SU1381423A1 - Optimal control signal driver - Google Patents

Abstract

The invention relates to automatic control and can be used to generate control signals of optimal in speed automatic systems. The aim of the invention is to increase the speed while observing the restrictions on adjustable variables and simplifying the configuration of the device. The goal is achieved by the fact that a second comparison device 3, a switch 8 of the coefficients of the first power series and the commutation switch 8 are introduced into the device containing the first comparison device 2, the deviation switch 5 and the series-connected multiplication unit 4 and the adder I

Description

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The tator 9 of the coefficients of the second power series, as well as the threshold blocks 6 and 7 and the blocks for calculating the sums 10 and P. The optimal control signal is obtained by multiplying the error voltage by the variable coefficient and summing it with the variable bias voltage. The variable coefficient and the variable offset are obtained by summing the terms of the power series from the controlled variables with the specified row coefficients, and to increase the speed of the transient processes and observance of the restrictions on the controlled variables, the deviation of the adjustable variables from the reference signals is additionally measured , determine the sequence number of the controlled variable, the absolute value of which deviation does not exceed the specified positive value, voltage Errors are formed equal to the deviation of this controlled variable, and the values of the coefficients of a power series commute with a change in the sequence number. 2 Il.

The invention relates to devices for automatic control and can be used for generating control signals of optimal speed automatic systems.

The purpose of the invention is to increase the speed (reducing the time of transients) while observing the restrictions on adjustable variables and simplifying the setup of the device.

FIG. 1 is a block diagram of a device for generating an optimal control signal; in fig. 2 is a block diagram of an amount calculation block.

The device contains the first 1, second 2 and third 3 adders, multiplication unit 4, deviation switch 5, first 6 and second 7 threshold blocks, first 8 and second coefficient switches 9, first 10 and second 11 sum calculation blocks, and also multiplication blocks 12 and adder 13.

The device works as follows.

Optimal control signal

U kl- | --Uc (1)

where k, Uc is a variable coefficient and a variable offset, varying as a function of adjustable variable systems; 1 is an error.

The control signal (1) ensures a smooth steady motion of the nonlinear system along an arbitrary optimal surface, on which the controlled variable takes the maximum allowable value of the singular optimal surface 3. The equation of the zth optical surface is given as

X. X, e (X, X2, ..., X,),

where X, - g- adjustable variable, g

 1,2, ...,

Hge is the reference variable defined for the switching surfaces as a function of adjustable variables, and for boundary surfaces it is equal to the maximum allowable value of the corresponding variable Xj. The deviation of the deviation from the rth surface is defined as

|, X, -H.e, (2)

The components K and Uc for each surface are in the form of power series of adjustable variables or smooth functions, also approximated by the series:

k 2 Q, .., xiXJ..x; (3)

j.-1

and,.

. D ,, ..., x; xJ ... x /.

(four)

The values of the coefficients of the series dj -i and D ,,,,, / are determined for each of the g-th surface, i.e., c ,,. 0,;.,., 7 ,,, l

The number of members of the series is determined analytically. 3. In those cases where the analytical solution is obtained as a function that is not a power series, their polynomial approximation is required. In this case, the number of terms of power series is chosen from the condition of obtaining an exact approximation of 4 |.

In order to obtain a speed-optimal transient process, taking into account the limitations of the controlled variables, the method of generating the control signal must ensure the successive passage of all optimal surfaces. This is achieved by switching the components 1l and c, (G "/, D ,,,,, / depending on the sequence number g of the surface of the small neighborhood to which the current state of the system belongs.

To find the order number g in a given order, the deviation 1 is measured, and the conditions of belonging to the neighborhoods are checked.

,(five)

where Kg - given positive numbers.

It is found r for which condition (5) is satisfied. Error 1 is assigned the value Ir, and the coefficients of the rows are assigned the values C, 7 ",;, DI /.,./

The order of measurement of variables is established in order to assign the corresponding deviations, surfaces, etc., to a single sequence number, which in fact determines the structure of the device. This order can be chosen arbitrarily, it is only important that it be well-defined (fixed, pre-specified). When a neighborhood of the next optimal surface is reached, condition (5) is fulfilled for a different number r, and the coefficients of rows (3) and (4) are switched.

In the initial parts of the transition process, i.e., when moving outside the vicinity of optimal surfaces, the control action should take the maximum permissible values, for example, - | -U. At the same time, as a result of the check (5), the sequence number r is not found, the error I is assigned the value O, a) oo ...

