SU1559328A2 - Non-linear servo system - Google Patents

Abstract

The invention relates to the automation of industrial equipment and can be used in precise follow up and power drives. The aim of the invention is to increase the speed and reduce the oscillation of the system. The nonlinear tracking system contains a setting device 1, a mismatch meter 2, an adder 3, an amplifier 4, the first 5 and second 7 nonlinear blocks, the first 6 and second 8 sources of reference voltage, the actuator 9, the speed sensors 10 and position 11 and the control object 12 . The goal is achieved by appropriately selecting the static characteristic of the second nonlinear unit 7 and the second source of the reference voltage 8. 4 Il.

Description

L.

The invention relates to the automation of industrial equipment, can be used in precise tracking and power drives for computer numerical control (CNC) equipment and is an enhancement of the device according to the author. No. 114281 1 ..

The purpose of the invention is to increase the speed of the reaction and reduce the oscillation of the system.

Fig. 1 shows the flow chart of the proposed follow system; figure 2 characteristics of nonlinear blocks; FIG. 3 shows the normalized transient process curves in various types of automatic systems using their single control object; Fig. 4 is an electrical block diagram of the device (highlighted by the dash line in Fig. 1),

The structural circuit contains successively connected setpoint 1, error meter 2, adder 3 and amplifier 4, first nonlinear unit 55 first source 6 of reference voltage, second nonlinear unit 7, second source 8 of reference voltage, actuator 9, with output which are connected to the speed sensor 10 and the sensor 11 position, as well as the object 12 of the regulation. Fig. 4 shows one of the possible technical implementations of the control device, built on analog integrated circuits and developed by prototyping. The device performs the functions of blocks 2, 3, 5, 7. The introduction of new elements makes it possible to regulate the value of the oscillatory system. For tracking systems, stability is a necessary requirement. It is known that systems operating at the stability boundary have oscillatory transients.

Therefore, expanding the area of stability, it is possible to provide a decrease in the oscillation of the system. It is proposed to introduce into the control unit a static link with a characteristic

F (x) | cf (x) | x, - (1)

and offer various options for selecting the function tp (x).

Meanwhile, an introduction to the feedback of a functional transducer is proposed.

 (

one

| x | + U

Oh x

(2)

on

if (0) --- Ј ° about

U

on

five

0

five

0

five

Thus, by introducing a source of reference voltage (realized much easier than multiplication blocks), it is possible to solve the same problem as in this work with minimal technical costs. However, a non-linear transducer is introduced only into the main feedback circuit. This means that the main feedback coefficient changes during the adjustment process, while the feedback feedback rate remains unchanged. Consequently, in the process of regulation, the d-mfp of the system also changes (since it depends on the ratio of the coefficient, o.). As a result, the transient is oscillatory. Additionally entered into the device blocks should reduce oscillation.

Let us find the static characteristic of the nonlinear block 7 for an object of the second order (this class includes, in particular, electric motors, as well as more complex objects, provided there are no delays, inertia networks, etc.). It is known that the object with zero roots (at the boundary of stability) is the most difficult for control purposes.

0

five

0

five

Heh7 k x in

(3)

Then the differential equation of the closed tracking system takes the form

Tt + T-2.11

ya - Y2 t7t u koc,,

-wasp

12

(four)

where.U. - tracking error. As is known, by choosing the values of T4 and T, one can achieve no overshoot (in linear systems). Suppose that this is possible in nonlinear systems, where koc and variables. As a result, we come to the scheme of the proposed device.

The system works as follows.

From the output of the setpoint device 1, the voltage U, proportional to the predetermined position of the control object 12, is fed to the first input of the error meter 2. At the second entrance po51

the last is the voltage U from the output of the nonlinear block 5. Two voltages U and IL are compared, and the output of the error meter 2 is the voltage U4, which is proportional to the set speed of the actuator 9, which is fed to the first input of the adder 3. On the second inverse input of the adder 3 receives the voltage U7 from the output of the second nonlinear element 7, which forms the output voltage in accordance with the signal coming from its output of the speed sensor 10 proportional to the rotation speed of the third input to its third input Mechanism 9 The second non-linear unit 7 predicts an op amp with an adjustable gain factor; the dependence of the gain factor on the sum of the voltages Uq. and it is shown in figure 1 (curve ty2) ",

