### REVIEWS

LARGE OPTICAL SPACE-BASED TELESCOPES
Dmitry V. Kirichenko, Kleymyonov Victor V., Novikova Elena V.

589

An overview of the current state and tendencies in development and construction of high-tech astronomical optical space surveillance systems abroad is provided. Creation of large optical telescopes is reported to be the main trend related to efforts to improve the quality of images by enhancing the basic characteristics of optical telescopes depending on the telescope aperture size. The trend leads to increasing requirements to material and quality of optical elements. Comparative characteristics of optical materials used in the manufacture of mirrors for space-based telescopes are presented. Operating orbital telescopes (HST, Spitzer, Hershel, Gaia) and large optical telescopes under construction (SPICA, JWST, ATLAST) with the composite and flexible mirrors controlled by active systems are considered.

### DEVICES AND SYSTEMS OF AUTOMATIC CONTROL

ENSURING DYNAMIC SYSTEM STABILITY UNDER CONSTRAINED PERTURBATIONS IMPACT
Vedyakov Alexei A., Tertychny-Dauri Vladimir Yu.

603

The problem of ensuring asymptotic stability of nonlinear dynamic system by means of tuning its parameters is considered for the case when the system is subject to constrained external perturbations. A solution to the problem is found with the use of a robust finitely convergent algorithm of parameters setting. An estimate of attraction domain proportional to the perturbation level is derived.

STABILITY OF DESIRED STATIONARY REGIME OF CLOSED-LOOP SYSTEMS WITH PERIODICALLY CHANGING STRUCTURE
Anatoly I. Korshunov

612

Closed-loop automatic system with structure subject to high-frequency changes is considered. Systems of this class are widely applied in power electronics. Calculation of the system parameters is proposed to be performed by a limiting continuous model which does not account for current and voltage pulsations in actual system. The discrete nature of the control may cause in the real system negative effects such as oscillations distorting the desired stationary mode with pulsation frequency of the output signal equal to the switching frequency of the system structure. The reason of the effects is usually a violation of the conditions of stability of the desired mode. Taking into account different variants of mathematical description of power part of the system within the periods of switching, a difference equation governing the system component is derived as well as a difference equation of the integral controller. For a given ratio of the parts of the switching period, the stationary vector of the phase coordinates of the system and the matrix of the linearized differential equations of perturbed motion are defined. Location of the matrix eigenvalues inside the circle of the unit radius guarantees asymptotic stability of the stationary regime. Using this matrix in the case of the stability of the desired stationary mode it is possible to construct quadratic Lyapunov functions to guarantee separation of at least part of stability domain. An example of practical application of the results to a voltage regulator with parametric control is presented. The study of stability of desired stationary regime of the regulator carried out with the use of mathematical modeling in MatLab, confirmed the urgency of the problem under consideration and correctness of the proposed solution.

SPACE VECTOR MODULATION IN MULTILEVEL INVERTERS OF THE SERVO DRIVES OF THE TRAJECTORY MEASUREMENTS TELESCOPES
Valentin S. Tomasov, Aleksander A. Usoltsev, Denis A. Vertegel , Strzelecki Ryszard

624

Using the MatLab/Simulink mathematical model of a three-phase three-level voltage inverter, the influence of the space-vector modulation (SVM) algorithm on the pulsations of the current (torque) of an AC motor in the range of low rotation speeds is considered. It is shown that the SVM of the second kind does not provide a pulsations level comparable to the pulsations of a sinusoidal pulse-width modulation (SPWM), both in the static mode of the drive operation and in transient modes. In such case, the current pulsations cannot be reduced by changing the modulation algorithm, which almost excludes the possibility of using such transducers in high-quality adjustable instrumental AC electric drives. At the same time, SVM of the first kind can be considered as an alternative to SPWM, as it allows to reduce the current pulsations in the largest part of the control range to a comparable level, and in the last quarter of the control range to values significantly lower than with the SPWM. The asymmetry of the inverter characteristics with the SVM is noted for different directions of the modulation vector rotation.

### COMPUTING TECHNIQUE

METHOD FOR PSEUDO-NOISE SIGNAL GENERATION BASED ON M-SEQUENCES WITH NON-MULTIPLE RECURRING PERIODS
Vladimir S. Bakholdin

635

A new method is proposed for generation of pseudo-noise signals. The method uses M-sequences with non-multiple recurring periods. Results of mathematical simulation of correlation and spectral characteristics of combined sequences are presented, comparison with Gold sequences is performed. The influence of the number of characters and the clock frequency of the original sequences on the characteristics of the combined sequences is studied. The histograms of distribution of side lobes levels for different combinations of number of characters and the clock frequency of the original sequences are presented.

ANALYSIS OF COMPLEX FILTERS WITH THE USE OF TRANSITION CHARACTERISTICS
Sergey I. Ziatdinov, Sokolova Yulia V.