The choice of the control law in formula (1) makes it possible to exclude the possibility of oscillations in the vicinity of optimal surfaces. Forming the voltage of the fault as deviations from the surface (2) t, the commutation of the coefficients of the power series (3) and (4) ensure the successive passage of the optimal surfaces, i.e., the transient process speed and the limitation of the controlled variables.

The inputs of the adders 2 and 3 and the inputs of the blocks 10 and 11 of the calculation of the sums are fed adjustable variables X: and X2, to the other inputs of the adders 2 and 3 - the reference variables Xp and Hu. The switches 8 and 9 of the coefficients contain signals proportional to the coefficients of the power series (3) and (4) corresponding to the first and second optimal surfaces. Adders 2 and 3, in accordance with formula (3), compare the adjustable variables X | and X2 with the reference signals Xp and X2, forming at the output a deviation voltage I ,, g 1,2, ..., which is fed to the inputs of the threshold devices 6 and 7 and the first and second inputs of the switch 5 deviations. At the beginning of the system operation, when none of the conditions (5) is fulfilled, the control signals to the inputs of the switches 5, 8 and 9 do not arrive, as a result of which a third input is connected to their outputs. At the output of block 5, a signal is generated which is fed to the input of block 4 multiplication. Since the output of block 4, regardless of the value of k arriving at its other input, produces a signal, the operation of the switch 8 coefficients in this mode can be disregarded. At the output of the switch 9 factors, voltages are obtained,. These signals arrive at the corresponding inputs of the sum calculation unit 10, which calculates the sums of the terms of the power series by the formula (4), i.e. This signal is fed to the input of the adder 1, on the other

the input of which there is a zero voltage from the output of block 4 multiplication. At the output of the adder 3, the corresponding maximum permissible value of the control signal is formed. The resulting tension is guaranteed. makes change of adjustable variables X | and Ha, corresponding to the fastest movement of the system.

When one of the optimal surfaces is reached, one of the conditions

5 (5), for example, when the threshold unit 6 is triggered, the signal from which is fed to the control input of all the switches 5, 8 and 9. The switches switch so that their first inputs are connected to their outputs. At the output of block 5, an error signal is generated, which is fed to the input of block 4 multiplication. At the output of the commutators of coefficients 8 and 9, signals С, С, and D ,, are formed. Blocks 10 and 11 of the calculation of the amounts carry out the calculation of k and

5 rows (3) and (4) with coefficient values from the coefficient switches. The value of k is fed to the input of block 4 multiplication, and the value of product kl obtained at its output is fed to the input of adder 1. Since the signal Uc is fed to the other input of sumQ of mat 1, a control signal corresponding to expression (1) is generated at its output. The control ensures smooth movement in the vicinity of the first optimal surface until the coordinates X | and x2 to the neighborhood

5 second surface. Then the condition (5) is satisfied,, the second threshold element 7 is triggered and switches the switches 5, 8 and 9 so that the second inputs are connected to their inputs. The output of the switch 5 deviations signal

0 errors, and at the output of the commutators of coefficients 8 and 9 - the corresponding signals of the coefficients C. U C, / and D ,, D, 7. At the output of the adder 1, a control signal is obtained, ensuring the movement along the second optimal surface.

The use of the device allows to increase the speed while observing restrictions on adjustable variables.

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Claims (1)

Invention Formula An optimal control signal generating device comprising two adders, a multiplication unit and a sum calculating unit, a multiplier output is connected to a first input of a first adder connected to an output of an optimal control signal generating device output, the sum calculating unit output is connected to a second the first adder input, the first input of the second adder is connected to the first reference input of the optimal control signal generating device, the second input of the second adder is connected to the first information input of the optimal control signal generating device and the first information input of the sum calculator, the second information input of which is connected The second information input of the device for the formation of an optimal control signal, characterized in that, in order to increase the speed, There are two threshold blocks, a variance switch, a second sum calculation block, a third adder and two coefficient switches, the second information input of the first sum calculation block is connected to the first input of the third adder, the second input of which is connected to the second reference input of the optimal control signal generating device, the output of the second adder is connected to 0 the input of the first threshold unit and the first information input of the deviation switch, the second input of which is connected to the input of the second threshold block and the output of the third adder, the output of the first threshold unit is connected to the first control inputs of the first and second coefficient switches and the first control input of the deviation switch, the output of the second threshold unit is connected with the second control inputs of the first and second coefficient switches and the second control input of the deviation switch; the outputs of the first to mmutatora coefficients connected to respective yn g ravl yuschimi inputs of the first unit for calculating the sums of the coefficients of the second switch outputs are connected to respective control inputs of the second sum calculation unit, whose output is connected to a first input of the multiplication unit, a second input coupled to an output switch deviations. 0