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SOME PROBLEMS OF THE THEORY OF LINEARIZATION OF RECEIVING INFORMATION OF A MICROPROCESSOR RECEIVER OF CODE AUTO-LOCKING RAIL CIRCUITS
Talat Gayubov
Ph.D., Associate Professor, Tashkent State Transport University Republic of Uzbekistan, Tashkent E-mail: gayubov.talat.6996@gmail.com
Azamat Sadikov
Assistant,
Tashkent State Transport University Republic of Uzbekistan, Tashkent E-mail: san.pgups@gmail.com
Saidazim Ubaydullayev
Assistant,
Tashkent State Transport University Republic of Uzbekistan, Tashkent E-mail: saidazim688@gmail.com
НЕКОТОРЫЕ ПРОБЛЕМЫ ТЕОРИИ ЛИНЕАРИЗАЦИИ ПРИЕМНОЙ ИНФОРМАЦИИ МИКРОПРОЦЕССОРНОГО ПРИЁМНИКА РЕЛЬЦОВЫХ ЦЕПЕЙ КОДОВОЙ АВТОБЛОКИРОВКИ
Гаюбов Талат Нуриддинович
канд. техн. наук, доцент,
Ташкентский государственный транспортный университет Республика Узбекистан, г. Ташкент
Садиков Азамат Нематуллаевич
ассистент,
Ташкентский государственный транспортный университет Республика Узбекистан, г. Ташкент
Убайдуллаев Саидазим Кахрамон угли
ассистент,
Ташкентский государственный транспортный университет Республика Узбекистан, г. Ташкент
ABSTRACT
This article discusses the static linearization problem consisting in finding a way to obtain a given non-linear transformation using a linear one. The paper reviews the application of the dispersion function to nonlinear objects with jointly static and harmonic linearization, comparing the results with other methods. Non-linear models are modeled in the form of various combinations of linear dynamic links and non-linear inertialess elements.
АННОТАЦИЯ
В данной статье рассматривается задача статической линеаризации, состоящая в отыскание способа получения заданного нелинейного преобразования с помощью линейного. В работе пересматривается применение к нелинейным объектам дисперсионной функции с совместно статической и гармонической линеаризацией сравнение полученных результатов с другими методами. Нелинейные модели моделируется в виде различных комбинаций линейных динамических звенев и нелинейных безынерционных элементов.
Keywords: linearization, nonlinearity, harmonics, dispersive, random, asymmetrically, statistical, correlation.
Ключевые слова: линеаризация, нелинейный, гармонической, дисперсионно, случайный, асимметрично, статистический, корреляционный.
Библиографическое описание: Gayubov T.N., Sadikov A.N., Ubaydullayev S.K. SOME PROBLEMS OF THE THEORY OF LINEARIZATION OF RECEIVING INFORMATION OF A MICROPROCESSOR RECEIVER OF CODE AUTO-LOCKING RAIL CIRCUITS // Universum: технические науки : электрон. научн. журн. 2022. 4(97). URL:
https://7universum. com/ru/tech/archive/item/13509
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The task of statistical linearization is to find a way to obtain a given nonlinear change statement using a linear transformation. Its solution is important in the study of complex systems.
Certain methods of statistical linearity based on correlation functions (1) in many respects do not lead to the expected goal in describing linear objects, because they do not satisfy the given level of accuracy of object description (description) in many practical cases [1, 2, 3].
In this connection, the idea of creating another, dispersive function-based method of statistical and harmonic linearization emerged, which is based on conditional moment descriptions (2).
There is a nonlinear object of the following type (appearance)
y=9(x+v),
where y - Is the output signal, 9 - is an arbitrary nonlinearity, x - random errors, v - sinusoidal signal, ie:
y(t) = mx + x(t),
v(t) = Amsin^t + x(t),
(1)
(2) (3)
where x - is a centralized random function. The output signal (1) for nonlinearity has the following appearance:
y(t) = Amsin^t + x(t),
(4)
where Am, y - are constant quantities (signal amplitude and frequency).
If the nonlinearity is not a definite (neodnoznachna), then by presenting the product of the input signal between the arguments we present it in the form of a definite inertial relation [4].
У = (X + 7,X +V)
(5)
The method of dispersive linearization (3,4) can be used to linearize the line (1) and relatively general (5). In this case, the statistical characteristics (description) of the nonlinear joint and the statistical coefficients of amplification are periodic functions of time due to the periodic dependence of the input signal on the mathematical expectation time.
mu = mx + Amsin^t,
(6)
On the other hand, when using harmonic linearization, the harmonic coefficients of amplification become a random value due to a random component in the input signal. In this case, co-dispersion and harmonic linearization should be used, i.e. it is expedient to replace the nonlinearity with an approximate dependence on the linearity with respect to the sinusoidal and centered random component of the input signal. In this case it is possible to apply first the variance linearization, and then
the harmonic type, after which they must be replaced [5, 6, 7].
