### DEVICES AND SYSTEMS OF AUTOMATIC CONTROL

CALCULATION OF DIGITAL TRACKING SYSTEMS OF COMBINED CONTROL
USING A LIMITING CONTINUOUS MODEL.
PART I. CONSTRUCTION OF A LIMITING CONTINUOUS MODEL
Ermolenko Artem I., Anatoly I. Korshunov

411

In the general case of continuous part of an arbitrary order, a limiting continuous model of digital tracking system (DSS) of combined control is constructed, so that the DSS properties approach indefinitely to the properties of the model with increasing frequency of the mismatch measurements. A discrete filter is considered which generates an additive to the master control, compensating for the speed error and the error in the DSS acceleration by variation of parameters of the continuous part of the system. An analytical expression for the filter coefficients is derived.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

METHOD OF CALCULATING TASK TREATMENT DURATION IN QUEUEING SYSTEM
WITH CONSIDERATION OF SPLIT-JOIN PROCESSES
Yury I. Ryzhikov, Vladimir A. Lokhvitsky, Roman S. Khabarov

419

A method is proposed for calculating the processing time of initial task in multi-channel queueing system with consideration of the task separation into independent subtasks that are treated parallelly with further assembling of the results. The process duration is represented as the distribution of the maximum from the random durations of the subtasks processing. The starting moments of the desired distribution are found by numerical integration along the semi-axis with the Chebyshev-Laguerre weight. Results of numerical calculations are compared with data obtained by simulations.

SYNTHESIS OF DISCRETE FILTERS
BY METHODS OF INVARIANT DIFFERENTIAL AND INTEGRAL EQUATIONS
Sergey I. Ziatdinov

424

Design of discrete filters on the base of invariant differential and integral equations of analogous continuous filters is considered. Method of invariant differential equations uses substitution of the differential equations by final differences. When synthesis based on invariant integral equations method is realized, integral equations are substituted by sums. The proposed methods make it possible to synthesize a variety of discrete low-pass and high-pass filters, bandpass and notch filters. With the correct choice of the discreteness period, the frequency properties of the synthesized discrete filters agree well enough with the frequency properties of the continuous analog filters. The choice of the method of synthesis of discrete filters by their continuous analogs is determined by the parameter specified by the continuous filter, e.g. frequency transfer function, pulse or transient response, differential or integral equation.

### INSTRUMENT-MAKING TECHNOLOGY

METHOD OF ESTIMATING THE VISUAL COMPLEXITY OF DYNAMIC IMAGES
Prokopenko Victor T., Matveev Nikolay V, Sapunova Natalia P. , Radik M. Akhmadullin, Firuza S. Usmanova

433

Results of the study of images with fractal nature as a type of visual stimulations in light therapy are presented. A comparative analysis of dynamic images of the urban landscape obtained using an optoelectronic system, objects of natural environment, and laser abstract dynamic images is performed with subsequent allocation of contours using a modified boundary detector. Calculation of the ratio of the fractal dimension D performed for images of different categories, shows that for laser-abstract dynamic images D = 1,33 ± 0,02; this allows one to use them in the form of a visual series as the basis of visual therap.

### INSTRUMENT-MAKING TECHNOLOGY

ACCURACY CHARACTERISTICS OF FRICTION MACHINES OF RECIPROCAL ACTION
Pechenko Roman V., Nuzhdin Kirill A., Abramchuk Mikhail V., Musalimov Victor M

442

Friction machines under consideration has a distinctive feature of implementation of forced movement of studied samples relative to each other due to force action transfer by friction. Analysis of evolution of structural components of the machines allowed to increase the accuracy characteristics of designed and developed friction machines by virtue of application of high-technology drives, precision guides, displacement sensors, as well as optimization of tribopair position. An original approach to comparing the errors of the machines of two design variants is proposed. The approach is based on the use of cyclic input-output diagrams for estimating the areas formed by the machines. Results of comparative analysis of qualitative characteristics and relative errors of the devices are presented.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

STUDY OF ELECTROPHYSICAL PROPERTIES OF SUNFLOWER OIL MISCELLAS
OF VARIOUS COMPOSITION
Volkov Sergey M., Kowalskiy Ilya S., Lukyanov Gennadiy N, Fedorov Alexander V.

