Basic research. Calculation of a self-oscillating system of VDRP and its dynamic characteristics

Mathematical model of steering gear

To design the control part and calculate the dynamic characteristics of the drive, we will use a RP model consisting of the following elements:

1. Actuator motor described by the following system

equations:

2. Adder:

DU = U in - U os

3. Relay element:

U in - trigger zone,

U p - maximum value of the relay amplifier.

4. Control electromagnet:

f - equivalent delay time.

5. Correction filter.

6. Sensor feedback: k os = 1 V/rad.

Structural scheme such a drive will look like this:

Fig 1.8 RP block diagram.

Calculation of the self-oscillating system of the VDRP and its dynamic characteristics

We will calculate the self-oscillating system of the air-dynamic RP using the following algorithm:

1. Calculate the frequency of self-oscillations:

- circular frequency, found for the lowest accuracy mode:

70°, T = +50°, = 2рf = 2р 14.06 = 88.3 rad/s.

Let's take = 6, then = 6M88.3 = 530 rad/s/

2. Let us determine the required equivalent delay time of the control electromagnet:

where c nel is the phase characteristic of the nonlinear element,

c nel = - arcsin l, l. = 0.1?0.15;

ts To- phase characteristic of the correction filter at the frequency of self-oscillations;

ts P - phase characteristic of the drive at the frequency of self-oscillations;

ts To = arctan

Let's find the drive transfer function:

Let us determine the phase-frequency characteristic of the drive with the following data: kg/cm = 3.3 Nm; kg/cm = 0.72 Nmm; rad/s; f = 0.01 kgM cmMc NMmMc 2; = =0.0436 rad; = 0.44 rad.

Electromagnet equivalent delay time:

without the influence of the correction filter.

3. Let's calculate the amplitude of self-oscillations according to the dependence:

Amplitude characteristic of the drive at the frequency of self-oscillations.

t o - time of movement of the electromagnet armature from the stop to the neutral position, t o = 1.15 ms;

0.21 rad =12 0

4. Let us determine the required amplitude characteristic of the open-loop drive at the operating frequency from the condition of ensuring the required phase shift of the closed-loop steering drive.

Phase characteristic of an electromagnet at operating frequency;

Phase characteristic of a nonlinear element;

Phase characteristic of the drive at operating frequency;

; = - 0,28; =0,076;

74,8 0 = 1,3 glad; = 88.3·2.3·10 -3 = - 0.2 glad= - 11,5 0

74,8-11,5 = -86,3 0

The required amplitude characteristic of an open-loop drive at the operating frequency will be equal to:

5. Determine the need to install a correction filter:

Since c k > 1, we conclude that it is necessary to install a correction filter.

7. Set up a correction filter of the form:

where we determine the time constants from the dependence:

Let us determine the phase characteristic of the filter at the operating frequency:

Amplitude characteristic of the filter at operating frequency:

Phase characteristic of the filter at the self-oscillation frequency:

Amplitude characteristic of the filter at the frequency of self-oscillations:

Let us determine the parameter of the correction filter at the frequency of self-oscillations:

This means that the selected parameter is suitable for the system.

Let us determine the amplitude-phase characteristics of the system taking into account the correction filter. We will make the calculation according to the following dependencies:

tg= - 0.354; = - 19.4 0 .

Since the resulting phase shift at the operating frequency satisfies the requirements, the selected filter is suitable for the system.

8. Now it is necessary to calculate and plot the dynamic characteristics of the drive for different modes work with different input signals. To calculate the dynamic characteristics, we will use a program designed for calculating the amplitude-phase characteristics of a closed-loop system. For each mode, we will consider the dynamic characteristics for three different input signals: Uвx1 = 0.088 rad; U inx2 = 0.314 rad; U inx2 = 0.44 rad.

1 mode: ; T = +50° C; t = 9.8 s; f = 14.06 Hz, Ш m = 65.6 rad/s;

M m = 3.3 N*m; M n = 0.72 N*m; P g = 4.85 atm; w 0 = 88.3 rad/s.

Let's calculate the required data to enter:

The calculation results are given in tables 1.9.1-1.9.3.

Table 1.9.1

U BX = 0.088 rad

Table 1.9.2

Mode 2: = 70°; T = -50° C; t = 0.6 s; f = 3.59 Hz, = 65.631.5 rad/s; M T = 0.82 N*m; M n = 0.324 N*m; Pg = 1.22 atm; w 0 = 22.57 rad/s, T n = 4.5-10 -3 s, = 0.15, = 722.5.

The calculation results are given in tables 1.9.4-1.9.6.

Table 1.9.4

Table 1.9.6

U bx = 0.44 rad

3 mode: = 70°; T = -50°C; t = 11.58 s; f = 11.57 Hz, = 59.6 rad/s;

M T= 2.49 N*m; M n = 0.764 N*m; P g = 3.699 atm;

T n = 2.9 -10 -3 s, = 0.098, k Sh = 1367.

The calculation results are given in tables 1.9.7-1.9.9.

Table 1.9.7

U bx = 0.088 rad






Table 1.9.8
U bx = 0.314 rad






Table 1.9.9
U bx = 0.314 rad

70°; T = -50°C; t = 11.58 s; f = 11.57 Hz, = 59.6 rad/s;

M T= 2.49; M n = 0.764 N*m; P g = 3.699 atm;

w 0 = 72.76 rad/s, = 0.307, m T= 1.74, T s = 0.024 s, T g = 0.0074 s,

T n = 2.9 -10 -3 s, = 0.098, = 1367.

