SU1488852A1 - System for simulating dynamic processes in discrete automatic control system - Google Patents

Description

The invention relates to computing, in particular to analog computing devices used to simulate discrete systems, and can be used in the study of dynamic processes in discrete control devices with amplitude-pulse modulation.

The aim of the invention is to expand the scope of the system.

FIG. 1 shows a block diagram of a system for modeling dynamic processes in automatic control systems, in Figures 2 and 3, the results of the analysis are dynamic 2

used to model discrete systems. The purpose of the invention is the expansion of the scope of the system. This is achieved by the fact that the fourth and fifth amplifiers and the second switch are additionally introduced into the known system. The introduction of these blocks provides, without any changes in the structure of the system, the simulation of dynamic processes in control systems with both pulse-amplitude modulation based on a generalized first-order extrapolator and pulse-amplitude modulation based on form-impulse transformation. 3 il.

processes in a discrete system. automatic control.

The system contains the first amplifier 1, the first and second differentiators 2 and 3, the second, third, fourth and fifth amplifiers 4-7, the first switch 8, the first adder 9, the control object model 10, the second adder 11, the multiplier 12, the generator 13 sinusoidal oscillations and the second switch 14. Under the model of the object 10 mathematical, physical or mechanical is understood} any technical device, the management process which you intend to simulate. The only restriction on the characteristics of the object imposed by the proposed system is the requirement not, -СЦ И88852

3

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four

transmission of higher harmonics, i.e. fulfillment of generalized filter conditions. This condition is satisfied by the majority of dynamic control objects encountered in practice. In this case, this restriction reduces to the need to satisfy the condition that the period of discreteness T <, be small compared with the main time constants T. (ί 6 1, K) models of the control object. When considering specific examples of the use of the proposed system, various models of moving, 5 moving objects (for example, airplanes) described by a system of nonlinear differential equations were used. In the simplest case, the control object is described by a transfer function of the form

"T’r * + 2§Т р +1

The development of the system is based on the use of an approximate equivalent representation of a discrete system with a generalized first-order extrapolator in the form of a continuous model, represented as the following expression:

y (s) = x (s) + x (s) -СОСЦЛ - (1-K ₀ ) [x '(s) + [x (s) cos _Hb +

-2

⁺ Ι ² * - ^1- I ΐ χ "(s) + [x (s) cone ^ s]" ^,

we will get a pre-40 with exgde ω ₀ = ₂₅

= 2) (/ 70 ~ quantization frequency by

time;

T _about - the period of quantization in time;

K _l - coesLiTsi transfer ⁰ PE

generalized extrapolator of the first order;

x (s) is the signal at the input of the pulse element.

Direct verification can make sure that the expression (1) at 35

K = 0 coincides with the expression for

about

equivalent representation of a discrete system with a zero-order extrapolator. When K ₀ = 1, the expression for the equivalent setting of a discrete system by a first order trapolator

Thus, the field of application of the system for modeling dynamic processes in discrete control systems is expanding.

When studying dynamic processes in discrete systems by amplitude-pulse modulation using the switch 8, the values of the gain factors of amplifier 1 are set K ₍ = 1, · amplifier 4 К _г = T _о / 2; amplifier 5 - К ₅ = Т П / 6 With the aid of the second switch 14 in the amplifier 6, the gain coefficient K 4 is set. = K ₀ - 1, in the amplifier 7 - K _? = 1 - -.

When the system is turned on, the signal x (b) from the output of the simulated object 10 moves to the first input of the multiplier 12 and to the first input of the second adder 1 1. The second input of multiplier 12 receives the signal cos ₍₀ and S. The output of the multiplier interference signal x (p) _e sozsch 1, is supplied to the second input of the adder 11. The output of adder 11 and has been exacerbated by the three circuits is fed to the inputs of the first adder 9 : on the first circuit - directly; on the second - on differentiator 2, amplifier 4 and amplifier 6 ·, on third circuit on differentiators 2 and 3 and amplifiers 5 and 7. A signal equivalent to the pulse-amplitude conversion result is output from the output of the first adder 9. to the input of the model of the object 10 control. processes the amplitude-converting the pulse to a different period of time quantization _of T carried rearrangement gain coefficients K ₂ and K ₃ in the amplifiers 4 and 5 pri'pomoschi switch 8.

