SU1383287A1 - Regulator limiting control efect - Google Patents

Abstract

This invention relates to automatic control and regulation and can be used in systems with limited control action. The purpose of the invention is to improve the quality of control - in that the regulator containing the serially connected differentiator, the first scale unit and the adder, the second scale unit, are inserted in series with the modulo unit of the signal module, the multiplier and the third scale unit. Implemented with the help of the regulator, the control law allows to bring the transient process in the system closer to the optimal performance and reduce the speed component of the error in the steady state. 4 il.

Description

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The invention relates to the field of automatic control and is intended to control the change

various parameters in auto systems

control, where the control action is limited in magnitude and is proportional to the acceleration of the parameter change.

The purpose of the invention is to increase the control accuracy.

FIG. Figure 1 shows a functional block diagram of an automatic control system with the limitation of the control action of an object with a second-order astatism in FIG. 2, is a functional block diagram of the proposed controller; in fig. 3 and 4 - phase portraits of characteristic lines.

FIG. 3 and 4 A - trajectories of optimal speed movement with limited control action, B - transition line of control action through zero, C - line of beginning of formation of maximum negative control action, D - line of beginning of formation of maximum positive control of, D - the phase trajectories of motion of the imaging point when using the proposed controller, E, F, I-- the formation line, respectively, zero, the beginning of the maximum negative and the beginning of the maximum positive control action when using a known regulator, K - phase trajectories of movement of the imaging point when using a known regulator.

The system for controlling the change of the X-object parameter 1 contains a sensor 2 parameter deviation, shown in c) element of the comparative element, controller 3 and the actuator 4. The proposed controller is most effective when used in systems

controls in which the control action is proportional to the acceleration of the current value of the parameter X and the maximum value of the control action is limited.

The sensor 2 provides the formation of the error signal according to the law

X xj x

t

where X is the mismatch signal between the driver and the current parameter values;

X - specifies the value of the parameter X - the current value of the parameter. Regulator 3 ensures the formation of a control signal Ur on the executive body 4. The executive body 4 ensures the formation of a control action according to the law

K, Ur at / Ur / g At sign Ur at

Mind

/ Yy /

MIND

To

about

0

five

five

0

Where

R

AL

K, control effect j control signal from controller 3;

the maximum value of the control action, the proportionality coefficient.

The control action of Y causes the acceleration of the current value of the parameter X-. In parallel, the control effect on the object 1 is usually affected by the disturbing effect Ud, which is conventionally depicted with the help of the adder 5.

The proposed controller 3 contains the first, second, and third mainframe blocks 6–8, the differentiator 9, the block 10, the module slot, the multiplier 11, and the adder 12; Then the output signal Vn from the regulator 3 will be formed according to the law

Ur K, X + + KjX / X /, where K ,, K,

H

k, 2--

gain factors of scale blocks 6-8, respectively.

The indicated law of forming the signal Up differs from the known one by the presence of the third term, the modulus i of which is proportional to the square of the velocity of the error signal X. The maximum speed in systems with a control action restriction is achieved with relay control, in which the sign of the formative maximum control action changes when the image point on the phase portrait hits the trajectory A, which is optimal in speed and given by the equation

X

- sign X,

where K is the proportionality coefficient between the controlling power

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31383287

action and acceleration of the parameter change.

However, the law of relay control, while ensuring optimum performance, cannot be used in steady state. Because of this, the transition to another control algorithm provides the required dynamic characteristics in steady state. This leads to a complication of the control system. On the other hand, for a relay law that is optimal in speed, small tolerances are needed on the variation of system parameters, since when choosing a switching trajectory to certain parameters in a real system, the true trajectory can pass below or above the selected one. In the first case, there will be no optimal speed, since the phase trajectory will go beyond line A and there will be a dynamic cast with a corresponding increase in the transient time. In the second case, an oscillatory process occurs with respect to line A, leading to frequent changes in the sign of the control action. If present, in a system of oscillatory links, this can lead to undesirable consequences.

When using the well-known regulator on the phase portrait (Fig. 4) there are three characteristic straight lines: the E is the switching line of the sign of the controlling influence, the W is the line of the beginning of the formation of a negative maximum controlling influence, and the I is the line of the beginning of the formation of the maximum positive control impact. In this case, the optimal speed is obtained only for the trajectory of the imaging point passing through the intersection point of lines I and A. For the trajectories of the imaging point, for example K, crossing the line And beyond line A, the time of the transition process increases dramatically due to the appearance of oscillations. For paths passing 50 on the other side of the intersection point of the lines A and A, the time also increases due to the fact that the speed does not reach its allowable value. Moreover, by increasing the coefficient K, which provides damping, it can be achieved that in the entire operating range of the line.

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For the sake of science and science

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And it will be between the X axis and the line A. However, with the initial deviations within the working range, the permissible speeds will be achieved and the time will increase due to the slow movement. On the other hand, an increased value of the coefficient K will lead to an increase in the speed error in the steady state, i.e. a change in xd at a constant speed will increase the steady-state value of x.

In the proposed controller 3, the presence of the third term in the control law with the appropriate choice of the coefficient K allows, instead of the straight lines E, g, to get the corresponding lines B, C, D, which are located in the phase portrait in such a way that The range is located close to line A on the side of the X axis. The exception is only small deviations, but with small deviations, it is no longer necessary to form maximum control actions.

The choice of the coefficients K ,, K, Kg for the proposed controller 3 can be carried out as follows. The coefficients K, and K should be chosen from the condition of providing dynamic characteristics with small deviations, i.e. in accordance with the theory of linear automatic control systems without taking into account the limitations of the magnitude of the maximum control action. And the coefficient K to choose the formula

Cs

- R.ZK.HE - K2-l | HeUMK + Um / k

to

Haumk

50 5

40

where XQ is the working range of the variation of the mismatch X.

Claims (1)

Invention Formula A control with limited control action, containing a series-connected differentiator and the first scaling unit, a second scaling unit and an adder, to the first input of which the output of the first scale unit is connected, the second input of the adder is connected to the output of the second scale unit and to the input of the regulator, the output of which is the output of the adder, characterized in that, in order to increase the quality of control, a module for extracting a module, a multiplier, is introduced into it there is also a third scale unit, with the input of the selection unit of the module connected to the output of the differentiator, the first input the multiplier is connected to the output of the allocation unit of the module, the second input is connected to the output of the differentiator, and the output of the multiplier is connected via the third scale unit to the third input of the adder. FIG. 2 1 §Ig.З FIG.