4 mode: = 0°; T = +50°C; t = 1.5 s; f = 13.75Hz, = 58.02 rad/s;

M T= 30.05 N*m; M n = 4.8 N*m; P g = 44.53 atm;

w o = 86.4 rad/s, = 0.16, m m = 10.9, T s = 0.047 s, T g = 0.0076 s,

T n = 1.17-10-3 s, = 0.04, k Sh = 1331.

The calculation results are given in tables 1.9.10-1.9.12.

Table 1.9.10

Table 1.9.12

U bx = 0.44 rad

5 mode: = 70°; T = -50°C; t = 5.8 s; f = 12.96 Hz, = 55 rad/s;

M ffl = 8.38 N*m; M n = 2.502 N * m; P g = 12.41 atm;

w 0 = 81.4 rad/s, y = 0.3, m m = 5.686, T s = 0.0267 s, T g = 0.008 s,

Tn = 1.16 -10" 3 s, f = 0.054, kSh = 1261.5.

The calculation results are given in tables 1.9.13-1.9.15.

Table 1.9.13

Table 1.9.15

U BX = 0.314 rad

6 mode: = 0°; T = -50°C; t = 10.1 s; f = 7.5 Hz, = 58.055.92 rad/s;

M m = 15.3 N*m; M n = 3.75 N*m; P g = 22.69 atm;

w 0 = 47.12 rad/s; y = 0.245; m m = 8.52; T s = 0.032 s;

T g = 0.00787 s, T n = 1.33 * 10 -3 s, and= 0.044, kSh = 1282.

The calculation results are given in tables 1.9.16-1.9.18.

Table 1.9.16

Table 1.9.18

U BX = 0.44 rad

From the point of view of the structure of a steering machine with discrete control, it can be represented (Fig. 2.33) as a series connection of a stepper motor (SM) and a hydraulic actuator with throttle control (hydraulic booster) closed by mechanical feedback, the output link of which, the piston, reproduces the angular movement of the CMM roller. The function of the device that sums the angular movement of the CV shaft and the linear movement of the piston, converted using a rack-and-pinion transmission into proportional angular movement, is performed by a planetary gearbox, the output shaft of which is connected through a gearing to a flat rotary spool that regulates the flow of working fluid into the piston valves. hydraulic cylinder cavities.

ETC

Rice. 2.36 Functional diagram of RM:

And - angles of rotation of the CMM shaft and opening of the spool; Q-flow of working fluid through the spool valve; x- moving the output shaft; ШМ - stepper motor; PR - planetary gearbox; GR - hydraulic distributor; HC - hydraulic cylinder; MOS is a rack-and-pinion type feedback mechanism.

The mathematical model of the steering machine is represented by a system of equations.

When developing the mathematical model, the following basic assumptions were made:

The design of the steering gear is absolutely rigid;

The characteristics of the distributor are assumed to be ideal, and the presence of volumetric losses that determine the nature of the dependence distributor, is taken into account by the leakage coefficient, losses in the channels are taken into account by turning on an equivalent choke G K in the PM injection and discharge hydraulic lines;

It is believed that when the steering gear is operating in damper mode, the “drain” cavity of the hydraulic cylinder has no effect.

1. Equation of error signal

As noted above, the mismatch signal in the PM circuit - the rotation angle of the spool - is formed on the output shaft of the planetary gearbox as an algebraic sum of the scaled angular displacement of the CM roller and the converted linear displacement of the rod:

Where And - angles of rotation of the CMM shaft and opening of the spool, q- gear ratio of the planetary gearbox ( ETC) from the entrance to the spool, - PM transmission coefficient along the mechanical feedback circuit (from the displacement of the rod to the angle of rotation (return) of the spool), X- piston displacement.

2. Equation of forces

The PM rod is acted upon by - a hinge load, - a dry friction force, - a force from the moment of asymmetry of the thrust vector, - a viscous friction force:

A p

)

(

where is the pressure drop across the piston, A p– piston area.

3. Fluid flow equation

Where , , - components of the total flow rate spent, respectively, on displacing the working fluid during the movement of the piston, non-productive flow rate (leakage) and flow rate for the compressibility of the volume of working fluid in the cavities of the hydraulic cylinder,

- unproductive consumption, without taking into account changes in fluid viscosity parameters with temperature changes,

(

)

(

- useful expense.

In the diagram fig. 3.7, the block in which the expression for the unproductive consumption of steering gears is implemented, taking into account the change in fluid viscosity with temperature changes, is highlighted in green.

Assuming that the injection and drainage hydraulic lines in the PM (from the corresponding hydraulic connector to the distributor) are the same and the pressure losses in them are estimated by connecting the throttle spool in series with the throttling slot by conductivity GK:

Where - change in the conductivity of the throttling gap when turning the spool by 1°.

Then the flow equation can be written as:

Where - inlet pressure, - pressure in the hydraulic cylinder.

