2017. № 93


Theoretical mechanics

Aslanov V. S.

The field of space tethers has received very much attention in recent decades. The central advantage of using tethers in many of these applications is that very little fuel needs to be consumed. The tethered systems offer numerous ways of beneficial implementation on modern spacecrafts and allow to perform multiple tasks including such as payload delivery from the Earth orbit. It is the task of payload delivery from an orbit is the closest to wide practical realization from all other space tether’s tasks. As demonstrated by the mission of YES2 a re-entry capsule can be returned to Earth by a tether. Braking of the capsule is achieved using momentum provided from the swinging tether. The more a deflection angle of the tether from the local vertical, the more braking effect of the capsule is achieved. The goal is to find the control law that allows one to increase the angle of deflection of the tether from the local vertical, i.e., to increase momentum provided from the swinging tether. This control law can be applied to the final phase of the deployment of the tether, both for dynamic so the static deployment. The control law is based on the principle of a swing with variable length. Simulations show that the system can be controlled quite well using the proposed control law for the tether length rate. For stability analysis in the neighborhood of the equilibrium position is used Lyapunov function. Opportunity to perform separation of the capsule is shown for to oscillation of the tether system, and for the rotation. The control method allows to reduce a required tether length for deliver capsules on Earth’s surface. Using this method, we have shown that it is possible to diminish tether length at 5 km as compared with YES2 mission. Results of the numerical modeling showed that the control law is effective for the final phase of the tether deployment, when the initial deployment occurs by means static or dynamic scheme.

Keywords: tethered satellite systems, re-entry capsule, tether length control law

Semenov M. E., Solovyov A. M., Popov M. A.

As is known, the problem of inverted pendulum plays a central role in the control theory. In particular, the problem of inverted pendulum (as a test model) provides many challenging problems to control design. Due to their nonlinear nature, pendulums have maintained their usefulness and now they are used to illustrate many ideas emerging in the field of nonlinear control. Typical examples are feedback stabilization, variable structure control, passivity-based control, back-stepping and forwarding, nonlinear observers, friction compensation, and nonlinear model reduction. The challenges of control made the inverted pendulum systems a classic tool in control laboratories. It should also be noted that the problem of such a system stabilization is a classical problem of the dynamics and control theory. Moreover, the model of inverted pendulum is widely used as a standard for testing of control algorithms, such as PID controller, neural networks, fuzzy control, etc.

The article investigates the dynamics of a mechanical system consisting of two inverted pendulums hinged on the moving platform and coupled by a spring. The force applied to the platform causing its horizontal motion is treated as a control. The purpose of this work consists in solving the problem of pendulums stabilization in vertical position using the horizontal motion of the platform at presence of the information on the angles of deviation. To solve this problem, we developed the algorithm of the pendulums stabilization near vertical position, found the stability zones and their dependence on the spring stiffness.

Keywords: inverted pendulum, coupled oscillators, stabilization, control

Fluid, gas and plasma mechanics

Volkov V. A., Semenov V. V., Sidhu J S. S.

For smooth and piecewise smooth planar relief structures with any periodic profile, within the framework of linear theoryan exact formula, linking the total wave drag coefficient of the aforementioned finite relief structures and their infinite counterparts were obtained. The specified exact formula contains a defect function, which arguments are two similarity parameters: the fractional part of the wave number and the phase value at the leading edge. The defect function is defined only for periodic relief structures, having infinite analogues. Those, where the defect function identically equals zero are called special, and all the rest are usual. The defect function of usual periodic relief structures becomes zero for integer values of the wave number. It can differ from zero only for fractional values of the wave number. The drag wave force of special relief structures is directly proportional to their length. For all the other planar relief structures, this rule may not be applied. The uniqueness of the special planar relief structures is stems from the fact that they have a saw-tooth profile, in which all the vertices of the teeth have the same obtuse angle, which bisector is parallel to the axis.

The presence of the abovementioned properties in the special relief structures make them promising candidates for the role of standards used during calibration tests of various installations. If the calibrated planar attachments have special relief structures, then the following advantages will be achieved. Firstly, the technology of special planar relief structures manufacturing is the simplest and virtually insensitive to defects of its practical realization. Secondly, using the same reference attachment with special planar relief structures, and successively cutting off from it by parallel forming bands, makes it possible to perform a precision calibration for a specified range of wave drag. The use of reference planar attachments with special relief structures can increase the accuracy of various installations, and, at the same time, reduce the amount and cost of testing carried out during calibrations.

Keywords: planar relief, velocity, Mach number, pressure, density, sine wave, wave drag, relief defect

Aeronautical and Space-Rocket Engineering

Aerodynamics and heat-exchange processes in flying vehicles

Leont'ev V. A., Krymskii V. S., Ignatkin Y. M., Makeev P. V.

In this paper, the computational-experimental studies results of the tail rotor (TR) aerodynamic characteristics at the helicopter yawing rotation mode, at hover are shown.

The experimental studies have been carried out by using the experimental model, developed in TsAGI. The experimental model main rotor (MR) diameter DMR=2,5 m, the tail rotor diameter DTR=0,586 m. The computational studies have been carried out using two models: the helicopter mathematical model, developed by TsAGI and the non-linear blade vortical model of a rotor, created by «Helicopter Design» department of MAI.

The computational-experimental relationships between the tail rotor thrust coefficient Сt and a yaw angular velocity ωу of the helicopter model showed, that for small values of the tail rotor pitch about φTR=3,8º an increase of ωу resulted in Сt increase, however starting from the tail rotor pitch φTR=9,2º and higher, the coefficient Сt decreased. The experimental results confirm the analytical and the mathematical modeling results in the paper [10].

Analysis of the computational-experimental studies results showed that when the angular velocity ωу is growing TR blades are subjected to high Coriolis forces in addition to aerodynamic forces. Coriolis forces have different direction from one side of the TR to the other and therefore, flapping motion of the TR is increasing. By reaching some rotation rate ωу, one side of the TR goes beyond stall, hence the TR thrust ceases to increase. On the other side of the TR blades angles of attack decrease reducing the total TR thrust.

