SU1215092A1 - Device for determining coefficients of statistical linearizing of non-linear dynamic systems - Google Patents

Abstract

The invention relates to the field of computing and can be used to determine the statistical characteristics of nonlinear dynamic systems. The purpose of the invention is to improve the accuracy and simplify the device, which is achieved by introducing three switches, a clock generator, a quad and an inverter. New elements and connections allow to increase the accuracy of the device by eliminating the influence of nonlinear errors; 1 il.

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 increase the accuracy and simplify the device.

The drawing shows a block diagram of the device.

A device for determining statistical linearization coefficients of nonlinear dynamic systems contains adders 1 and 1, amplifier 2 with adjustable gain, inverters 3, Sg and Rear, averaging blocks 4, and 4, switches 5, 5g and 5, quadr 6, voltage amplifier 7, 8 clock pulse generator and recording unit 9

According to the theory of statistical linearization, a nonlinear dynamic system can be linearized by a function of the form:

and (t) cp + kx (t),

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

tf is a statistical characteristic of a nonlinear dynamical system by the mathematical expectationJ

k is the equivalent statistical gain of a nonlinear dynamic system over a random component.

The coefficients of statistical linearization C | and k are determined by for1215092 2

The input signal y (t) is fed to the first inputs of the sum of the tors, and the random signal x (t) is fed to the information input of amplifier 2 with a controlled gain factor of 5, from the output of which the signal Uk (t) x (t) goes to the second the input of the adder 1) and through the inverter 3, to the second input of the adder 1 (k (t) - the coefficient of the gain of the amplifier 2).

The output of the adder Ig has a signal:

25

35

U, y (t) -k (t) .x (t),

(3)

15 at the output of the averaging block 4, the signal

U, (t) -k (t) .- x (t) j, (4)

Which arrive at informational 20 inputs of switches 5 and Sg.

At the moment when the switches 5 (, Sg and 5 are in the position, as shown in the drawing, the output of the adder 1J has a signal:

j

U.y (t) + k (t) .x (t) + U - and

(five)

thirty

 the output of the quadrant 6 and PA input, block averaging 4 signal:

,

B is the moment when the switches 5 ,, 5 and 5j are in a position opposite to that shown in the drawing e at the output of the adder 1 (there is a signal:

(t) + k (t) x (t) - (), (6) at the output of quadrant 6 and at the input of averaging unit 4, signal: U, U ,.

.i b

Clock Generator

0 8, having implemented the principle of time separation of signals, generates at the input of the averaging block 4 a variable signal having the form: meander, the amplitude of the positive immunity:

((t) -kx (t) j,

1, | mShK) G.

(ABOUT

(2)

(t) J

de x (t) is a random function at the input of a real nonlinear dynamical system and its model;

y (t) is a random function at the output of a real nonlinear dynamical system; M is the expectation; for I tti (), centered random.

functions.

The device works as follows.

U, y (t) -k (t) .x (t),

(3)

15 at the output of the averaging block 4, the signal

U, (t) -k (t) .- x (t) j, (4)

. Which arrive at the information inputs of the switches 5 and Sg.

At the moment when the switches 5 (, Sg and 5 are in the position, as shown in the drawing, the output of the adder 1J has a signal:

j

U.y (t) + k (t) .x (t) + U - and

(five)

 the output of the quadrant 6 and PA input, block averaging 4 signal:

,

B is the moment when the switches 5 ,, 5 and 5j are in a position opposite to that shown in the drawing e at the output of the adder 1 (there is a signal:

(t) + k (t) x (t) - (), (6) at the output of quadrant 6 and at the input of averaging unit 4, signal: U, U ,.

.i b

Clock Generator

8, having implemented the principle of temporal separation of signals, generates at the input of the averaging block 4 an alternating signal having the form: a square wave, the amplitude of the positive pulses of which is Ug-, and of the negative pulses (-Uy). At the output of the averaging unit, there is a signal Ug proportional to the estimate of the expectation of the incoming

its input is an alternating signal, which through amplifier 7 is fed to the control input of amplifier 2 with a guided gain factor, whose coefficient changes

gain k (t) until the output signal of averaging block 4 has a steady signal. In this case, the parameter cp is the signal

Uj from the output of averaging unit 4, and the parameter k estimate is the gain of the amplifier 2 k (t).

Improving the accuracy of the device is provided by eliminating the influence of the error of the nonlinear element (multiplication unit, quad) on the determination of the coefficients of statistical linearization.

Claims (1)

Invention Formula A device for determining statistical linearization coefficients of nonlinear dynamic systems containing first and second adders, the first inputs of which are connected to the first input of the device, an amplifier with an adjustable gain factor, whose information input is connected to the second input of the device, and the output directly to the second input of the first adder and through the first inverter - with the second input of the second adder, the first averaging unit, the input of which is connected to the output of the second adder, the second inverter, then second connected averaging unit and a voltage amplifier, the output of which is connected to the control 2I5092.4 An adjustable gain amplifier input, the output of the first averaging unit and the output of the voltage amplifier are connected respectively to the first and second inputs of the recording unit, characterized in that, in order to improve the accuracy and simplify the device, a quad is entered into it. the third inverter, three switches and a clock pulse generator, - connected by an output to the control inputs of the switches, the informational first and second inputs of the first the switch is connected to the outputs of the second adder and the first averaging unit, and the output to the third input of the first adder, the informational first and second the inputs of the second switch are connected respectively to the outputs of the first averaging unit and the second adder, and the output through the second inverter is connected to the fourth input of the first adder, the quad input is connected to the output of the first adder, and the output directly to the first information input and through the third inverter to the second information the input of the third switch, the output of which is connected to the input of the second averaging unit. VNIIPI Order 905/55 Circulation 837 Subscription Branch PPP Patent, Uzhgorod, Projecto st., 4