4. Pressure in the hydraulic cylinder cavity

A p

)

(

The presented article presents a developed linearized mathematical model that describes the dynamics of the electrohydraulic drive of the launch vehicle. The model consists of transfer functions of its main components. It is proposed to move from using traditional time characteristics to frequency characteristics to evaluate the quality of functioning of electrohydraulic drives in dynamic modes. The simulation of this system was carried out in the Matlab+Simulink environment, which allows you to introduce nonlinearities various types and describe the dynamic processes of an electrohydraulic drive that cannot be linearized. To analyze the stability of the hydraulic control system under study at given values of the coefficients, logarithmic amplitude phase frequency characteristics were obtained. Frequency characteristics make it possible to analyze the structures of electrohydraulic systems at the design stages, as well as during the operation of existing drives, and to solve synthesis problems by selecting corrective links.

electrohydraulic drive

Transmission function

amplitude-phase frequency response

1. Borovin G.K., Kostyuk A.V. Mathematical modeling of a hydraulic drive with LS control of a walking machine. Preprint No. 54. – M.: Institute of Applied Mathematics. them. M.V. Keldysh RAS, 2001.

2. Dyakonov V.P. MATLAB R2006/2007/2008 + Simulink 5/6/7. Application Basics. – 2nd ed., revised. and additional Professional's library. – M.: SOLON-Press, 2008. – 800 p.

3. Krymov B.G., Rabinovich L.V., Stebletsov V.G. Actuators of the aircraft control system. – M.: Mechanical Engineering, 1987.

4. Navrotsky K.L. Theory and design of hydraulic and pneumatic drives. – M.: Mashinostroenie, 1991. – 384 p.

5. Ratushnyak A.I., Kargu D.L. Research on ways to construct and justify new circuit solutions for diagnostic and control systems for dynamic operating modes of drives rocket engines // Contemporary issues improvements tactical and technical characteristics rocket and space technology, its creation, testing and operation: proceedings of the All-Russian scientific and practical conference. – St. Petersburg: VKA named after A.F. Mozhaisky, 2013. – pp. 115–121.

Despite the trend of widespread introduction of computers into the field of analysis and synthesis of automatic systems, frequency methods for studying the dynamics of designed systems have not lost their importance. Their implementation on a computer makes it possible to short term obtain valuable information about the system being designed. Based on the amplitude-phase frequency characteristics, one can judge such quality indicators as stability margins in amplitude and phase, resonant frequency, and others.

The main task for the experimental determination of frequency characteristics is the mathematical description of the dynamics of automatic control systems in the form of transfer functions.

The widespread use of electrohydraulic drives (EGD) of launch vehicles is due to the high density of generated forces per unit area of the hydraulic booster.

The hydraulic drive uses proportional controlled distributors and a hydraulic cylinder.

When designing an EGP, assessing the stability, quality of regulation and correction of the dynamic characteristics of the drive is an important task. To accomplish this task, it is necessary to develop a mathematical model of the processes occurring in the drive.

In Fig. Figure 1 shows a functional diagram of the electrohydraulic drive.

The electrohydraulic drive of the launch vehicle includes: an electromechanical converter, a hydraulic booster, a spool valve, a hydraulic power cylinder, a control current driver, and a feedback unit. EGP is automatic system regulation with negative feedback.

Rice. 1. Functional diagram of the electrohydraulic drive

When compiling a linear model of the EGP, the following assumptions and assumptions were made: the flow coefficients of the throttles and the working windows of the spool are constant; leakage of working fluid through the radial clearances of spools and hydraulic cylinders is negligible; drain discharge pressure is constant; the values of viscosity and bulk elastic modulus do not change.

The equation of the electromagnet control circuit in an electromechanical converter has the following form:

where i is the current in the EMF; TYa is the time constant of the eddy currents of the EMF armature; iK - command current.

The equation in operator form and the transfer function of the electromagnet control circuit will take the form

(TYs + 1)i = iK;

(2)

The error signal equation is presented as follows:

C h = K FI (i - i OC) - K C A C ΔP TZ, (3)

where i OC = K OC X ШТ - feedback current; K OC - feedback coefficient; X ШТ - movement of the actuator rod; C h - control signal; h - damper displacement value; K FI - EMF force transfer coefficient; K C - coefficient taking into account the ratio of the diameter of the nozzle end to the diameter of the nozzle; A C - effective damper area; ΔP ТЗ - pressure drop at the ends of the spool.

On the other hand, the dynamics of changes in pressure drop at the ends of the spool are described by the expression

(4)

where TGU is the time constant of the hydraulic booster; KPh - pressure gain.

After the transformation, the transfer function of the link that determines the dependence of the pressure drop at the ends of the spool on the valve displacement will have the form

(5)

The equation of motion of the spool has the form

where X Z is the movement of the spool; m W - spool mass; A ТЗ, C ТЗ, f mp З - the area of the ends, the stiffness of the springs at the ends and the coefficient of viscous friction of the spool.

Hence the transfer function of the spool will have the form

(7)

where is the coefficient of the spool transfer function; - spool time constants.

For the block diagram of the control unit, which includes the EMF, hydraulic booster and spool, from expression (3) we obtain

(8)

The flow rate of working fluid through the power hydraulic cylinder is presented in the following form:

and the equation of motion of the rod with the piston of a hydraulic cylinder with mass mP

where X ШТ - movement of the rod; P NAG, P SL - discharge and discharge pressure; P1, P2 - pressure in the cavities of the hydraulic cylinder; mP, AP - mass and area of the hydraulic cylinder piston; VЦ1,2 - volumes of hydraulic cylinder cavities; KSF is a coefficient that takes into account the compressibility of the working fluid; fmpP - coefficient of viscous friction of the piston; CE - equivalent stiffness of steering wiring; ΔX - mismatch between the coordinate of the rod and the coordinate of the mass of the swinging part of the engine; PRNAG1,2, PRSL1,2 - conductivity of spool windows; and

PRN1 = PRS2 = KZ(XZ - XZ0) for XZ > XZ0;

PRN2 = PRS1 = KЗ(-XЗ - XЗ0) at XЗ< -XЗ0,

KZ - flow coefficient; XЗ0 - spool overlap.