Carrying out the dispersion linearization of nonlinearity (1), we present it in the following form:
(t) = y0(mx + Amsirnpt1DxlGxx) + K1(mx + Amsin^t1Dxl9xx)x(t) (7)
It is known from formula (7) that 90 and h are periodic functions of time. Suppose that the mathematical expectation of a random signal mx(t), its variance Dx(t), and the variance function 0xx(i) change much more slowly to make them constant over the period of the sinusoidal part of the input signal [8, 9]. We apply harmonic linearization (4) to the functions 90 and ki, i.e. by placing them in the Fure series, leaving only the constant component and the first harmonic of the function
y0(mx + Amsin^tiDxi8xx) « y'0(A m, mx, Dx, Qxx) +
a*(Am,rnx,Dx,6xx)Amsin^t, (8)
where
9*o = ~ J** (mx + Amsin^, Dx , 0xx)d^ (9)
a* = -^С^ФоОпх + AmSin^Dx )sin^d^. (10)
nAm -u
In order to prevent the occurrence of nonlinear terms in the propagation of the function ki, we leave only the constant component:
ki(mx + AmSin^t;Dxi Gxx)
~ K (mx , Ami Ddftx)= — f0"Ki(mx +
Amsin^ Dx , Qxx )d ^
(11)
As a result, we have the following apparent approximate linerization:
y(t) ~ 9*0 + a* Amsin^t + ki*x(t). (12)
Using the asymmetry of the variance function, we apply different options and coefficients of amplification of ki depending on the nonlinearity [10], i.e.:
ki=0yX ■ [0XX]-', ki=0yy [0XXJ-1,
ki=0 Xy ■ [0xxJ (13)
0yx (t,s) = M {{M {yt / Xs}-M{yt }}2}, (14)
0xy (t,s) = M {{M {xt / ys}-M{xt }}2}, (15)
0xx (t,s) = M {{M {xt / xt' }-M{xt }}2}. (16)
Similar modifications of the joint linearization can also be made for a non-definite function provided in connection with (2). The only difference is that the gain coefficients on the arbitrary numbers x and v appear [11, 12, 13].
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The linear relationship for (2) in this case looks like
this:
y(t)=^ fT<Po(™* + +Amsirnp,Amcosxp, Dx ,D'X ,QXX ^'^d^+^-f^yo^ +
+Amsin^,Amcos^,Dx ,D'X ,dxx ,9'xx)sin^d^ -Amsinyt+-^ C"Vo(™-x +
+Amsin^,Amcos^,Dx ,D'X ,6XX ,d"xx) ■ cos^d^x +Amcosyt+ —fQ"Ki(mx + + Amsin^, Amcos^, Dx ,D'X , 6XX , 9"xx)d$x(t)+ + ^fonK2(mx + Amsin^,Amcos^, Dx ,D'X ,9XX , 9i±)d^x(t) (1 T)
The considered approach to linearization is modeled on a computer for Hammerstein and Wiener type y = ax3 (18)
objects. In this case, higher (positive) results were
obtained than the results of the combined statistical and For this nonlinearity, we find the analytical view
harmonic linearization method [14, 15]. of the coefficients (p*0 and a* as follows:
Example: We have a Hammerstein-type object with a nonlinear cubic description:
$0 = ~ f290(mx+Amsiny, Dx , 0xx)dy = A- -costot • sin2tot + 2 f2sintotd(tot)]+3A™J^t'1 f2sin2 totd(tot) +
^ Cnsintotd(tot) + f2dtotx3 (t) = ^
2n J0 v ' J0 K J 2na>
2n 2n 2n 2n
-i ^A^ vCf) 1 1A A3
[- -costot • sin2tot + -COStot | ]| - [ -sintot • COStot + tot | ]+^-costot) | + tot | x3(t) = — [ -
3 3 2nw 2 2n 2nw
0 0 0 0
— 9 2 2
-cos2ntosin22nto — - + ^cos2n:to] (19)
[-sin2ntocos2nto + 2^to]+^ • (-cos2nto + 1) + 2nto • x3(t) (20)
a* = J2 Wo(™k + Amsimp, D k ,9XX )sinydy (21)
^—f^si^totdto) +3^^^^^^f2nsin3totd(tot) +
3Amx3(t) r2n . 2 >. x3(t) r2n . - —
-I sin2totd(tot)+-I sintotd(tot)=-(-
Amwn J0 w 0 v ' Amnoi
-cos2^to • sin32nto + 3 (2n — sin2nto • cos2nto)) (22)
3A$nx(t) r — „ . 2_ 2 2. ,l3Am-x2(t)r
[~cos2ntosin22nto--^cos2^to]H—-—— [-
Amam 4 3 3 2wAmn
sin2ntocos2nto + 2nto]+A ^(1-cos2^to) (23)
Conclusion. This article discusses a new way of lin- variance function. The proposed method describes more
earizing nonlinear objects. The paper uses a dispersive accurately than the linearization method based on the
method of linearization based on the properties of correlation function. The results were tested using the
mathematical expectations based on conditional moments. Hammerstein-Wiener computer modeling method. The advantage of the obtained results is the symmetric
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