RU2069370C1 - Device for determination of transient response - Google Patents

Abstract

FIELD: determination of transient response. SUBSTANCE: the device has two selector switches, three analog storage units and two summers. The device uses two integrators, a division unit and a clock pulse generator; the integrator output is connected to the information inputs of the first and second analog storage units, whose outputs are connected to the inputs of the first summer, whose output is connected to the first information input of the first selector switch, whose second information input is connected to a common bus; the third information input is connected to the input bus, and its output is intended for connection to the input of the object to be examined. The information input of the second selector switch is intended for connection to the output of the object to be examined; the output of the second selector switch is connected to the input of the second integrator and first input of the second summer. The output of the second integrator is connected to the information input of the third analog storage unit, whose output is connected to the second input of the second summer. The second input of the storage unit is connected to the output of the first analog storage unit. The output of the division unit is connected to the device output bus; the output of the clock pulse generator is connected to the clock inputs of all analog storage units and selector switches. EFFECT: improved design. 2 dwg

Description

 The invention relates to the field of automation and is intended to determine the transient characteristics of systems with lumped parameters.

 It is known [1, p. 467 478] a device designed to determine the transient response. The device consists of a model of a calculator of the required output quantity, a linear predictor, a calculator of the control function, a step function generator, a component calculator, determined by the energy reserve, a division unit, a spectral analyzer, and a jump reaction calculator.

 The disadvantage of this device is the need to include a step function generator in it, the complexity of the technical implementation and low accuracy. The low accuracy is due to the large error arising from the error in the implementation of the step function.

 Closest to the proposed (prototype) is the device proposed in [2], intended for the correction of input signals, which allows (thanks to the convolution theorem) direct application to the determination of the pulse transition and transition characteristics of linear objects. The device consists of three switches, four memory blocks, four adders, four multiplication blocks.

 The disadvantage of this device is: 1) a limited scope, due to the fact that the determination of dynamic characteristics is possible only if the values of the function X (ω), which is the Fourier transform of the input signal x (t), are located inside the corner with the center at the origin of the plane complex variable and with a solution less than π; 2) a large computational time, depending on the number of iterations; 3) the dependence of the accuracy of the calculations on the form of the function X (ω).

.The purpose of the proposed device is to increase the accuracy of determining the transition function in the segment [0, T] of arbitrary duration, reduce hardware costs and the ability to use as a test any signal x (t) that satisfies the conditions: x (t) ≡ 0 at t≅0 and t ≥ T;

.

 This goal is achieved by the fact that in a known device containing three switches, four memory blocks, four blocks of multiplication by a constant, four adders, an additional clock pulse generator (GTI), two integrators, a division block are introduced, and a completely new system of connections between elements. At the same time, four blocks of multiplication by a constant, two adders, one memory block and one switch are derived from the composition of the known device.

 Moreover, the output of the integrator 2 is connected to the information input of the analog memory block 3 and the information input of the analog memory block 4, the output of the analog memory block 4 is connected to the adder 5, the second input of which is connected to the output of the analog memory block 3, and the output is connected to the information input of the switch 6, the second information input of which is connected to the common bus, and the third information input of which is connected to the input bus, and the output of the switch 6 is connected to the input of the test object 7, the output of the test object 7 is connected inen with the information input of switch 8, the output of which is connected to the input of the integrator 9 and the input of the adder 1, the output of the integrator 9 is connected to the information input of the analog memory unit 10, the input of which is connected to the input of the adder 11, the output of the adder 11 is connected to the input of the division unit 12, the second the input of which is connected to the analog memory unit 3, the output of the division unit 12 is connected to the output bus of the device, and the output of the GTI-1 is connected to the clock inputs of the analog memory units 3, 4, 10 and switches 6, 8.

 Improving the accuracy of correction of the output signal is achieved by removing a number of elements from the device, introducing a number of new elements and the relationships between them.

, где X(ω) преобразование Фурье входного сигнала x(t). Это условие означает, что значения X(ω) лежат внутри угла раствора, меньшего π, с вершиной в начале координат плоскости комплексной переменной. Указанное ограничение является достаточно существенным.The condition for the correct operation of the prototype is the requirement for the existence of a constant γ such that

, where X (ω) is the Fourier transform of the input signal x (t). This condition means that the values of X (ω) lie inside the angle of the solution, less than π, with a vertex at the origin of the plane of the complex variable. The specified limitation is quite significant.