Due to the impossibility of obtaining an analytical solution of the dependence of the pressure difference in the cavities of the hydraulic cylinder P1, P2 on the movement of the spool X3, we transform the equations for the flow of working fluid through the power hydraulic cylinder by linearizing their left parts. As a result we get

Where

- linearization coefficients; QЗ - flow through the main spool; ΔP2 - P1 - pressure drop in the cavities of the hydraulic cylinder; VЦ0 is the volume of the cylinder cavity with a symmetrical position of the piston; X30, РЦ0 - spool movement and load pressure at the linearization point.

After transformations, we obtain the linearized equation of flow through the main spool in operator form

From the equation of motion of the rod with the piston of a hydraulic cylinder, the transfer function of pressure in the power hydraulic cylinder will have the form

Block diagram of the electrohydraulic drive shown in Fig. 2, consists of the transfer functions of all elements included in it.

The block diagram of the electrohydraulic drive was simulated in the Matlab + Simulink environment. In this case, it is possible to enter nonlinearities of various types, which make it possible to describe processes that cannot be linearized. The drive model uses nonlinearities that limit the output value. Such blocks simulate the restriction of the movement of the damper and spool, which are part of the control unit, as well as the restriction of the movement of the power hydraulic cylinder rod.

Simulation results

An important dynamic characteristic of automatic control systems is frequency characteristics, the advantage of which is that frequency characteristics make it possible to simply identify the influence of a particular parameter on the dynamic properties of the system (stability, transient process, etc.). To analyze the stability of the hydraulic control system under study at given values of the coefficients in the differential equations, logarithmic amplitude phase frequency characteristics (LAFC) of an open circuit were obtained. The LFC and LFFC for the electrohydraulic drive are shown in Fig. 3.

Rice. 2. Block diagram of the electrohydraulic drive

Rice. 3. Logarithmic amplitude and phase frequency characteristics of an open circuit electrohydraulic drive

The frequency and amplitude margins must be no less than certain values. Recommended amplitude margins are 6-8 dB, phase margins are 40°. For this electrohydraulic drive, the amplitude margin is 115 dB, the phase margin is 56°, which is quite sufficient for stable operation of the drive. The analysis shows that this electrohydraulic drive is stable.

Conclusion

Designing control systems using amplitude-phase frequency characteristics makes it possible to analyze the structures and influence of the parameters of an object and its individual parts, solve problems of controller synthesis by selecting corrective links, perform identification using experimentally measured frequency characteristics, and solve other problems.

Bibliographic link

Ratushnyak A.I., Kargu D.L., Chudnovsky Yu.A., Shubin D.A., Gridin V.V. MATHEMATICAL MODEL OF THE ELECTROHYDRAULIC DRIVE OF THE LAUNCHER ROCKET // Basic Research. – 2016. – No. 9-2. – P. 294-298;
URL: http://fundamental-research.ru/ru/article/view?id=40738 (access date: 10/17/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

Goal of the work

Purpose laboratory work is the study of the design, operating principle and mathematical models of electric, hydraulic and pneumatic steering actuators, as well as the analysis of the static and dynamic characteristics of a typical steering actuator using a mathematical model of the actuator compiled in the Matlab programming system.

Exercise

When performing work you must:

Study the structure, operating principle and mathematical models of electric, hydraulic and pneumatic steering actuators (RS).

Plot the LFC and LPFC values calculated in step 4. Compare experimental and theoretical solutions.

Work order

Laboratory work is performed by teams on computers.

The team performs a version of the assignment given by the teacher. The options differ in the initial data for the calculations.

All calculations are carried out in the Matlab programming system using the Simulink visual programming package.

It is assumed that initial skills in working in Matlab and Simulink were acquired by students when performing their first laboratory work in this discipline.

Determine experimentally by conducting a computer experiment with a drive model the values of the logarithmic amplitude and phase frequency characteristics of a closed steering drive at three values of the frequency of the harmonic input signal rad/sec.

Method of doing the work

Creating a drive model

The following steps must first be completed:

Launch MATLAB

Open the Simulink application.

Create a linear and nonlinear RP simulation program shown in the figure.

Calculation of the static characteristics of the drive

The static characteristic of the RP is constructed by assigning a slowly varying input action to the input of the drive model, which increases linearly in the operating range of the required steering angles.

The simulation program is shown in the figure. In addition to the blocks that implement models of the system itself, it contains a Ramp block at the input and two

XY Graph block for plotting static characteristics for linear and nonlinear RP models.

The Ramp block (linearly increasing signal) is taken from the Sources section of the Simulink block library.

XY Graph blocks are taken from the Sinks section of the Simulink block library. They serve to build dependencies based on data

The resulting graphs of static characteristics for linear and nonlinear models of the steering drive should be redrawn and compared with each other.

Experimental construction of frequency characteristics

To experimentally determine individual points of the logarithmic amplitude and phase frequency characteristics of the RP, we create the program shown in the figure. To construct the frequency characteristics, we use the linear model of the steering drive shown at the top of the diagram. The lower part of the circuit is blocked using a Terminator block (Sinks section of the library).