The computational relationships Сt=f(ωу) and mk=f(ωу) of the TR at the helicopter yawing rotation mode with the MR are in general agreement with the experimental results. They show that the MR vortex wake insignificantly affects on the TR aerodynamic characteristics.

Keywords: single-rotor helicopter, hover, yawing rotation, main rotor, tail rotor, interference of rotors, experiment, computational studies

Design, construction and manufacturing of flying vehicles

Kurmazenko E. A., Kochetkov A. A., Proshkin V. Y., Kiryushin O. V., Pushkar' O. D.

Solution of certain partial problems of ensuring the crew life and activities cannot be regarded as a process of creation of an interplanetary manned vehicle ecological-engineering system development. Such system is designed for long-term manned missions to the planets of the Solar system, in which rather complex interaction of separate elements and products serve as initial materials to ensure functioning of the other in abiotic part of the of ecological-engineering system — integrated life-support system.

The determinants of the of integrated life-support system development are space mission program, the type of interplanetary manned vehicle, characteristics of interfaces with onboard systems and its technological structure.

The goal of this paper consists in developing selection principles of advanced technologies for integrated life-support system for long-term space missions design, with account for current design constraints.

The paper considers natural morphological classification of the technologies based on the following attributing features. These features represent crew metabolism products ‒ a form of energy and primary power services for transformation processes, produced by components of the crew habitat; a special technology and formulated efficiency factors for integrated life-support system technology selection, reflecting its properties as a complex integrated system and features of the considered technologies.

The basic principles of technology selection and the list of critical technologies for integrated life-support system of interplanetary manned vehicle developing are formed.

Keywords: integrated life-support system, technological structure, interplanetary manned vehicle, initial synthesis problem, crew, efficiency model, system approach the design

Strength and thermal conditions of flying vehicles

Egorov I. A.

When flying at high speeds, the surface temperature reaches high values. In this regard, is the role of radiant heat flow in the heat exchange process increased. There is a need for more accurate recording.

This article is on the radiant heat flow accounting by numerical integration of the aircraft construction heating process directed.

The task is reducing to calculation about the skin one-dimensional heating (along thickness). The heat equation is recorded in the central finite differences form. As a result is create the algebraic equations system. For the boundary points used equations of boundary conditions. For the outer surface used the balance equation of heat flow.

The heating process is calculated numerically by the method of numerical integration. The nonlinearity of the dependence of radiant heat flow on the surface temperature is eliminated by using the value of the surface temperature at the previous integration step. Investigated the validity of this approach under various intensity of heat. It is shown that in some cases it is possible to obtain divergent process.The scheme formulated solutions to ensure the sustainability of the process and increase its accuracy.

The calculation is performed in the following sequence:

  1. Sets the initial value of the surface temperature is equal to the value of the surface temperature for the previous step of time integration.

  2. For this value of the surface temperature calculated heat flux radiation and determines a value of heat transfer coefficient.

  3. Calculation of the temperature field of a multilayer structure, which defines the new value of the surface temperature for a given step of the time integration.

  4. Inaccuracy of specifying the value of surface temperature.

  5. If the error in determining the surface temperature does not exceed a predetermined value, the process moves to the next stage of the calculation.

  6. If the error in determining the surface temperature exceeds the specified value, restores the original temperature field and the adjustment values of the surface temperature by a given amount. The adjustment is made in the direction of increasing or decreasing values of the surface temperature depending on the sign of the increment of the magnitude of radiant heat flux.

Proposed scheme solution allows to properly take into account radiant heat flux for the intensely hot designs.


  1. Determination of radiant heat flux using the temperature at the previous step of time integration is an effective way of taking into account the boundary conditions for the numerical calculation of heating of the aircraft in flight.

  2. To ensure stability of the calculation process, it is necessary to control the accuracy of determining the surface temperature at each step of time integration and, if necessary, to clarify the obtained values.

  3. It is advisable to use high values of accuracy parameters (the acceptable accuracy of determining the surface temperature 0.5%, step approach temperature of 2°) , which will provide not only the stability of the calculation and the high accuracy of the results, but also decrease the time of calculation.

Keywords: temperature field, numerical integration, aircraft, outer surface, boundary condition, radiant heat flow

Nesterov M. S., Popelo V. D.

The paper introduces the characteristic for quantitative description of infrared (IR) visibility with account for aircraft’s intrinsic equilibrium radiation. The most important state of an aircraft sample’s thermal field, wherein the IR visibility is evaluated, is the state of the intrinsic equilibrium radiation. The aircraft intrinsic equilibrium radiation technical characteristics currently applied for IR evaluation are defined by current observing conditions.

The presented work aims at introduction of characteristics, defining the properties of IR visibility in thermal equilibrium with the environment, satisfying the following basic principles:

— Measured value must be constant, while changing the conditions of the object observation in a wide range, if the object’s properties as the goal, do not vary in time;

— Measured value must be associated by linearly dependence with the parameter of the received reflected or emitted signal;

— The value measured in the optical range must be comparable to similar variables used as characteristics of the object in the other electromagnetic spectrum bands.

In contrast to currently applied IR visibility figures, the introduced characteristics of effective radiating surface (ERS) does not depend on external observing conditions. The authors considered physical quantities derivations from ERS for the case of linear and distributed objects surveying. Specificity of the introduced characteristics consists in constancy at an object observation conditions variation, as well as existence of linear relationship with a signal value on the radiation receiver (radiant flux density).

The presented characteristics allow obtain unambiguous solution of the inverse problem of restoration of a value of an object characteristic according to the measured value of the received signal.

Keywords: aircraft, infrared visibility, visibility characteristics

Titov V. A.

Algorithms are discussed for loads and stress analysis of space and rocket technology articles’ structural units in conditions when direct measurements of dynamic impacts are absent but there are available readings of recorded structure response parameters which are characteristics of external loading conditions. The problems discussed are divided in three groups and at each of them an impact may be characterized by:

— deterministic quasi-static behavior, at that measured kinematic parameters include separating signal components, which characterize displacement of a structure as a solid;

— deterministic behavior, at that its temporal characteristics correlate with vibration frequencies of a structural unit;

— random behavior distributed over space, and measurement results are structural responses with account of dynamic character at a wide frequency range.

