### SYSTEM ANALYSIS, CONTROL, AND INFORMATION PROCESSING

ADAPTIVE OBSERVER OF STATE VARIABLES
OF A NONLINEAR NONSTATIONARY SYSTEM
WITH UNKNOWN CONSTANT PARAMETERS
Kozachek Olga A., Bobtsov Alexey A., Nikolaev Nikolay A.

627

For a nonlinear nonstationary system an adaptive state vector observer using output variable measurement is developed the control matrix (vector) and the nonlinear component of the equation of state of the system contain unknown constant parameters. When synthesizing the observer, a preliminary parametrization of the original nonlinear system is carried out. Then the derived system is reduced to a linear regression model. At the next stage, unknown constant regression parameters are estimated using the least squares method with a forgetting factor. The result of the previous work by the authors, which considered a linear non-stationary system containing unknown parameters in the control matrix (vector), is extended to the case when the equation of state of the system contains a partially unknown nonlinearity. The performance of the proposed algorithm is illustrated by mathematical modeling.

CONSTRUCTION OF AN ADJUSTABLE AUTONOMOUS STRAPDOWN INERTIAL VERTICAL GYRO
Ilya L. Surov, Ksenia S. Alekseeva, Anastasia А. Sizova , Tatyana Yu. Lemeshonok

637

A variant of constructing a strapdown inertial vertical gyro with the use of correction for the indicated speed and barometric altitude is studied. Integration is performed on the basis of an extended Kalman filter for an aircraft of the airplane scheme. The pitch and roll angles are used as parameters of the local vertical direction. Mathematical modeling is carried out.

### INFORMATION TECHNOLOGIES AND SYSTEMS, COMPUTER TECHNIQUE

DETERMINING THE CLUSTER SIZE
AND THE NUMBER OF REPLICAS OF HIGHLY LOADED
INFORMATION SYSTEMS
Tatarnikova Tatiana M., Evgeny D. Arkhiptsev, Karmanovskiy Nikolay S.

646

The problem of ensuring the quality of customer service for highly loaded information systems is discussed. Existing solutions for scaling highly loaded information systems are considered. A procedure for determining the required number of nodes in a computing cluster based on the queuing theory is proposed. Results of a computational experiment on choosing the size of a computational cluster to ensure the average time for a user request executing to be below the established allowable time, are presented. A model for determining the number of replicas is proposed, in which, at a given intensity of incoming update requests, it is possible to avoid the critical level of the write-write conflict.

### COMPUTER SIMULATION AND DESIGN AUTOMATION

MODELING SHOCK-FRICTION INTERACTION
OF THE FOOT WITH THE SUPPORTING SURFACE USING THE BASIS
OF GENERALIZED HERMITE FUNCTIONS
Musalimov Viktor M., Erofeev Mikhail A., Yury S. Monakhov, Mikhail S. Malov

652

A number of basic mechanisms of formation of the reaction of the supporting surface during human walking are studied. As a methodology, biomechanical analysis of movements is used with the account for the phases of foot movements. A fundamentally new approach to the construction of foot friction models using the Hermite functions is proposed, which enables accounting for the shock impulses of the friction forces and normal pressure for estimating the sliding and spinning friction coefficients of the “foot–support surface” system. The work practical significance is determined by the value of developing experimental and analytical approaches to the problems of modernizing lower limb orthopedic products (prostheses, orthoses, orthopedic shoes and insoles) and their functional elements.

### NAVIGATIONAL INSTRUMENTS

GRAPHICAL-ANALYTICAL METHOD FOR OPTIMAL SYNTHESIS
OF PENDULUM CORRECTION CONTOUR
OF VERTICAL GYROS
Kirill O. Lukin, Sergey V. Krivosheev

660

A graphical-analytical method of optimal synthesis of pendulum (positional) correction contour for gyroscopic verticals on a movable base is presented, the model of the gyro is reduced to a complementary filter. The variance of the complementary filter error is used as an optimality criterion. Characteristics of the gyroscope drift in the form of white noise and zero instability are determined from the Allan variation, and the satellite errors are determined from the spectral power density of horizontal acceleration, determined with the account for assumed operating conditions. Determination of the optimal correction time constant and the maximum permissible gyroscope drift parameter at a given gyro accuracy, taking into account the moving object dynamics, is carried out using a specially formed graph with the axes "correction time constant — gyro drift parameter". The proposed method can be used for both analytical and power vertical gyros.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

DIGITAL OPTOELECTRONIC MEASURING DEVICE
FOR MONITORING LARGE-SIZED SHELLS OF REVOLUTION
Shilin Aleхandеr N., Alexeу A. Shilin, Ramez G. Atamaniuk