To make it convenient to determine the amplitude of the output harmonic signal and the phase shift of this signal compared to the input on the graph, the simulation time in each of the three calculation options should be set differently, approximately equal to 4 periods of the input harmonic signal. The period of a sinusoid is related to its frequency by the relation: , therefore. When you can take sec.

In each experiment, the following parameters must be removed from the input and output graphs:

Output amplitude;

The time interval between points in time when the input and output harmonic signals corresponding to each other reach maximum values equal to the amplitudes of these signals.

You should pay attention to the fact that when the output lags relative to the input, the interval is a negative value.

Using the experimental results and initial data, it is necessary to calculate the values of the amplitude and phase frequency characteristics of the system at the specified three frequencies. It is convenient to present computer experiments and calculations using a table, the form of which is given in the table.

Table form for plotting the frequency response of the drive by points

	Characteristic	Sinusoid frequency, rad/sec
	Characteristic
Sinusoid period,
Simulation time
Amplitude of the output sinusoid,
Delay of the output sinusoid relative to the input, sec
The value of the logarithmic amplitude frequency response,
The value of the phase frequency response,

Constructing frequency characteristics using a blockLTIViewer

The LTI Viwer program is designed to analyze the characteristics of a linearized model corresponding to a given nonlinear system model compiled in Simulink. The program allows you to calculate and construct the transient process in the system, the pulse transient function, the frequency response of the system and others.

To connect the program to the created system model, you must perform the following steps:

Execute the Tools\Linear Analysis... command in the Simulink model window.

As a result of executing the command, the Model_Inputs_and_Outputs window will open, as well as an empty Simulink LTI-Viewer window.

Install the Input Point block and the Output Point block at the entry and exit points of the model of the system under study.

In the LTI Viewer window, run the Simulink\Get Linearized Model command.

To obtain other system characteristics, you must run the Edit\Plot Configuration... command in the LTI Viewer window.

Construction of transient processes

The transient process of the drive can be constructed by applying a step action to the input of the drive model and observing the response using the Scope block.

For a linear system, the type of transient process does not depend on the magnitude of the input action, i.e. changes proportionally to the magnitude of the step signal. Therefore, when analyzing linear systems, the transient process is constructed with a single input step action l(t).

For nonlinear systems, the system response depends not only on the properties of the system, but also on the magnitude of the step effect. Therefore, in order to evaluate the influence of drive nonlinearities on the type of transient process, calculations should be carried out with a large step input signal.

Step action can be set using the Step and Constant block.

To compare transient processes for linear and nonlinear gyroscope models, it is advisable to plot the process curves for these two models on the same graph. In Simulink, two or more curves can be plotted on the same graph by combining two or more scalar signals into a single vector signal and feeding that vector signal into the input of the Scope block.

Combining scalar signals into a vector signal is done using the Mux block from the Signal Routing section of the Simulink block library.

The inertia of the steering drive, characterized by its time constant T, is relatively small (up to 0.05 sec). Therefore, to construct a transient process, the simulation time can also be set small, approximately equal to (10-20) T, i.e. 0.5-1 sec. This time is set on the program toolbar under the Simulation/Simulation Parameters/Stop Time buttons.

The transient graphs corresponding to the linear and nonlinear models of the steering drive should be sketched and compared.

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Technical task

Design of the actuator motor of the gas steering drive system

1. General information

3. Mathematical models of gas and pneumatic steering actuators

4. Schematic diagram of the steering tract

5. Design of gas power control system

6. Simulation

Literature

Technical task

Design a gas power control system operating in proportional mode. The input signal is harmonic with a frequency in the range. In the frequency range of the input signal in all operating modes, the system must ensure the processing of a useful signal with an amplitude of at least d 0 with phase shifts not exceeding the phase shifts of an aperiodic even with a time constant T GSSU.

Basic input data:

a) system transmission coefficient;

b) maximum steering angle deflection d t;

c) estimated operating time;

d) quantities characterizing the dynamic properties of the system; in the simplest version, this includes the values of the limiting frequency of the input signal u 0, the amplitude d 0 of the signal processed by the drive at the frequency u 0 (the value is usually set in the range 0.8 ... 1.0), the value of the time constant of the equivalent aperiodic link T GSU;

e) loads on the steering bodies - inertial load specified by the moment of inertia of the load J N;

Friction coefficient f;

Hinge moment coefficient t w.

If the coefficient t w. changes over time, then a graph of its change over time can be specified. In the simplest case, extreme values of this coefficient are specified. Typically, the maximum value of the negative load corresponds to the initial moment of operation; at the final moment the proportional load is often positive and also has extreme stiffness.

Table of initial simulation parameters

Option No.
TK parameters
Load moment, Nm
Maximum angle, rad
Deviation amplitude RO, rad
Maximum input signal frequency, Hz/amplitude, in
Friction coefficient N*s/m
Weight of moving parts RO kg
Gas pressure in GIS bar
Gas temperature in ISG deg C

Design of the actuator motor of the gas steering drive system

pneumatic gas steering motor

1. General information

Pneumatic and gas actuators are widely used in control systems for small aircraft. An alternative to traditional systems with primary energy sources of actuators - systems with gas-cylinder sources of compressed gases and systems with preliminary gasification of various substances, was the creation of devices belonging to a fundamentally new family - air-dynamic steering drive systems.

Actuators of this class are complex servo automatic control systems, which, as part of the product during storage, transportation and operation, are subject to significant climatic, mechanical and other external influences. The above-mentioned features of the conditions of use and operating modes, the consideration of which is mandatory when developing new systems, allow us to classify them as mechatronic systems.