General idea of the algorithms consists in determination of external loading through mathematical processing of telemetry data using equations of motion and further integration of these equations with known right-hand member for estimation of internal load factors and mode of deformation at examined structural units.

The dynamic models used possess high dimensionality, and force impacts to be restored ‑ long duration. Here high computational recourses are required for operation calculations on decision-making and for statistical computations (with varied structural parameters or external loading characteristics). This defines requirements on computational speed of devising algorithms, which are realized in the program complex developed.

The results’ reliability is provided by fulfillment of requirements imposed on high degree of dynamic models’ adequacy to full-scale structures. Quality of inverse problem solution (restored impact) in all cases is estimated by agreement of parameters telemetered (measured in tests) with calculation results on these parameters obtained through the dynamic models with restored force impact.

Special attention is paid to identification of dissipative characteristics, which influence significantly on restored time dependences of loading and stress parameters at structural units.

The program complex was developed basing on suggested algorithms and it was used for loads analysis of structural units of launch vehicles, International Space Station and at liquid-propellant engine firing tests.

Keywords: loads, mode of deformation, external loading, telemetry information, dynamic models

Thermal engines, electric propulsion and power plants for flying vehicles

D'yakonov G. A., Nechaev I. L., Semenikhin S. A.

In this paper, we study the prospects for improving the mass-dimension characteristics of ablative pulsed plasma thrusters (APPT) designed for small spacecraft (SSC) weighing up to 1000 kg. The urgency of this direction development arises from connection with the needing of high-efficiency electric propulsion systems (EPS) of low thrust. It should combining low mass and power consumption with a large resource and total thrust impulse.

One of the promising areas is the creation of EPS based on ablative pulse plasma engines (APPT). Prospective increased resource propulsion system should have significant reserves of working fluid and autonomous systems for their storage and supply, through which temporary reconciliation between the energy supply and the mass acceleration into the discharge channel can be. The also necessary parameters are the space propulsion system mass decreasing, the accelerating channel geometry invariance, as well as stability and high specific characteristics during the entire life of the thruster.

The most studied version of the APPT is rail-type, with solid dielectric plates. We experimentally investigate its characteristics in this paper.

The most important for the EPS practical application are such characteristics as the thrust total impulse PΣ, which determines the SSC characteristic speed, the power consumption N and the EPS total mass, including the mass of the power processing unit (PPU).

Currently, the direction emergence problematic assessment was investigated. The possibilities of reducing the mass of the APPT are considered by using new plasma acceleration schemes like channels with an asymmetric discharge. The characteristics of the best pulse thruster flight prototype samples are presented as the result of laboratory experimental testing. The test equipment brief description and the measurement error is giveto assess the error of the results. The main problems that have arisen during the development of new laboratory samples of APPT are considered. In the short term, it is possible to reduce the total mass of the APPT by approximately 15%, using the obtained results.

Keywords: small spacecraft, ablation pulse plasma thruster, improvement of mass-dimension characteristics

Gurevich O. S., Gol'berg F. D., Zuev S. A., Busurin V. I.

Basically, the control of modern gas-turbine engines is carried out according to variables which implicitly describe engine basis characteristics, such as a value of thrust, a specific fuel consumption and so on, because their measurability is out of contact. Hardware development of digital automatic control systems (ACS) has broken new ground for an engine control, health monitoring and diagnostic. It has become possible to bring into ACS software (SW) sufficiently detailed simulation model «virtual engine» and calculate unmeasurable engine critical parameters with high fidelity while in engine operation.

The article describes new principles of based on such SW control of high-pressure compressor mechanization, which is adaptable to engine operating conditions — closed loop control of guide vanes angle and air bleed valve position according to calculated values of compressor stall margin and efficiency, along with controlling according to excess air ratio in the combustor chamber. A functional block-diagram and heart of software of such control system have been developed in respect to modern turbofan engine with high bypass ratio.

As a result of accomplished researches it was shown that using of new control methods may allows:

— decrease specific fuel consumption without sacrificing required value of thrust on cruise modes;

— decrease up to 10% spent stall margin of HPC during acceleration;

— decrease by 5...10% spent stall margin of LPC add stage and decrease by a factor of 1,5...2 maximum values of excess air ratio in order to keep steady combustion in the combustor chamber.

Keywords: automatic control system, gas-turbine engine, compressor mechanization, virtual engine

Sha M., Agul'nik A. В., Yakovlev A. A.

Aerodynamic characteristics of blade machines can be determined with high accuracy by experimental studies of models in wind tunnels. However, the cost of such experiments is quite high and, in addition, this method of research does not allow full-scale optimization of all geometric parameters. In this connection, numerical modeling is becoming increasingly important.
Studies in the numerical simulation of the flow of a subsonic flow over the NACA-0012 profile were carried out on two grids that were created in the Ansys ICEM program. In the process of mathematical simulation of the subsonic flow over the NACA-0012 profile, a series of data was obtained and a comparison was made with the experiment.
Carrying out a numerical study in the presented modes with respect to the Reynolds number and the turbulence models under consideration made it possible to identify the most optimal variant, namely the regime M = 0.184, Re = 8000000, and the corresponding turbulence model:  .
As a result of the numerical calculation, values were obtained on which the graphs of the dependence of the coefficient Cya on the angles of attack were plotted for different Reynolds numbers and turbulence models.
In all calculation modes, a good qualitative coincidence of the result is observed, while the difference in the results in the region of the leading edge of the profile may be due to the influence of the geometry of the computational grid.
The numerical study showed that the selected calculation grids and the turbulence model can be used to analyze the flow of subsonic flow over the wing and blade profiles.

Keywords: Ansys ICEM-Fuent, mesh, turbulence model, aerodynamic coefficients, numerical Methods

Dynamics, ballistics, movement control of flying vehicles

Woo S. W.