449

One of the stages of vegetable oil production — distillation, which is the most energy-intensive process, is considered. The system of operational sensor-based control of concentration of miscella, together with other parameters allows for principle of feedback more effectively regulate the process flow of miscella and heat transfer in all forms of distillation. A new method for determining the concentration of n-hexane in sunflower oil and high-oleic sunflower oil is proposed. The method is based on the study of the electrophysical properties of sunflower oil.

CODE SCALE BASED ON CYCLICALLY REARRANGED DE BRUIJN
Ozhiganov Aleхander A.

458

A code scale of the bit width n=4,6,10,12 with the only information track made in accordance with the symbols of regrouped de Bruijn sequence with the period l=2n, is proposed. The rearrangement is performed by cyclic sampling of de Bruijn sequence symbols with step m, where m=(2n-1)/(n+1). Reading elements in the number of n are placed along the code track of the scale also in increments of m. With equal resolution of such a single-track scale and n-bit code scale, the proposed code scale is easier to manufacture and has smaller dimensions.

### SCIENTIFIC AND TECHNOLOGICAL EXPERIMENTS ON AUTOMATIC SPACE APPARATUS AND SMALL SATELLITES Based on the materials from the IV International Conference, September 2018, Samara

CONVOLUTION ALGORITHM AS THE METHOD FOR RECONSTRUCTION
OF TWO-DIMENSIONAL ELECTRON DENSITY DISTRIBUTION
IN THE SATELLITE CONSTELLATION ORBITAL PLANE
Filonin Oleg V., Nikolaev Peter N.

462

The problem of reconstructing the two-dimensional distribution of electron concentration of the ionosphere in the plane of the orbit of a cluster of satellites is considered. Solution to the problem is be-lieved to allow for an operative monitoring of the ionosphere state. To solve the problem, a method of tomographic reconstruction of two-dimensional electron density distribution based on the convolution algorithm is proposed. The method includes three stages: formation of an initial approximation to the electron concentration; redefining the missing projection data in the radon image of a priori information about its form; application of the known convolution algorithm. Accuracy of the proposed method is analyzed using results of statistical modeling. The quality of recovery of small local disturbances is estimated.

MULTI-SATELLITE CLUSTER
TO DEFINE PARAMETERS OF THE GRAVITATIONAL FIELD OF THE EARTH
Vyacheslav F. Fateev, Davlatov Ruslan A.

470

Possible application of a cluster of small-sized spacecraft to detect parameters of the Earth’s gravitational field is considered. The analyzed approach is based on the use of onboard receivers of Global Satellite Navigation Signals.

ESTIMATION OF THE MEASUREMENT ERROR OF TERRAIN RELIEF
WITH BISTATIC SPACE-BASED RADAR SYSTEM
Oleg V. Goryachkin, Ivan V. Maslov

477

Results of theoretical study of the influence of the ionosphere on the accuracy of the terrain ele-vation measurements using a bistatic interferometer are presented. The interferometer under consideration is based on space radar with synthesis of the P-band aperture and ground receiving point. The necessary statistical characteristics of random signal fluctuations are determined. A method for calculating the error in the height estimates depending on the interferometer geometry, the effect of ionosphere parameters, additive noise, and spatial decorrelation of radar images is described. According to the presented numerical dependences, it is possible to estimate the optimal range of values of the interferometric base and the error in determining the height for both point and extended targets. In the case of reflection from extended targets, the error due to the spatial decorrelation of the reflected signals in a single resolution element is considered additionally.

SPACE BISTATIC RADAR TO MONITOR THE OCEAN SURFACE PROFILE
BASED ON GNSS SIGNALS
Vyacheslav F. Fateev, Lopatin Vladislav P.

484

A passive space bistatic GNSS-radar to be mounted on board of small spacecraft, is presented. The radar is designed for measurement of the ocean profile using GNSS signals. The system may be applied to monitor the ocean level and water surface roughness. Results of simulation and experimental studies are presented.

MINIATURE MULTI-WIRE DETECTOR FOR NANOSATELLITES
Filonin Oleg V., Nasonov Konstantin S.

492

Information about ionizing radiation as a factor of outer space is analyzed. A 3D track detector of radiation developed and designed for nanosatellites is presented, the layout and principle of design are discussed. The detection ability and information capacity of the instrument are assessed.