In accordance with the difference between the post-supply voltage of the U7 and Uz voltages, adder 3 produces a control voltage for the actuator 9, which is fed to the input of the amplifier 4. From the output of the amplifier 4, the voltage U is fed to the core circuit of the actuator 9, which leads in the movement of the control regulation 12

The first, the stroke of nonlinear blocks 5 and 7, receives the voltage U, from the output of amplifier 4. To set the linearity of the nonlinear blocks 5 and 7, sources 6 and 8 op. ph. The voltage Ug from the whole of the source 6 of the reference voltage goes to the second input of the first nonlinear element 5, and the voltage U. from the output of the source 8 of the reference voltage goes to the second input of the second nonlinear element 7,

In the mode of small deviations, when the condition U U6 is fulfilled, the characteristic of the first nonlinear block 5 becomes linear, similarly

U4 Ug becomes the linear characteristic of the second non-linear block 7 (Fig. 2). The static characteristics of the nonlinear blocks 5 and 7 are shown in FIG.

The characteristic of the first non-linear, block 5, is the dependence of the transfer coefficient k5 on the sum of the stresses | U4 | + Ug, analytically expressed by the following formula

Ml + U6 k, i 5

(five)

which ensures the linearity of the characteristic with small deviations. The characteristic of the second non-linear unit 7 is the dependence of the transfer coefficient kT on the sum of the voltages Ug and is chosen in such a way as to satisfy the ratio -,

I

U4I + “{

(6)

The magnitude of the output voltage U6 of the source 6 of the reference voltage is chosen to be equal to the magnitude of the transfer coefficient kH of the position sensor 1.

t „e„ Ufi k

eleven

what provides one-t

single main feedback.

Denoting the block transfer coefficients as kj (where i is the block number as shown in FIG. 1), the expression for T and TQ from (A) can be written through the block transfer factor as 1

m-m- (-k, k, k7k «, k, 0 t i (LI

(7)

+ () g - 4k2kJk5k, kH / 2

So that the minsh-tziroBlt oscillator ™ ness, i.e. to satisfy the requirements imposed on the system, as it is known, it is necessary to satisfy the equality

(k3k4k7kqk From here

) - 4k2k, k5k9k 0

0

.jk (k7k, y

-k,

C, (8)

where b is constant depending on pa

2

This topic is as follows, k3k4kekfo

way

(9)

Choosing k in accordance with relation (7) makes it possible to eliminate oscillation in the system, which is very important for a number of practically important control objects. The introduction of non-linear unit 5 in speed feedback distinguishes the proposed follow-up system from the known one, since this improves the quality of the regulation (the overshoot is minimized).

To prove the existence of a positive effect and compare the processes in linear and nonlinear systems, mathematical modeling of a number of automatic systems was performed. The simulation was performed on a SM-3 computer using the Runge-Kutta method with

automatic step selection. The simulated normalized transient process curves are shown in FIG. The duration of transients, as in automatic control theory, was determined by the entrance to the 5% tube. In all cases, the driver was limited and was given by the function I (t).

Curve 1 is the acceleration characteristic of the engine of the propulsion system. It characterizes the limiting dynamic possibilities of an open-loop system with a selected object. .

Curve 2 is a process in a time-optimal system (with a control action limited to + 1). It characterizes the limiting dynamic capabilities of closed systems.

Curve 3 corresponds to the process in the proposed system

Curve 4 depicts the transition process when tuning to the technical optimum,

Finally, curve 5 corresponds to the transition process in a linear system, calculated by the method of model control (binomial distribution of coefficients).

Claims (1)

Comparison of the curves and transients normalized at the breakdown of that time shown in FIG. 3 shows that the known device provides a gain in transient time equal to 228% (in comparison with the linear system) g The proposed device provides, in turn, The time is 66% in comparison with the prototype (or 294% in comparison with the linear system), and the processes in it are aperiodic. The speed of the proposed follow up system is only 22% less than that of the optimal one in terms of speed. Invention Formula The nonlinear tracking system according to the author, No. 1142811, characterized in that, in order to increase the speed and reduce the oscillation of the system, it further comprises a second nonlinear unit and a second source of reference voltage, the first input of the second nonlinear unit being connected to the output of the amplifier The second input is connected to the output of the second voltage source; and the third input is connected to the output of the speed sensor, the output the second nonlinear block is connected to the second input of the adder. 0.5W FIG. 2 Xfa # AND /,, 0 TO TJ ch fie.Z 1.5 l + uon B Q 4.0 b