Interplanetary space missions often require large velocity increment leading to necessity to use the main solar electric propulsion systems (SEPS) with high specific impulse to decrease propellant consumption. Electric propulsion system with constant power consumption makes it necessary either excessive increase in the size and mass of the solar arrays or excessive decrease in the consumed power and thrust to provide SEPS operation at the greatest distance from the Sun. Therefore usage of non-adjustable thrusters leads to necessity of using a cluster of the thrusters in the composition of SEPS to permit most efficient power regulation of SEPS using maximum permissible number of operating thrusters depending on the available electric power. The interplanetary trajectory optimization of spacecraft driven by solar electric propulsion system with cluster of similar thrusters is considered. Fixed-time propellant minimization problem is considered. The technique uses Pontryagin maximum principle to reduce the optimal control problem to the boundary value problem and continuation method to reduce the boundary value problem to the initial value problem. Solution of the power-limited trajectory optimization problem is used as initial guess values for initial values of the costate variables. The power-limited trajectory optimization method does not require a user-supplied initial guess. The continuation parameter is introduced into right-hand parts of differential equations of optimal motion to provide the coincidence of these differential equations to the power-limited problem at zero value of the parameter and to the staircase-thrust problem when the parameter equals to one. The smoothed dependencies of the step function of thrust switching and staircase-thrust function are used to provide convergence of the continuation technique. Numerical experiments show good convergence and computational productivity of the presented technique. Presented numerical examples demonstrate importance of consideration the stepped thrust profile at early phases of mission design.

Keywords: solar electric propulsion system, heliocentric trajectory, Pontryagin maximum principle, continuation technique

Smorshko I. A.

There is a need in the 21st century to implement elaborate methods combining the use of knowledge fr om various areas of science and technology.

The article presents the solution technique for design-ballistic analysis problem of technical implementation conditions of “lunar” runway for a takeoff and landing spacecraft. The example of its implementation while special research conducting is given.

As a result of work the equation is obtained:

Equation (1) is basic for this technique development. The developed technique consists of two main parts, namely, ballistic and design.

Ballistic calculations allow obtain the relative finite mass of a spacecraft and the relative mass of the consumed fuel by the known values of characteristic speed while realization of this or that branching operation.

The problem of characteristic speeds determination is the most complex and depends on concrete mission statement, sel ected flight scheme, landing technique, maneuvers and other dynamic operations.

Depending on an input data set and task purposes, equation (1) allows obtain calculated values of such parameters as  and different variations of these parameters’ dependences from each other and fr om the values of .

To assess the conditions of a spacecraft technical implementation and the maximal frequency rate of the carried-out operations without refueling and other specified conditions, it is necessary to consider the denominator of the equation (1), on account of a condition:

Varying  parameters gives the possibility to define the necessary value of the  coefficient and the denominator’s solutions region existence in the form of  dependence for the concrete number of operations n.

The computational algorithm scheme is shown on the Figure.

Figure. The computational algorithm scheme based on a the design-ballistic analysis technique of technical any takeoff and landing spacecraft implementation conditions (general view)

The first option is not limited to a set of the obtained dependences specified in flowcharts, any variations of quantity (the solution of the equation, sufficient for an opportunity) and the structure of initial parameters are possible and, respectively, at the exit various results can be received (see Figure).

The second option represents formation of  coefficients possible values area. Depending on the input data the following dependences can be obtained:  and  depending on the number of operations n. These values can also be set initially, and vary the solution of a problem as well. Moreover, the situation in which  , and  are known is possible, and then this computation option reduces to finding the limiting value of a number of operations n (Fig.).

Earlier published materials contain results of the carried-out design-ballistic analysis on the opportunities of the “lunar” runway creation for a takeoff and landing spacecraft obtained during conducted studies based on the developed technique.

The developed design-ballistic analysis technique of conditions of technical implementation “lunar” runway for a takeoff and landing spacecraft is a flexible, efficient and convenient “tool” for conducting studies, that can be applied by specialists of the branch while spacecraft projection and educating students of an appropriate profile at higher education institutions.

Keywords: design-ballistic analysis, technique of the analysis, reusable spacecrafts

Markin N. N.

The workload of the pilot while takeoff is extremely high. Thus, an aircraft decision speed V1 is defined for particular take-off conditions. After reaching the decision speed, V1, the aircraft keeps on accelerating until the rotation speed, VR, is reached. At this moment, the aircraft nose is lifted.

The angular movement of an aircraft on take-off is considered atypical, if a pilot cannot lift the nose wheel and perform the take-off at the estimated speed. Thus, the situation when negative pitching moment is greater than its expected value may create prerequisites for flight accidents. The equal situation may occur when wing’s icing reduces the lift, and the error in determining the aircraft alignment increases the diving moment and other factors. A pilot can use stabilizer to increase the positive pitching moment.

The pilot can use stabilizer to increase the positive pitching moment. The angular movement dynamics in this case is considered after the aircraft takeoff to analyze the stalling at a large angle of attacks.

The state space system describes the aircraft angular motion and actuators of stabilizer and elevator. The linear quadratic regulators are used for the given two-input linear system. The simulation reveals possibility of stalling at large attack angle with negative pitching moment, if braking force is greater than its expected value.

Keywords: aircraft, takeoff, angular movement, control, elevator, stabilizer, stalling, analytic design of optimal regulator

Instrument making, metrology, information and measuring equipment and systems

Navigation instruments

Petrukhin V. A., Mel'nikov V. E.

The paper considers the possibilities of stability increasing of a physical of mathematical pendulum to perturbing horizontal accelerations by forming corrective actions on the pendulum from accelerometer and introducing relay control of the compensating signal level. The conducted studies and simulation results authenticate the realizability and high accuracy characteristics of a pendulum vertical reference of such kind. A number of technical applications in the form of control, orientation and navigation problems for aircraft of various classes and purposes can be realized on its basis.

Features and benefits of the proposed pendulum vertical reference (PVR) consist in a sufficiently high accuracy with no accumulated errorsin in time, inherent to the vertical channels in SINS, operating in an autonomous mode.

This article considers one of the VPR channels with a pendulum and correcting accelerometer to identify the specific and basic features of the VPR. The second channel is implemented in a similar way. In addition to previous studies, to extend the capabilities of the VPR, a relay control mode of the pendulum motion in the vicinity of the vertical is proposed to extend the capabilities of the VPR.