If necessary changes rearrangement gains K and K * $ amplifiers 6 and 7 by means of the second switch 14. Setting the oscillator frequency transmission coefficient 13 w ^ generalized first-order extra polyatora osuschest S THE _d-g is produced in accordance with the value of the quantization period

five

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time T _s in proportion

ω _β = 2 ?? / T ₀ .

In the study of the processes of form-impulse transformation in a discrete system, the values of the gain factors K _l , K ₂ , in amplifiers 1, 4 and 5 using the switch 8 are set:

1 b

ten

15

K, = - _n

h = [Ζ (21-1) <. t 3/2 · Σ ·,

111 '' ¹ b b

= ΐ Σ [3 _; (.ί-ΐ) + υ οί · τ ^ / 6Η ί Σ / ί · The values of the gain K and ₅ in the amplifiers 6 and 7 with the second switch set K ^ | = K 1.

With such values of the gain factors K ₄ ... K ₆ amplifiers 1.4-7, the block diagram of the proposed system becomes identical to the known system.

FIG. 2 and 3 show the results of the analysis of dynamic processes in a discrete automatic control system using the proposed technical device. The presented processes correspond to a change in the output signal of the control object x (s) with a disturbing effect in the form of a single jump function ί () = 1 (C) with zero initial conditions, and the control object is a second-order oscillatory link with the transfer function '

20

25

thirty

35

40

1% * + 2? T _p + 1

R —y-p where K = 5.8 ^ T = 0.2 s; ξ = 0.6.

FIG. 2 shows the results of the simulation of the transient process in a discrete control system with a <pulse-impulse transformation of the signal with a generalized first-order extrapolator at two values of the coefficient K ₀ . Curve 1 corresponds to the value of the coefficient K _o = 0, · curve 2 - the coefficient K ₀ = 1 Curve 3, formed by discrete values of x (n) at discrete instants of time C = nT ₀ , is obtained by solving the difference equation of the system under study, whose coefficients change abruptly at each regular moment of the closure of the pulsed ele45

55

50

cop. Curve 3 is an ideal characteristic of the transition process in the system under consideration with the proviso that the conduct of this curve between fixed points in time is not defined.

FIG. 3 shows the results of the simulation of the transient process in a discrete pulse-amplitude modulated control system, in which the form-impulse transformation is performed. The parameters of the controller T _about = 0.1; cc = 20; _r = - 1 0. Claims

A system for simulating dynamic processes in discrete automatic control devices, comprising a first switch, the outputs of which are connected to the input inputs of the transfer ratio of the first, second and third amplifiers, respectively, the output of the first amplifier is connected to the first input of the first adder and the input of the first differentiator, the output of which is connected to the information the input of the second amplifier and through the second differentiator is connected to the information input of the third amplifier, the output of the first adder dinene with the input model of the control object, the second adder, a multiplier and a generator of sinusoidal oscillations, the output of which is connected to the first input of the multiplier, the output of which is connected to the first input of the second adder, the output of which is connected to the information input of the first amplifier, the output of the control object model connected to the second inputs the multiplier and the second adder, characterized in that, in order to expand the scope of the system, the fourth and fifth amplifiers and the second switch are introduced, and the information input is four the primary amplifier is connected to the output of the second amplifier, and the output of the fourth amplifier is connected to the second input of the first adder, the information input of the fifth amplifier is connected to the output of the third amplifier, and the output of the fifth amplifier is connected to the third input of the first adder, the first and second outputs of the second switch are connected to the reference inputs transmission ratios of the fourth and fifth amplifiers, respectively.

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FIG. one

Claims (1)

The invention relates to computing, namely analog computing devices,