The accuracy of the calculation of the dynamic characteristics in the prototype is q ⁿ / (1-q), where n is the number of iterations. Therefore, the accuracy depends on the type of input signal, and in some cases a large number of iterations n are required to achieve the desired accuracy.

.In the proposed device, this error source is eliminated due to the fact that any signal satisfying the conditions can be used as a test signal: x (t) ≡ 0 for t <0 and t> T,

.

 On the segment [0, T], the signal x (t) can be arbitrary.

 In FIG. 1 shows a block diagram of a device for determining a transition function, FIG. 2 timing diagram of the device.

A device for determining the transient response contains:
a clock pulse generator (GTI) with a period of T-1,
integrators 2, 9, analog memory blocks 3,4,10,
adders 5, 11,
switches 6, 8,
division block 12.

 The output of the integrator 2 is connected to the information input of the analog memory block 3 and the information input of the analog memory block 4, the output of the analog memory block 4 is connected to the adder 5, the second input of which is connected to the output of the analog memory block 3, the output is connected to the information input of switch 6, the second information input of which is connected to the common bus, the third information input of which is connected to the input bus, and the output of the switch is connected to the input of the test object 7, the output of the object 7 is connected to the information the input of the switch 8, the output of which is connected to the input of the integrator 9 and the adder 11, the output of the integrator 9 is connected to the information input of the analog memory unit 10, the output of which is connected to the input of the adder 11, the output of the adder 11 is connected to the input of the division unit 12, the second input of which is connected with the information input of the analog memory unit 3, the output of the division unit 12 is connected to the output bus of the device.

In the inventive device uses analog memory units (ABP), using a capacitor charge and fixing the input voltage at certain points in time. The corresponding analog storage blocks are described in monographs [3, p. 67 68] and [4, p. 163,170]
These analog memory blocks work as follows.

 The recording and playback intervals are equal to T, where T is the time interval (0≅t≅T), on which the characteristic h (t) is determined. The information storage time in the UPS is not less than 2 T.

Consider the recording process in the UPS in the time interval [a, b] ba + T. The interval [a, b] is divided into N equal parts by the points t _k a + kT / N, k 0, 1, N. During recording in the UPS, the values of f (t _k , k 0, 1, N-1, of the input function f (t) (a≅t≅b).

, k 0, 1, N и в каждом интервале времени [τ_к, τ_к+1] выход АБП равен f(τ_к), k = 0,1,..., N-1. Таким образом на выходе АБП моделируется, начиная с момента с, кусочно-постоянная аппроксимация функции f(t), c≅t ≅d.Consider the process of reading from the UPS, starting at time t s. Reading also occurs during a time interval equal to T: (с≅t≅c + T d). The segment [c, d] is divided into N equal parts by points

, k 0, 1, N and in each time interval [τ _k , τ _{k + 1} ] the output of the UPS is f (τ _k ), k = 0,1, ..., N-1. Thus, the piecewise constant approximation of the function f (t), c≅t ≅d, is simulated at the output of the UPS.

(1)
где g(t) импульсная переходная функция, x(t) и f(t) входной и выходной сигналы.We describe the principle of operation of the device, assuming that the transition function of the linear device described by the equation

(one)
where g (t) is the pulse transition function, x (t) and f (t) are the input and output signals.

где h(t) переходная функция.Since x (t) is a compactly supported function with support [0, T], equation (1) can be represented as

where h (t) is a transition function.

где f произвольный элемент пространства L₂ [0, T] функций, суммируемых с квадратом.We introduce, following [5], the operators

where f is an arbitrary element of the space L ₂ [0, T] of functions summable with a square.

с разностным ядром, имеет место равенство

где M(t) ≡ S(t), N(t) -S(-t), 0≅t≅Т,
Φ(t))) произвольная функция из пространства L₂ [0, T]
Применим тождество (2) к оператору kх, определяющему, согласно (1), исследуемый объект.It was shown in [5] that for any bounded operator

with a difference kernel, equality holds

where M (t) ≡ S (t), N (t) -S (-t), 0≅t≅T,
Φ (t))) an arbitrary function from the space L ₂ [0, T]
We apply identity (2) to the operator kx, which determines, according to (1), the object under investigation.

Так как h(-τ)=0 при τ≥ 0,

Учитывая, что kx f и предполагая, что

, имеем

(3)
где f₁(t) выходной сигнал объекта при подаче на его вход сигнала

.It is easy to see that

Since h (-τ) = 0 for τ≥ 0,

Given that kx f and assuming that

, we have

(3)
where f ₁ (t) is the output signal of the object when a signal is applied to its input

.