Keywords: pendulum vertical reference, pendulum, accelerometer, relay control

Vavilova N. B., Parusnikov N. A., Filatova G. A.

In the article the navigation problem for an autonomous underwater vehicle (AUV) is under consideration. In AUV’s navigation the following sensors are usually used: transponders that measure the distance from the AUV to transponders in known locations, velocity sensor, depth sensor, gyroscopic course sensor. A peculiarity of this work consists in the usage of Strapdown Inertial Navigation System (SINS) of medium accuracy together with mentioned above sensors. AUV’s navigation problem is posed as SINS correction problem with aiding measurements. Principal possibilities of this approach are investigated on the basis of the analysis of covariance with experimental data.

AUV are used in a wide range of scientific and applied research of ocean, such as a marine geological research, a study of the seafloor, ecological research of water environment. The value of the data provided by the underwater vehicle depends on the accuracy of a navigation system used. That is why the development of high-precision AUV’s navigation system is relevant today.

The presented paper differs from previous investigation in this domain by taking SINS of medium accuracy into consideration. Furthermore, data provided by SINS is regarded as the main data. Resulting navigation solution is based on SINS integration with aiding measurements delivered by special sonar beacon with known location (by means of GPS), sensors of velocity and depth. The estimation algorithm is based on technique of Kalman filtering. Mathematical models take into account specific peculiarities of AUV motion (low speed, relatively short distance between a vehicle and a beacon). The two typical types of the AUV’s motion were taken into account. The research method was based on analysis of covariance analysis with implementation of real data.

The experimental data was provided by scientific educational center «Underwater robotics», Far Eastern Federal University and IPMT RAS. Marine Autonomous Robotic System «MARK» has two main hardware parts — an autonomous underwater vehicle and an afloat vehicle. An equipment of a shore control center is also included. The afloat vehicle is a mobile beacon with a transponder. The location of the latter is determined by GPS. Vehicles have radio links with hydroacoustic communication system.

The presented article studies two representative mechanical trajectories of MARK’s motion. In the first case AUV moves rectilinearly with the constant depth, an afloat vehicle moves along a «zigzag» path with the side 200 m, intersecting the AUV’s trajectory. In the second case AUV moves along a square path clockwise with the side 100 m, an afloat vehicle moves along a square path counterclockwise with the side 200 m. In both cases the direction on the beacon was being changed and as a result the problem of position’s estimation became well-conditioned.

Derived results show that the standard deviations of the position’s estimation errors are less than 3 m. It was discovered that navigation solution is not possess the same accuracy. Estimations of the coordinates stabilize after some interval of time, which is depended on the trajectory. Therefore, a preparing method is proposed to achieve equal precision of the estimations on the whole interval of movement.

The results of the preliminary analysis that was done give evidence the proposed algorithm can improve the accuracy of aided AUV’s navigation system in several times.

Keywords: strapdown inertial navigation system, calibration, high-precision turntable

Optical and optical-electronic devices and complexes

Bogdanov I. V., Velichko A. N.

Solution of the tasks given in the work proposed developing of the background and target situation (BTS) forming method for special optronic systems of missile and space purpose in wide range (from UV to long-wave IR region) that are used in defense and research goals, practical implementation of the method to confirm the correctness of selected schematic circuit, as well.

BTS is formed in optronic devices field of view to solve integrated task enabled to conduct different tests types including: reliability testing of single or one of group objects autodetection during background lateral noise simulation of entrance pupil; estimate of characteristics accuracy (for example, constant and random errors of angular deviation measuring); checking of different algorithms of an object under observation selection (spectral, spatial, trajectory and other characteristics).

First part of the work analyses current methods and modes of BTS forming. It is examined both national and foreign experience, marked out main advantages and shortcomings of implemented methods, given their schematic circuits, as well.

Second part of the work considers realization of BTS forming methods for optronic device as benches on the base of Nudelman Precision Engineering Design Bureau laboratory. It is presented structural assemblies and elements, optical schematic circuits, software for the benches control and testing procedure.

The result of the done work is the ultimate method of BTS forming for optronic devices of space and missile purpose that is realized in special benches and enables to reduce optronic devices development expenses due to operability tryout in laboratory environment and to improve the devices quality before space launch.

Keywords: stand, background and target situation, optoelectronic, infrared, measurements

Instrument production techniques

Smirnov K. K., Sukhov A. G., Tsimbalov A. S.

The article focuses on the problems related to a special purpose chipping in metal-polymeric packages with ball leads of the BGA-type (Ball grid array). During microcircuits’ burn-in test and functional control within the specified temperature range a lot of cases of the ball leads separation occurred. This separation led to the need to discard the operable ICs at the final phase of testing. Furthermore, the separation was occurring during the transportation of products.

The author analyzed the reasons for strength decline of the leads on various production and testing stages. The method for minimization of the the leads’ strength reduction was worked out. Moreover, the sound arguments are presented in favor of moving the ball-leads formation from the ICs manufacturing to the printed board assembly.

The author made the following conclusions:

  1. The second burn-off process of the ball leads at any stage of the process improves the strength of their attachment. Besides, the greatest increase of that strength is noted during the second burn-off process after the first burn-in stage.

  2. Increase of the holding strength is also observed during the burn-off process before and after the burn-in, and the specified strength for various types of ICs differs significantly, its maximum increase is on the weakest ball leads.

  3. After burn-off of all types of ICs displayed the similar data on the shear force that indicates the elimination of the causes reducing the strength of ball leads.

  4. Physical form confirms the assumption on the existence of parasitic intermetallic layers.

  5. After an additional burn-off of the ball-leads:

a) Control of their geometry did not reveal deviations from the initial state;

b) Functional control did not reveal changes of electric parameters of IC.

The obtained results demonstrate the necessity to include the interim and maybe finishing burn-off operation in the process of the metal-polymeric packages with ball-leads of the BGA type to increase the strength of their attachment.

Keywords: metal-polymeric BGA-casing, strength of leads’ mounting, microcircuits testing, burn-in testing, thermocycling, functional control

Radio engineering and communication

Radio engineering, including TV systems and devices

Aldohina V. N., Demyanov A. V., Gudaev R. A., Byk V. S., Vikulova Y. M.