When choosing the type and determining the parameters of the BULA steering drive system, two control methods are usually used: aerodynamic and gas-dynamic. In control systems that implement the first method, the control force is created due to the active influence of the speed pressure of the oncoming air flow on the aerodynamic rudders. Steering actuators are designed to convert electrical control signals into mechanical movement of aerodynamic rudders, rigidly connected to the moving parts of the actuator motors.

The actuator motor overcomes the hinge loads acting on the steering wheels, providing the necessary speed and the necessary acceleration when processing specified input signals with the required dynamic accuracy.

Control systems that implement the second method include:

Autonomous gas-reactive automatic control systems;

Thrust vector control systems (TSVTC).

Currently, for the first control method, devices that use gas as an energy source are widely used. high pressure. For example, this class of devices includes:

Steering drive systems with gas-cylinder sources of compressed air or air-gas mixture;

Systems with powder pressure accumulators or other sources of working fluid, which is a product of preliminary gasification of solid and liquid substances.

Such systems have high dynamic characteristics. This advantage arouses great interest in such steering drive systems from developers and makes them important objects of theoretical and experimental research.

The creation of high-tech steering drives for BULA control systems is traditionally associated with the search for new circuit and design solutions. A special, radical solution to the problem of creating high-tech steering actuators was the use of energy flowing around the rocket for control. This led to the creation of a new, special class of actuators - air-dynamic steering actuators (ADRS), using the energy of the oncoming gas flow as a primary energy source, i.e. kinetic energy BULA.

These instructions are devoted to the design, application and methods of research and design of executive mechatronic modules of control systems for small-sized BULA. It reflects information that may primarily be useful for students of the specialties “Mechatronics” and “Aircraft Automatic Control Systems”.

2. Design of actuator motors

Steering drive systems include the following functional elements.

1. Devices that ensure the creation of force on controls:

Power sources - primary energy sources (compressed gas sources and electrical energy- batteries and turbogenerator sources of electrical energy);

Actuating motors, kinematically connected to the controls, and elements of energy lines - for example, air and gas filters, check and safety valves, gas pressure regulators of systems with gas-cylinder sources of compressed gas, combustion rate regulators of powder pressure accumulators, air intake and discharge devices VDRP and etc.

2. Functional elements that establish the correspondence between the control signal generated in the control system and the required force action - converters and amplifiers of electrical signals, electromechanical converters, various types of sensors.

To specify the areas of research for the tasks facing the development of steering drives, they include power and control systems (Fig. 1.2).

Rice. 1.2. Aircraft steering gear diagram

The power system combines the functional elements of the steering drive, which are directly involved in converting the energy of the power source into mechanical work associated with the movement of positionally loaded controls. The control system consists of functional elements of the steering drive, which ensure a change in the controlled variable (coordinates of the position of the controls) according to a control law specified or developed during the flight of the aircraft. Despite the somewhat conventional nature of the separation of power and control systems, which is associated with the need to include a number of functional elements of the steering drive in both the power and control systems, the practical usefulness of such separation lies in the possibility of a diverse representation of the steering drive when solving various problems in the development process .

The following subsystems can be distinguished in the gas steering system:

Primary source of energy;

Executive motor;

Gas distribution device with a control electromechanical converter;

Electrical control system - amplifiers, correcting devices, forcing oscillation generators, etc.;

Primary transducers are sensors for linear and angular movements of moving parts of mechanical subsystems.

To classify gas steering systems, in general case, the following classification criteria can be used:

Type of power system, i.e. type of primary energy source;

The principle of controlling aerodynamic rudders;

Control loop type for devices with proportional steering motion;

Actuator motor type;

Type switchgear and a control electromechanical converter.

1. Systems with a gas-cylinder source of compressed gas. The source of high-pressure gas is an air-valve unit, which, in addition to a cylinder with compressed air or an air-helium mixture, includes safety, shut-off and distribution and regulating gas fittings and fittings for filling and monitoring the pressure in the cylinder. In the technical literature, such systems are often called “pneumatic”.

2. Systems with a powder pressure accumulator. High pressure gas source in in this case is a solid propellant powder charge of a special design that ensures constant productivity of the working fluid - combustion products of the charge, having high temperature. In addition to the direct gas source and the device for switching the gas source into operation, such systems may include fuel combustion rate regulators and safety devices. In technical literature, when describing such systems, the term “hot-gas” or simply “gas” is often used.

3. Electromagnetic steering drives. The basis of such devices is usually a neutral-type electromechanical converter, which directly carries out the specified movement of the aerodynamic steering elements.

An actuator is a device that converts the energy of compressed gas into the movement of steering elements, overcoming the force created by the air flow of the flowing BULA.

Based on their design, the following groups of actuator motors can be distinguished.

1. Piston - single-acting and double-acting. Devices most often used both in special equipment and in process automation systems.

Rice. 1. The SGRP executive engine is a closed type - piston, with one power cylinder.

Fig.2. The SGRP executive motor is a closed type - with two power cylinders.

The operation of the executive engine is controlled by a gas distribution device (GRU).

The purpose of the GRU is to alternately communicate the working cavities of the drive actuator motor with a source of compressed gas or with environment(the atmosphere of the onboard drive compartment). According to the nature of the switching problem being solved, GRUs are generally divided into devices:

With control “at the entrance” - the areas of the inlet openings into the working cavities change;

With “output” control - the area of the outlet openings from the working cavities changes;

With “inlet and outlet” control - the areas of both inlet and outlet openings change.