641

A method for studying complex filter with the use of the transition characteristics is developed. Presentation of input signal as a sum of step functions shifted relative to each other leads to a new form of complex superposition integral allowing to determine the filter output signal for a given complex-valued input and a known complex transition characteristic. Application of complex filters is shown to enable variation of their frequency settings without a change in shape of the amplitude and phase-frequency characteristics. The concepts of complex delta function and complex transition characteristics are introduced; the concepts are employed in the study of dynamic properties of the filters and transmission of
various signals. In contrast to the known method of analysis of linear systems based on the pulse characteristic, the proposed method may be used to synthesize complex discrete filter with dynamic properties coinciding with those of a continuous filter-analog. The developed theoretical principles are confirmed by presented examples.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

QUALITY ASSESSMENT CRITERIA FOR IMAGE FUSION IN MULTISPECTRAL OPTICAL-ELECTRONIC SYSTEMS
Vasiliev Alexander S, Alexander N. Timofeev, Vasilieva Anna V., Sergey A. Ryaposov

647

The problems related to fusion of digital images in multispectral optical-electronic systems are considered. The presented analysis of the procedure of fusion image creation is used as a base for development of criteria of the resulting image quality evaluation with the account for spatial distortion and brightness change. To evaluate the quality of spatial transformation at image fusion, it is proposed to use such criteria as the dispersion of brightness levels difference for original image and image after spatial transformation, and the correlation coefficient for initial (without spatial distortion) and the transformed images. To assess the quality of brightness transformation in fusion image, the cross-entropy value is calculated to reduce the influence of the noise component of the image on the information quantity estimate. Another criterion is a characteristic of symmetry distribution of the fusion image Fourier spectrum – excess of Fourier spectrum – which allows to define the contrast of the image by the frequency components.

POTENTIAL ACCURACY OF SLANT RANGE MEASUREMENT WITH THE INERTIAL INPUT CIRCUIT OF RECEIVING SYSTEM
Le Vu Dinh, Lebedko Yevgeny Georgievich, Nguyen Huc Tung, Liu Lu

654

Potential accuracy of slant range measurement for ground objects at the complex structure of the underlying surface is estimated with the account for inertial receiver and the amplifier circuit noise. Effectiveness of the receiver-amplifier path bandwidth expansion is analyzed as a mean to avoid superposition of signals from a local object with returns from the underlying surface. An estimate of energy loss and an accuracy assessment are presented.

AFOCAL COMPENSATORS OF OPTICAL SYSTEMS ABERRATIONS
Lev Andreev, Vasilisa Ezhova

660

Schematics of new afocal compensators of optical system aberrations, including spherical and chromatic aberrations, astigmatism, and field curvature are presented. A method for calculating the compensators schematics in Seidel region is described.

### HEAT REGIMES AND RELIABILITY OF INSTRUMENTS AND SYSTEMS

UNCERTAINTY OF NON-STATIONARY HEAT FLUX RECOVERY BY PARAMETRIC IDENTIFICATION OF DIFFERENTIAL-DIFFERENCE MODEL OF HEAT TRANSMISSION
Pilipenko Nikolay V.

664

A method is proposed for assessment of uncertainty in recovering non-stationary heat flux by parametric identification of differential-difference models of heat transfer in the system of bodies. The requirements imposed upon the structure of non-stationary heat flux transducers, mathematical models of heat transfer in the body system, and the nature of heat flux change and the used recovery methods are formulated. A Kalman filter with required parameters is employed to minimize the discrepancy between measured values and the model parameters. Mathematical expressions derived for the sensitivity functions describes the effects of all relevant factors of non-stationary thermometry including type and parameters of heat transfer in the heat flux transducers (HFT), number and location of temperature measuring points or drops, the quality of recording channels of measured quantities, specific of input actions. Obtained dependences determining the Gram matrix (the Fisher information matrix) for system of vectors of sensitivity functions allow to calculate the confidential region for measurement of the desired parameters. The proposed method of uncertainty estimation for heat flux recovery makes it possible to determine the boundaries of the method applicability with the account for permissible uncertainty, to formulate requirements for the used HFT, select the type and structure of HFT that meets the requirements, create HFT with desired characteristics. An example of confidence region determination for non-stationary flux measurement using battery HFT is presented.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

PRODUCTION TESTING OF REFRACTOMETRIC DEVICE FOR CONTROL OVER LIQUID-PHASE MEDIA
Prokopenko Victor T., Majorov Evgeniy E., Tsygankova Galina A., Fedorov Alexander L., Zharkova Tatiana V., Dagaev Alexander V.

672

Results of field tests of a refractometric instrument designed to measure characteristics of liquidphase media, in particular food products, are presented. The developed device meets the requirements of production control and surpasses foreign analogues in technical and operational characteristics. The structural-functional diagram of the instrument is described, and its technical and operational parameters are discussed. The results of liquid-phase solid residual concentration measurements of by the Brix scale of the refractometer are compared with standard laboratory test; convergence of the results is found to be not worse than ±0,3 %.

STUDY OF ACOUSTO-ELASTIC PROPERTIES OF THIN WIRES
Muraviev Vitaly V., Platunov Andrey V.

679

Results of studies on measurement of speed and amplitude of rod waves in thin wires, using developed instrument and a setup, are presented. Measured values of velocities, elastic moduli, and acousto-elastic coefficients in speed and amplitude are obtained for ferromagnetic wires with a diameter of 0.3—0.5 mm of steel 65G, U9A and alloy 52K12F. The studies were conducted in the uniaxial stressstrain state of the wire at loads from 0 to 1100 MPa; samples of wires were subjected to annealing at a temperature of from 200 to 1200 °C. The results can be used in quality control of thermal and mechanical processing of steel wires.