The aim of the work is to increase the probability of correct recognition of the type of object in the airspace based on the analysis of the radio technical characteristics of emissions, taking into account the informativeness of the recognition features to a level not lower than required by the regulatory documents.

To achieve this goal, we propose a method of recognition using the principle of multichannel with discrete accumulation and using weight coefficients calculated on the basis of the entropy approach. Based on the analysis of the data presented, an increase in the number of characters makes it possible to increase the probability of correct recognition, and the application of weighting coefficients gives, albeit a small, but guaranteed increase in the indicator under consideration.

The scientific novelty of the method of recognizing the types of radiating objects on the basis of a set of radio engineering features and weighting coefficients is that it differs from existing ones in that the determination of the type of the radiating object is made on the basis of comparing the additive convolution of particular solutions multiplied by the corresponding weight coefficients reflecting their informativeness with Threshold calculated for the current recognition situation.

The theoretical significance of the developed method for recognizing the types of radiating objects on the basis of a set of radio engineering features and weighting coefficients is that it is a development of the theory of pattern recognition and differs from existing ones in that the definition of the type of the observed object is made on the basis of a comparison of the additive convolution of particular solutions multiplied by the corresponding weighted ones Coefficients reflecting their informativeness, with a threshold calculated for the current recognition situation.

The practical significance of the method for recognizing the types of radiating objects on the basis of a set of radio technical features and weighting factors is to improve the methodological and algorithmic support of the space monitoring system aimed at providing the required probability of correct recognition.

The result of this method implementation will be a decision on the recognition of the type of radiating objects based on the analysis of radio technical information taking into account its informativeness. The considered method of recognition of types of radiating objects allows:

— to make the recognition of the types of radiating objects on the basis of radio technical information;

— expand the characteristic space used to describe types of recognized radiating objects;

— determine the informativeness of the features of the recognition of the types of radiating objects;

— minimize the error in recognizing the types of radiating objects;

— Reduce the computational cost of conducting recognition of the types of radiating objects.

Keywords: detection, signs of recognition, entropy

Boev S. F., Pimenov P. N., Pronin S. A., Shevyrev A. V.

The ultra-short pulsed electromagnetic radiation is relatively new kind of man-made electromagnetic radiation featuring by the pulse duration less than 10 ns. Such radiation forms an obstacle with a spectrum width up to several GHz. It is known that the ultra-short electromagnetic pulse is most dangerous because of its high penetration capability due to continuous filling of the spectrum.

Ultra-short electromagnetic pulse (EMP) can have a significant impact on the operation of the modern devices with information pulses durations is comparable with the pulse durations of the EMP. Ultra-short EMP has an impact on the majority of modern wireless broadband data transmission devices, due to interference of overlapping the EMP spectrum of operating frequencies. There are two channels of EMP influence on electronic devices:

— Pulse broadband interference

— Surge of electromagnetic energy

This gives us grounds to consider the potential impact of ultra-short EMP through the foster paths of the devices due to the bandwidth pulse spectrum as well as a direct effect of electromagnetic radiation on hardware (the conductive structure), due to the high concentrated energy of the pulse. Influence on the reception paths of the devices due to the fact that on working frequencies in the reception paths gets part of the generated by EMP broadband interference. The most interesting fact is ultra-short complex sequence pulses with a relatively low pulse repetition frequency package and a short interval between pulses in the package can be regarded as the least expensive energy, but the most dangerous EMP when exposed to radio-electronic devices. The further study of the EMP impact on the radio-electronic devices will identify their vulnerabilities and minimize the impact of EMP.

Keywords: ultrashort electromagnetic pulse, electromagnetic terrorism, pulse sequence, influence the efficiency

Surovtsev R. S., Zabolotsky A. M., Gazizov T. R.

The possibility of pulse signal transmission in a turn of meander line without distortions of its waveform by near-end crosstalk is shown. First of all, the paper presents a brief review of investigations devoted to meander delay lines and approaches to minimization of the signal distortions in these lines. Then the condition of the signal transmission without distortions is formulated and the optimization of cross section parameters and the length of meander line turn is performed in accordance with this condition and for line matching with measuring tract. According to the optimization, a printed circuit board with meander line turn prototypes is produced from the two-side fiberglass FR-4, and the experimental investigations based on combined oscilloscope С9-11 are executed. Finally, the experimental results are presented as an example of one turn with length of 151 mm providing delay of 1 ns. Signals with duration of 440 and 280 ps at half of the maximum amplitude value are accounted. It is shown that waveform of the pulse with duration of 440 ps is affected by near-end crosstalk, which is evident at the signal rise and fall as the positive and negative step with amplitude of 53 mV. If duration of a signal is decreased to 280 ps, the near-end crosstalk pulse with amplitude 52 mV arrives before the rise beginning and after the fall ending and has no impact on its waveform and makes up 10% of the signal amplitude. Thus, the possibility of pulse signal transmission without distortions by near-end crosstalk is experimentally proved.

Keywords: meander line turn, per-unit-lengths delay, even and odd modes

Systems, networks and telecommunication devices

Samartsev N. S., Kolotilov E. D., Koshelev B. V.

During last two decades the dramatic growth of air traffic intensity in civil aviation was continuously increasing the workload on the air traffic service (ATS) controllers and the flight crews of the aircraft. This problem was becoming critical and affected the flight safety, especially in terminal airspace.

According the CNS/ATM concept improving the efficiency and safety of the modern air traffic management (ATM) system can be achieved through the development and implementation of advanced information technologies and air traffic procedures.

One of the most promising technologies recommended by ICAO is the automation of the process of information exchange between aircraft and air traffic control (ATC) centers. For its implementation, modern and prospective flight management systems (FMS) should have a new functional capability such as to support communication via data-link “ground-to-air-to-ground”.

As a part of the work on creation of a prospective FMS, an algorithm which allows the generation and processing of data-link messages was developed. The structure of the algorithm was presented in the paper. The concrete algorithm for the flight plan data exchange via the data link “ground-to-air-to-ground” was made in the form of the FMS software module, which is a complete module that allows it to be easily integrated into the software architecture of other FMS.