 The proposed device implements the formula (3).

 The device operates as follows. In the initial state, the GTI-1 does not work, the memory blocks are reset.

0≅t ≅T, с выхода интегратора 9 подается на информационный вход аналогового блока памяти 10, где она запоминается. Одновременно входной сигнал x(t) подается на интегратор 2, где производится интегрирование

. Результат интегрирования поступает на информационные входы аналоговых блоков памяти 3, 4. В аналоговых блоках памяти 3, 4 запоминается функция

.The first clock pulse from the GTI-1 switches 6 and 8 are transferred to position 3. The input signal x (t) through the switch 6 is fed to the input of the object 7; from the output of the object 7, the output signal f (t) through the switch 8 is fed to the integrator 9. Function

0≅t ≅T, from the output of the integrator 9 is fed to the information input of the analog memory unit 10, where it is stored. At the same time, the input signal x (t) is supplied to integrator 2, where integration is performed

. The integration result is fed to the information inputs of the analog memory blocks 3, 4. In the analog memory blocks 3, 4, the function is stored

.

и

в аналоговых блоках памяти 3, 4 и 10, переключатель 6 переводится в положение 2 и на вход объекта подается нуль. Третий тактовый импульс с ГТИ-1 переводит переключатели 6 и 8 в положение 1.(Recall that the values y (t _k ) are stored, where t _k kT / N, k 0, 1, 2, N-1, N is the number of registers in the UPS. In this case, when reading from the UPS 4, the piecewise constant function y _N (t), where y _N (t) y (t _k ) for t _k ≅t <t _{k + 1} , and when reading from UPS 3, a constant function is reproduced, which we will denote y _N (T) and which is equal to the voltage stored in the N register of the UPS 3. The second clock pulse from the GTI-1 stops the memorization of functions

and

in analog memory blocks 3, 4 and 10, switch 6 is turned to position 2 and zero is applied to the input of the object. The third clock pulse from the GTI-1 switches the switches 6 and 8 to position 1.

The functions y _N (T) and y _N (t) from the outputs of the UPS 3 and 4, respectively, are fed to the inputs of the adder 5.

с выхода сумматора 5 поступает через переключатель 6 на вход объекта 7. Выходной сигнал

объекта 7 через переключатель 8 поступает на первый вход сумматора 11, на второй вход которого подается кусочно-постоянная функция Φ_N(t), равная Φ(t_к) при t_k ≅t<t_k+1. Результат сложения делится в блоке деления 12 на значение y_N (T), поступающее с выхода АБП 3.Function

from the output of the adder 5 through the switch 6 to the input of the object 7. The output signal

object 7 through the switch 8 is fed to the first input of the adder 11, the second input of which is supplied piecewise constant function Φ _N (t), equal to Φ (t _to ) for t _k ≅t <t _{k + 1} . The result of the addition is divided in the division unit 12 by the value of y _N (T) coming from the output of the UPS 3.

 The output characteristic h (t) at 0≅t≅T is taken from the output of division block 12. After applying the fourth clock pulse from the GTI 1, all memory devices are reset.

As adders, integrators, and a division block, standard blocks of analog technology are used [3] In particular, the used adders are described in [3, p. 79 85]; integrators in [3, p. 99 100] and a division block in [3, p. 197 214]
Compared with the prototype, the use of this device allows you to expand the scope, increase the accuracy of the calculation of the transition function and reduce the time of determination of the transition function and hardware costs.

Claims (1)

 A device for determining the transient response, comprising two switches, three analog memory blocks and two adders, characterized in that two integrators, a division block and a clock generator are introduced into it, while the integrator output is connected to the information inputs of the first and second analog memory blocks, the outputs of which are connected to the inputs of the first adder, connected by the output to the first information input of the first switch, the second information input of which is designed to connect to a common bus oh, the third information input with an input bus, and its output is designed to connect to the input of the test object, the information input of the second switch is designed to connect to the output of the test object, the output of the second switch is connected to the input of the second integrator and the first input of the second adder, the output of the second integrator is connected with the information input of the third analog memory block, the output of which is connected to the second input of the second adder, connected by the output to the first input of the division unit, the second input which is connected to the output of the first analog memory block, the output of the division block is connected to the output bus of the device, the output of the clock generator is connected to the clock inputs of all analog memory blocks and switches.

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