamic systems.

The purpose of the invention is to improve accuracy.

Figure 1 shows the structural diagram of the device; Fig. 2 shows stress diagrams for operation of the device.

The device (Fig. 1) contains an adder 1, averaging blocks 2.1-2.3, an inverter 3, switches 4.1-4.3, quad 5, blocks 6.1 and 6.2 multiplied by a sign, voltage amplifiers 7.1 and 7.2, multiplication block 8, amplifiers 9.1 and 9.2 with adjustable gain, outputs 10 and pulse generator 11.

The voltage plots are removed at the input and output of block 2.1 (Fig. 2a), at the output of switch A.1 (Fig. 2b), at the input and output of block 2.2 and at the output of amplifier 7.1 (Fig. 2b), the transmission gain of amplifier 9. 1 (FIG. 2d) at the output of the amplifier 9.1 with adjustable gain (FIG. 2e at the input and output of the unit 2.3 and the output of the amplifier 7.2 (FIG. 2e).

According to the theory of statistical linearization, any non-linear dynamic system can be linearized by a function of the form

U (t) if + Kx (t),

(one)

where U (t) is an approximating random function at the output of the model of a nonlinear dynamic system:

t /.

y is the statistical characteristic of a nonlinear dynamic system;

K is the equivalent of statistical linearization; t - mathematical expectation.

The statistical characteristic i / and the statistical linearization coefficient K are determined by two equivalence criteria. G1 of them requires equal expectation and variance, respectively, of the finite y (t) and the approximating U (t) functions, i.e.

3223292

(t) (t), (2)

(t) -m / t) (t) -ni, (t) | (3)

or

ha

6 // 6,

(A) (5)

The coefficient K shows that it is found by the first criterion of equivalence. The second equivalence criterion is satisfied if the mean square of the process difference is minimal, i.e.

y (t) - U (t) J

min

 2

 x (t) Xlt).

6v

(6)

(7)

From expressions (4) - (7), it can be seen that the statistical characteristics of nonlinear dynamical systems coincide according to the mathematical expectation, and the transfer coefficients with respect to the centered component differ.

The first criterion for the statistical equivalence of nonlinear and linearized elements gives a higher value of the correlation function R (f), and the second criterion is underestimated. In this case, the first criterion provides the best match of the correlation 5 function at the output of the linearized and nonlinear elements at small values of t, the second equivalence criterion gives the best match of these functions at large values of J.

The device works as follows.

The input signal y (t) is fed to the first input of the adder 1, block 2.1 and the second input of the switch 4.2, and the random signal x (t) to the information input of the amplifiers 9.1 with a regular gain factor, the first information input of the switch 4.2 and the second input of the block 8 At the output of the average filter 2.1, the value 7 (t) j is set.

At the output of the adder 1

0

0

five

is

signal and y (t) - m, j (t) y (t).

The output signal of the amplifier with a controlled gain of 9.1 and K, x (t).

At the first moment, when the switches 4.1-4.3 are in the position as

silt

shown in the drawing and b; currents 6.1 and 6.2 have a gain equal to +1, the following signals are set at the outputs of blocks 2.2 and 2.3 respectively: U, y (t); U Kjx (t) 2.

At the next time point, the switches 4.1–4.3 are in the opposite position, and the amplifiers 6.1 and 6.2 with a variable sign of the coefficient, the input of the adder is connected to the output of the gain, have a coefficient equal to –1, the filter outputs are signals Uj (t) 2; 114 -y (t) .x (t).

The generator 11 implements the principle of temporal separation of signals, generates at the output of the averaging blocks of movements a signal having the form

the multiplier by the sign whose informational output is connected to the output of the quad, the control input of the first multiplier for the sign is connected to the output of the clock generator with the control input of the second multiplier by the sign, the first input of the adder is the second information} the input of the device, in the water of the first inverter, is about the fact that, in order to improve the accuracy, three switches are introduced into it, the second amplifier

15, the second amplifier with a variable {gain factor, multiplication unit, the input of the second averaging unit is connected to the first information input of the first commutator and connected to the first information input of the adder, the second information input, the first switch connects to the first input of the multiplication unit and connected to the information input of the first amplifier with an adjustable gain factor, the second multiplication input is connected to the output of the first switch, the control input of which is connected to the control inputs W cerned and third switches and connected to the output of the clock, the adder output being connected to the first information do WMOs second switch, the second infor

meander, the amplitude of positive pulses of which is equal to 2.2Uj at the input of the block, 2.3 U block, and negative and and and, respectively.

As a result, signals are set at the outputs of blocks 2.2 and 2.3.

25

15

and, Cy (t) (t) p d 5-K; 62.

Ufc K2 (t) -y (t) x (t) K i2-y (t) x (t),

those. Conditions 8 and 5 are fulfilled and the device outputs signals

and I / M y (t);

g - /;

and - y (t) x (t).

Claims (1)

Invention Formula A device for determining statistical linearization coefficients of nonlinear dynamic systems comprising adders, a first voltage amplifier, a first amplifier with adjustable gain, a clock generator, two inverters, two sign multipliers, a quad, two blocks averaging, information input-first ycH- The fO on input of which is connected to a variable gain variable output is the first information input of the device, the control input of the first amplifier with an adjustable gain. ientom gain soe- 55 th and second averaging units and perdinen yield first amplifier (voltage, whose input is connected to the output of the first averaging unit, whose input is connected to the output of the first four silt The other input of the adder is connected to the a multiplier for the character whose informational output is connected to the output of the quad, the control input of the first multiplier for the character is connected to the output of the clock generator with the control input of the second multiplication unit for the sign, the first input of the adder is the second information} In the second, the adder input is connected to the about five the house of the first inverter, which is due to the fact that, in order to increase accuracy, three switches were introduced into it, the second amplifier 5, a second amplifier with a variable {gain} gain, a multiplication unit, the input of the second averaging unit is connected to the first information input of the first switchboard and connected to the first information input of the adder, a second information input, the input of the first switch is connected to the first input of the multiplication unit and connected to the information input of the first amplifier with adjustable gain, the second multiplication input is connected to the output of the first switch, the control input of which is connected to the control inputs of the watt of the third switch and connected to the output of the clock generator, the adder's output is connected to the first information input of the second switch, the second information input of which is connected to the output of the first amplifier with adjustable gain, the output of the second switch is connected to the quad input, the output of the multiplication unit is connected to the first information input of the third switch and the information input of the second amplifier with adjustable gain, the second input of which is connected to you In the course of the second voltage amplifier, the input of which is connected to the output of the second averaging unit, the input of which is connected to the output of the second multiplication unit by the sign, the information 0 five The third switch, the second input of which is connected to the output of the second amplifier with an adjustable gain factor, the outputs of the primary voltage amplifier are the outputs of the corresponding statistical linearization coefficients of the device. .2 Editor N.Rogulich Composition1 tel I.Muhin Tehred L.Oliypyk Order 2868/48 Circulation 572 Subscription VNIIPN USSR State Committee for inventions and discoveries 113035, Moscow, Zh-35, Raugska nab. 4/5 Production and printing design, Uzhgorod, Proektna str., 4 Proofreader L .Patay