For debugging purposes a simulator of the communication management unit data was developed.

The algorithm of a flight plan data exchange via data-link «ground-to-board-to-ground» was successfully tested in the modelling laboratory of MIEA. All work was performed under appropriate standards ARINC 429,ARINC 702A-3, and ARINC 619.

Keywords: data link, flight plan, data exchange, situation awareness, communication management unit, automation

Radiolocation and radio navigation

Ivanov V. F., Koshkarov A. S.

High reliability and adequacy of navigational sightings is the definitive requirement to the aircraft modern navigation complexes. This requirement is especially topical for spacecraft navigation systems in conditions of jamming impact. Experience of navigation equipment operation reveals the presence of a pronounced threshold effect occurring due to implementation of tracking systems for navigation signals processing, i. e. with noise intensity increase the increase of position measurement error is observed, and a certain noise threshold intensity leads to navigation task failure. To enhance the noise tolerance of navigation complexes methods of the user’s navigation equipment complexation with inertial sensors can be used. The proposed method of deep complexation compared to conventional methods allows reduce the probabilities of false captures by tracking meters and signal parameters tracking failure; compensate the object’s dynamics impact on tracking systems; and reduce the tracking rings’ astatism. The pointed above method was used to simulate the navigation complex operation on a software receiver. The ability of using incomplete set of navigation equipment structural elements while realization of deep complexation method is demonstrated. Simulation of navigation complex operation based on deep complexation method revealed the possibility of noise tolerance enhancement to certain types of noise by the stable operation of tracking systems. The proposed complexation method combined with software realization of navigation equipment should increase the efficiency and reliability of navigational sighting in conditions of complex interference situation.

Keywords: users’ navigation equipment, noise tolerance, complexation, inertial navigation systems

Informatics, computation engineering and management

System analysis, control and data processing

Kozirevskiy V. K., Veselov A. I.

The article suggests a method for computational complexity reducing of Viola-Jones face detecting teaching procedure. The reference detector teaching procedure is based on AdaBoost algorithm, representing an iterative procedure of algorithmic composition construction (strong classifier). Each element (weak classifier) of the composition analyzes only one feature of an image. In Viola-Jones method feature is the result of image convolution by some pre-defined filter. A set of possible filters is developed in advance and the best feature in terms of strong classifier’s classification errors decreasing is selected at each learning iteration of AdaBoost. The proposed method is a modification of AdaBoost algorithm where complexity reduction is achieved by adaptive selection of the features to be analyzed. The idea of the modified method is based on the observation that at each iteration of the learning procedure the reference algorithm selects weak classifiers, correcting errors of the previously selected weak classifiers. It means that the weak classifiers with similar performance are unlikely to be selected at the adjacent iterations. Thus the space of the tested weak classifiers can be reduced. The proposed method includes two modifications of the reference algorithm. The first modification consists in a feature pre-analysis operation which is performed to estimate the correlation between the responses of different filters. This stage is performed before the reference AdaBoost algorithm is started. In the process of teaching, only the features with low correlation can be analyzed at the adjacent iteration, thus reducing the number of weak classifiers to be evaluated for boosting the final strong classifier.

Practical relevance: the proposed algorithm reduces the computational complexity of Viola-Jones face detector teaching, which is an open issue in computer-vision-related systems.

Keywords: computer vision, face detection, Viola-Jones algorithm, boosting, AdaBoost, FFS, complexity reduction

CAD systems

Kyi M. H., Markin L. V.

The goal of the study is geometric modeling of solar batteries illumination process onboard a spacecraft or while their location on the surface (on Earth, or, for ex-ample, in lunar settlements). With a specified geometry of their location, the issues of their effective area are studied herewith with account for their mutual shading by each other, as well as by other foreign objects. Solution of these issues should form the basis of software and mathematical sup-port development for solar batteries and concentrators placement and orientation automation on both the ground surface and onboard a spacecraft. The goal of the study consists in effectiveness evaluation of solar batteries layout both among themselves and with other objects, such as a space station hull.

This article describes both physical and mathematical statement of the optimization problem on solar batteries placement either in space, or on Earth. It demonstrates that in mathematical statement this problem is considered as an optimization problem of mathematical programming aimed at maximally effective utilization of these high-tech energy sources for both space orbital stations and space settlements. The solution method of this problem is geometric modeling of space station and solar batteries with a certain orientation. The receptor geometric models, discretizing both batteries location area and a space station itself were used as a modeling method.

Using C# the software complex allowing solar concentrators’ effective area modeling was developed based on the developed receptor geometric model. The graphic shell was developed herewith, allowing display numerical values of the obtained results. When the software complex is operating after the station and batteries geometry loading in parametric form, geometric model is converted to matrix form, and layer by layer sections’ scanning starts. In each layer of the 3D matrix a 2D matrix is formed, presenting a kind of a 3D matrix slice through a specified distance. Current solar batteries slices’ areas and effective (accumulated) area of a space station’s hull sections are calculated in each section (slice) of receptor matrix. This accumulated area is the spacecraft solar batteries’ effective working area of a specified geometry and sun orientation with account for all kinds of solar batteries’ geometry.

The authors developed also a method allowing converting geometry models of the studied objects, developed with any geometry modeling system, such as Solid Works, into receptor models, used for computation operations. The developed mathematical support and software allow evaluating the solar batteries’ effective area at spacecraft specified design parameters and its solar energy flow direction orientation. Simulation procedure allowing optimize the spacecraft solar batteries’ design and geometry parameters among permissible constructive solutions based on the described above receptor model is outlined either.

The application area of the obtained results is the design automation of spacecraft and geo-electric power stations located on Earth, or in space colonies.

Keywords: spacecraft, solar cells, external layouts, solar cells shading, design automation, geometry modeling, receptor geometry models, rational design solution, simulation

Mathematica modeling, numerical technique and program complexes

Lisov A. A., Chernova T. A., Gorbunov M. S.