3. Mathematical models of gas and pneumatic steering actuators

When mathematically modeling the steering gas drive system (SGG), as an element of the BULA control system operating in the air flow flowing around it, the area of research is a set of geometric, electromechanical parameters and parameters of the working fluid - air or other compressed gas, as well as state functions of electromechanical, aerogasdynamic processes and management processes occurring in all the diversity of cause-and-effect relationships. Given the ongoing transformations of one type of energy into another, the presence of distributed fields and a structurally complex representation of real mechanisms in the physical field of research under consideration, the creation of mathematical models that provide the required degree of reliability of engineering calculations is achieved through the introduction of theoretically and experimentally substantiated idealizations. The level of idealization is determined by the goals of the software being created.

Mathematical model of the steering drive:

p 1, p 2 - gas pressure in cavity 1 or 2 of the steering gear,

S P - area of the steering piston,

T 1, T 2 - gas temperature in cavity 1 or 2 of the steering gear,

Т sp - temperature of the walls of the steering gear,

V - steering piston speed,

F pr - spring preload force,

h - viscous friction coefficient,

Hinge load factor,

M is the reduced mass of moving parts.

Rice. 3 Typical graphs of transition processes.

4. Schematic diagram of the steering tract

The steering tract of a gas power control system can be built with mechanical, kinematic, electrical feedback or have no main feedback. In the latter case, the drive usually operates in relay mode (“yes - no”), and in the presence of feedback - in proportional mode. In this development, steering tracts with electrical feedback will be considered. The error signal in these paths can be amplified by either a linear or relay amplifier.

A schematic diagram of the steering tract with a linear amplifier is shown in Fig. 5.

Rice. 4. Steering circuit diagram

The diagram shows: W F (p), W Z (p), W p (p), W os (p) - transfer functions of the correction filter, electromechanical converter, drive, feedback circuit, respectively. The gain of the linear amplifier in this circuit is included as a multiplier in the EMF primary coefficient.

The choice of drive parameters is made in such a way that in a given range of frequencies and amplitudes of the processed signal there is no limitation on the x and X coordinates. In this regard, nonlinearities in the form of restrictions on these quantities are not taken into account when forming the steering tract.

5. Design of gas power control system

Design methodology

The type of actuator and the schematic diagram of the steering tract are selected. The type of drive is determined based on the requirements and operating conditions. For long operating times and high temperatures Tp, a drive circuit with output control is preferable. For selection schematic diagram it is advisable to carry out a preliminary study of various schemes, approximately evaluate their capabilities (operational, dynamic, weight, dimensions) and select best option. This task, consisting of an approximate calculation of the characteristics of the GSSU of various schemes, should be solved at the initial stage of system development. In some cases, the type of circuit diagram can be clearly selected already at the initial stage of work and specified in the technical specifications.

Generalized drive parameters are calculated. The method of this calculation is determined by the type of the selected circuit diagram of the steering tract. Here is the methodology as applied to the steering tract with electrical feedback:

a) select the load factor value y:

Maximum value of the hinge load coefficient;

Mt - maximum torque created by the drive,

where l is the mechanical transmission arm.

The required drive power depends on the choice of value y. The optimal value for opt, corresponding to the minimum required drive power, can be determined as a solution to the cubic equation

The numerical value of opt usually lies in the range of 0.55 ... 0.7. When atom, the value is assigned in the range 1.2? 1.3. The magnitude of the ratio and depends on the type of actuator selected. So. for drives with a gas distributor of the nozzle-flap type, ; for actuators with jet pipe, .

The parameter q, depending on the value, must correspond to mode I. Its value is determined either from the results of thermal calculations or from experimental data with analytical devices. Here we will assume that the law of change of parameter q over time is given in the form of an approximating dependence for different values of the ambient temperature.

The value b 0 - the amplitude of movement of the EMF armature for the steering tract with a linear amplifier is assumed to be equal to y m, i.e. , and for systems with a relay amplifier operating in PWM mode on the switchgear, the value is taken in the range of 0.7? 0.8;

b) for the selected value of y, the maximum torque developed by the drive is calculated:

c) the required value of the angular velocity SHt provided by the drive is determined.

The value Sht is found from the conditions for the gas drive to process a harmonic signal with frequency Sht and amplitude d 0. The amplitude of movement of the EMF armature b 0 is taken to be the same as in the previous calculation.

In the region of low frequencies (), the dynamics of the drive with a relatively low inertia of the mechanical link can be described by an aperiodic link. You can get the following expressions:

For an aperiodic link

From the last dependence after transformations we obtain a formula for calculating the required value Ш max:

The design parameters of the drives are calculated.

The mechanical transmission arm l, the piston diameter of the power cylinder D P, the free play value of the drive X t are determined.

Fig.5 Design diagram of ID.

When determining the arm l, you need to set the relationship between the free stroke of the piston and its diameter.

For reasons of compactness of the power cylinder design being developed, we can recommend the ratio.

At X = Xt, the maximum torque generated by the drive must be several times greater than the maximum torque from the load, i.e.

Taking into account the accepted relationship, from the last equality we obtain the dependence

The maximum pressure drop in the cavities of the power cylinder Dr max depends on the value of p p, the type and ratio of the geometric dimensions of the distribution device, as well as on the intensity of heat exchange in the cavities. When calculating the value of l, it can be approximately taken for drives with a nozzle-flap type gas distributor Dr max = (0.55 × 0.65) r r, when using a jet distributor Dr max = (0.65 × 0.75) r r.