671

Shells of revolution, such as barrels, are the main basic parts of aerospace, petrochemical, and power equipment. The shells are made from sheet material on roller bending machines. The quality of products depends on the technological accuracy of manufacturing basic parts. The technological tolerance for the shell diameter is 1%, however, the existing control tools do not provide the required accuracy. An optoelectronic measuring device is developed to control the shell dimensions during its manufacture; the device contains a microcontroller and measuring transducers of the angular position of the workpiece edge relative to the optical axis, the part temperature and its distance from the device. A digital camera is used as a workpiece edge position transducer, and the temperature is measured using a pyrometer. In the process of the part manufacturing, the optical-electronic device measures the deviation of the diameter from the nominal size and temperature of the part, and then, with the help of a microcontroller, brings the measurement result to normal temperature conditions.

METHOD FOR OVERALL CALCULATION OF AN INTEGRAL-FIELD MIRROR MODULE
Maria K. Orekhova, Alexey V. Bakholdin

680

A method for overall calculation of an integral-field mirror module is developed. A schematic solution based on mirror elements is described, features are considered, and an approach to design is proposed. An example of calculating the optical system of the mirror module of the integral field of the KST-3 solar telescope-coronagraph is presented. To achieve the goal, methods for calculating optical systems, mathematical and computer modeling, as well as methods for optimizing optical systems are used. The practical significance of the result lies in achieving a high temporal resolution of solar telescopes while maintaining high spatial and spectral resolution. The considered approaches can be extended for use in the modernization of spectrometers and the expansion of the observatory instrumental park.

SPATIAL MICRO-SCANNING OF PLANE-PARALLEL
GLASS PLATE SURFACE BY THE INTERFERENCE METHOD
Majorov Evgeniy E., Yuriy M. Borodyansky, Viktor V. Kurlov, Irina S. Tayurskaya, Vera P. Pushkina, Ramiz B. Guliyev

688

Plane-parallel glass plates for spatial micro-scanning of the surface by the interference method are studied. The need to control the quality of optical surfaces for high-precision optical instruments and systems determines the relevance of the work. The appearance of the interferometer is presented, the optical scheme and technical characteristics of the device are given. As a result of experimental measurements, interferograms of the surfaces of optical plane-parallel plates are obtained with an error of no more than 0.05λ. The dependences of the reflection coefficient on the longitudinal and transverse displacements of the surface are obtained. Graphic dependences shows that all surfaces of the studied samples have uniform distributions in the range from K = 19–20.2 %.

### INSTRUMENTS AND METHODS FOR MONITORING AND DIAGNOSING MATERIALS, PRODUCTS, SUBSTANCES AND THE NATURAL ENVIRONMENT

METHOD FOR DETECTING A SMALL AMOUNT OF OIL CONTAMINANTS IN A LIQUID
USING LASER FLUORESCENCE TECHNOLOGY
Natig H. Javadov , Asadov Hamid Hicmed ogly, Aishen E. Azizova

696

A method for multi-cell laser-fluorescence detection of a small amount of oil pollutants in water, as well as for measuring the concentration of such pollutants in water samples is developed. A technique is proposed for adaptively setting the length of the laser beam path through liquids in samples under investigation, which makes it possible to determine both the average total contamination value for the samples and contamination in each sample. A mathematical justification is presented, an algorithm for implementing the method is compiled, and a variant of the cuvette constructing with the implementation of adaptive tuning of the length of the laser beam path through the liquid in the samples is shown.

EXPERIMENTAL STUDIES OF A THERMOELECTRIC DEVICE FOR COOLING DISCRETE
ELECTRIC RADIO ELEMENTS
Ibragimova M. Asiyat, Oleg V. Evdulov

704

A device is developed for cooling discrete electrical radio elements (DERE). The sources of cold in the device are standard thermoelectric modules (TEMs), which form two sections with the main and additional heat exchange systems. An experimental stand is described, and results of full-scale tests of the device are presented. Graphs of temperature changes over time at various points of the thermoelectric device (TED) structure - the DERE simulator for a set of values of the TEM supply current and the power of the DERE simulator are obtained experimentally. It is determined that the developed thermal power plant can use TEM of the DRIFT-1.5 type produced by Cryotherm (St. Petersburg). It is been found that when using this type of thermal modules, the temperature of the DERE can be reduced to 272 K at a power current close to the optimal (5 A), while the time to enter the mode is 90 s. The discrepancy between experimental and calculated data is estimated to be no more than 10 %.