The presented work discussed the problems of modeling and mathematical methods for diagnosing the degradation wear of an electric motor in case of bearing unit destruction ‒ one of the most drasic failures. The investigations were carried out on the example of an induction motor with a «squirrel-cage» type rotor widely used in industry and for home appliances. For the degradation wear modeling, the mode of motor switch off from the network, the so-called «run-out» mode was sel ected. As a rule, the run-out mode is considered as the final one in the electric motor work cycle, and is not given due attention. It turned out that this mode presents a source of important information, which implementation makes possible to make judgement on the status of electric motor, its wear, operational safety and the residual resource.

This processes occurring in the electric motor is modeling as a second-order link has been carried out. The mechanical rotation of the rotor in the run-out mode is described by an ordinary homogeneous differential equation of the second order with constant coefficients. Parameters of the differential equation, i. e. its coefficients, reflect physical and mechanical properties of the electric motor: its geometry, material properties, etc.

The authors proposed to determine the state parameters of the electric motor differential equation fr om the known empirical function of its rotor rotational speed damping, registered in each cycle of its switching off. The paper presents the algorithm of mathematical approximation of the rotor damping rate empirical function by an analytic function with the required levels of accuracy and further determination of the corresponding differential equation parameters.

Moreover, the distortion of the rotor rotational speed damping function suggests mathematical methods for diagnosing the degradation wear of the electric motor elements, mainly wear of its bearing assembly. With the degradation of bearings, with embrittlement, dying of metal surfaces with small particles, the moment of resistance of their rotating parts increases substantially. In the run-out mode, the braking torque is increased in the bearings, the stopping time is shortened. Thus, if in the run-out mode the initial speed is less than the passport speed and the braking time is shortened ‒ the degradation processes begin in the bearings. The mechanical time constant TM of the rotor shaft braking function is the characteristic parameter of the degradation processes in bearings.

These features can be obtained with the simplest measuring instruments (voltmeter, stopwatch and tachometer) without planning and implementing special experiments, but directly during lectric motor operation.

Keywords: differential equation of natural damped vibrations of electric motor rotor, degradation changes modeling, mathematical methods for state diagnostics, service reliability

Gavva L. M.

The paper discusses the stress-strain state of flat rectangular laminated panel from composite materials, which casing is eccentrically supported by the longitudinal-transverse stiffening set. The panel is subjected to arbitrary distributed transverse load per unit area in the stationary temperature field. Boundary conditions on the contour are assumed of quite general type.

The following technological factors occurring during the composites manufacturing herein should be taken into consideration: residual thermal stresses arising during cooling after hardening, and pre-stressed tension in reinforcing fibers.

Schematization of the panel as structurally anisotropic, when thin-walled reinforcing elements are in the complex resistance, was proposed as a design model. Further development of the theory of thin-walled elastic rods, related to the contact problem for the skin and the rib, with the refinement of the above said model reflects the scientific novelty of the research.

The problem of determining strain-stress state of structurally anisotropic panels is reduced to the solution of the boundary value problem for equation of the eighth order in the partial derivatives in a rectangular field. The resolved eighth order equation and natural boundary conditions are obtained with Lagrange variation procedure. The solution in closed form is constructed by unitary trigonometric series for the particular case of conformable boundary conditions on two opposite sides, and by the method of uniform solutions for arbitrary non-conformable boundary conditions at the contour. We examine all possible variants of the boundary edges restrictions in relation to the connecting plane problem and the bending one.

Computer software package has been developed in MATLAB for multi-criterion optimization for the design of structurally anisotropic composite panels of FA. Since the solution obtained by exact analytical methods, the calculation time was minimized, that is of interest from the viewpoint of practical design using parametric analysis. The results of the stress analysis calculations offer the possibility for reducing and optimization of the aircraft elements’ weight characteristics.

Keywords: panels of composite materials, eccentric longitudinal and lateral set, thin-walled rib, asymmetric package structure, powered and temperature loading, Lagrange variation principle, strain-stress state, MATLAB

Rybin V. V., Tsvetaev V. E.

Today a variety of Computer Mathematics Systems (CMS) and expansion packs are applied for the spectral method of non-stationary control systems computer simulation. Modern technologies associated with fractal approach in different applied areas, and in radio engineering, radiodetection and theory of dynamic systems in particular, produce new element base, where mathematical models contain fractional integrating and derivative operators.

For example, control systems with PID control realize control laws, increasing processing speed and stability margin compared to the similar systems realizing classical control laws. Technical implementation of such derivatives and integrals can be realized with several methods: by Gruenwald’s approximate dependencies, or continued fractions, or Fourier transform and spectral transform.

Spectral method is already propagated to control systems for models containing fractional integrating and derivative components, and the expansion packs MLSY_SM, Spektr_SM+Simulink+Matlab, Spektr_SM+VisSim+Mathcad CMS have been modified for such systems’ simulation. This software commplex does not contain program packs in the Faber-Schauder function system.

The presented paper considers the development of the MLSY_SM SCM Mathcad expansion pack for non-stationary uninterrupted non-stationary control systems with integer number and fractional order spectral method in the Faber-Schauder functions system analysis.

Derivation of spectral algorithms with fractional integrating and derivative components of an arbitrary order and of some other spectral characteristics is based on using a symbolic processor of Computer Mathematics Systems Mathcad. Software implementation of the expansion pack MLSY_SM_SH+Mathcad contains software modulus developed using the derived symbolic algorithms. The structure of the pack and its program modules calls are described in Appendix. The expansion pack itself is used for analyzing and parametric synthesizing of the control system for homing missile. Mathematical model of the missile uses a target coordinator (mounted on a gyro-platform) for measuring the sight line rotational speed. Differential equation, describing the target coordinator, contains a fractional order derivative.

As a result of the performed work the expansion pack MLSY_SM_SH of Computer Mathematics Systems Mathcad applied for investigation on a stochastic model homing system which uses a fractional target seeker was developed. The dependence of the root mean missing value from differential operator fractional order of target coordinator and navigation constant of command generation block was studied. Optimal values of a fractional parameter and navigation constants were selected. A comparative analysis of homing missile system’s classical and fractional models was carried out.

Keywords: non-stationary control systems, spectral form of mathematical description, Faber-Schauder function system, Computer Mathematics Systems, fractional integrating and derivative elements

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