When calculating the value of l, the value of Drmax must correspond to mode I.

At relatively small values of dmax

During the calculation process, all linear geometric dimensions must be rounded in accordance with the requirements of the standards.

Calculate the parameters of the gas distribution device of the drive. This calculation is carried out from the condition that in the worst case, i.e. in mode I, the drive speed was ensured not lower than, where Sht is the value of the angular velocity. Here we will give methods for calculating geometric parameters for two design types of gas distributors: with a jet tube and with a nozzle and damper. The first of these distributors implements gas flow regulation according to the “inlet and outlet” principle. In this case, the maximum steady speed of the drive is determined by the relationship

What follows

When calculating based on the dependence, the values of T p and q must correspond to mode I.

Taking into account the size ratios characteristic of a given distributor, it is accepted that .

A rational ratio of areas c and a provides the best energy capabilities of the drive and lies within the limits. From these considerations the value C is found. Having calculated the values a, c, the main geometric dimensions of the distributor should be determined.

Rice. 6. Design diagram of the “jet tube” gas distributor.

The diameter of the distributor receiving window is determined from the condition

where flow coefficient m = 0.75 ... 0.85.

The magnitude of the maximum movement of the end of the jet tube, and the length of the jet tube.

With a known value of x m, the values of b and d are calculated.

A gas distribution device of the “nozzle-flap” type implements regulation of the gas flow “at the outlet”.

Ad hoc

Therefore:

The ratio should be taken into account when making calculations. The values of T p and q correspond to mode I.

Rice. 7 Design diagram of the “nozzle-flap” gas distributor.

The nozzle diameter d c is selected so that the effective area is at least 2 times the maximum area of the outlet:

For the selected value of d c, find the value of b: b = mрd c ; calculate the maximum value of the coordinate xt and the value

After developing the design of the gas distribution device, the loads on its moving parts are determined and the EMFs are designed or selected. The required flow rate of the working fluid is also determined, which is necessary for the design (or selection) of a power source.

With known design and operational parameters of the drive, the parameters of its jet circuit can be determined from dependence (I) for both mode I and mode II, after which the steering tract can be formed.

The contour of the steering tract is formed taking into account the extreme modes of its operation. At the first stage of formation, the frequency characteristics of an open circuit in mode I are plotted (the value of the coefficient k 3 is temporarily unknown).

Based on the requirement for dynamic accuracy of a closed loop, we find the permissible value of the phase shift at frequency u 0:

ts z (w 0) = arctg w 0 T GSSU.

With a known value of the phase shift for an open-loop circuit c p (w 0), determined as a result of constructing frequency characteristics, and a certain value c z (w 0), we find the required value of the amplitude characteristic A p (w 0) of the open-loop system at frequency w 0. For this purpose it is convenient to use the closure nomogram. After this, the amplitude characteristic of the circuit in mode I turned out to be uniquely determined, and therefore, the value of the open-circuit coefficient K p is determined.

Since a correction filter has not yet been introduced into the circuit, the value of K r is determined by the dependence K r = k e K n k oc . The magnitude of the feedback coefficient can be determined by the closed-loop transmission coefficient: . Then you can calculate the value of the coefficient k e: , and subsequently calculate the required value of the voltage amplifier gain

6. Simulation

Using the data from the table, we will first simulate the system in the PROEKT_ST.pas program. Having thus calculated the suitability of the system parameters, we will continue modeling in PRIVODKR.pas and calculate the response time there.

Let's fill in the tables based on the obtained parameters:

Let's increase the temperature:

Let's lower the pressure:

Let's increase the temperature (at reduced pressure)

Main literature

1. Goryachev O.V. Fundamentals of the theory of computer control: textbook. allowance / O. V. Goryachev, S. A. Rudnev. - Tula: Tula State University Publishing House, 2008.-- 220 pp. (10 copies)

2. Pupkov, K.A. Methods of classical and modern theory automatic control: textbook for universities: in 5 volumes. T.5. Methods of modern automatic control theory / K.A. Pupkov [and others]; edited by K.A. Pupkova, N.D. Egupova. -- 2nd ed., revised. and additional - M.: MSTU im. Bauman, 2004. -- 784 pp. (12 copies)

3. Chemodanov, B.K. Servo drives: 3 t. T.2. Electric servo drives / E.S. Blaze, V.N. Brodovsky, V.A. Vvedensky, etc. / Edited by B.K. Chemodanov. -- 2nd ed., revised. and additional - M.: MSTU named after N.E. Bauman, 2003. - 878 p. (25 copies)

4. Electromechanical systems: textbook. allowance/G.P. Eletskaya, N.S. Ilyukhina, A.P. Pankov. -Tula: Tula State University Publishing House, 2009.-215 p.

5. Gerashchenko, A.N. Pneumatic, hydraulic and electric drives aircraft based on wave actuators: textbook for universities / A.N. Gerashchenko, S.L. Samsonovich; edited by A.M. Matveenko. - M.: Mashinostroenie, 2006. - 392 p. (10 copies)

6. Nazemtsev, A.S. Hydraulic and pneumatic systems. Part 1, Pneumatic drives and automation equipment: Textbook / A.S.Nazemtsev.-- M.: Forum, 2004.-- 240 p. (7 copies)