# Optoelectronics, Instrumentation and Data Processing (v.53, #4)

Method of quadrotor flight control in the target tracking problem by K. Yu. Kotov; A. A. Nesterov; M. N. Filippov; A. P. Yan

*(309-315)*. A problem of control of trajectory motion of a quadrotor vehicle is considered. The choice of the form of required differential equations in the previously proposed method of tracking of a moving target is justified. The workability of the control system in the presence of measurement noise and external perturbations is confirmed by results of experiments with the AR.Drone quadrotor.

**Keywords:**AR.Drone quadrotor; target trajectory tracking; structural synthesis of automatic control systems; forced motion

Technology of solving multi-objective problems of control of systems with distributed parameters by E. Ya. Rapoport; Yu. E. Pleshivtseva

*(316-328)*. A constructive technology of multi-objective optimization of control of distributed parameter plants is proposed. The technology is based on a single-criterion version in the form of the minimax convolution of normalized performance criteria. The approach under development is based on the transition to an equivalent form of the variational problem with constraints, with the problem solution being a priori Pareto-effective. Further procedures of preliminary parameterization of control actions and subsequent reduction to a special problem of semi-infinite programming make it possible to find the sought extremals with the use of their Chebyshev properties and fundamental laws of the subject domain. An example of multi-objective optimization of operation modes of an engineering thermophysics object is presented, which is of independent interest.

**Keywords:**multi-objective optimization; systems with distributed parameters; optimal control; semiinfinite optimization; alternance method

Analytical synthesis of a functional observer of the state of a bilinear dynamic system by A. Z. Asanov; D. N. Dem’yanov

*(329-336)*. The problem of asymptotic estimation of a linear combination of the state variables of a bilinear dynamic system using a minimum-order observer is considered. An algorithm for calculating the matrix coefficients of a functional observer using the technology of canonization of matrices is proposed, and solvability conditions for synthesis problem are derived..

**Keywords:**bilinear system; functional observer; synthesis algorithm; canonization of matrices

Autonomization of control channels for multidimensional objects based on the formalism of linear-quadratic optimization by A. B. Filimonov; N. B. Filimonov

*(337-344)*. The problem of dynamic decoupling of control channels for multidimensional objects is aimed at autonomization of control of output variables of the object, which is ensured by means of including special correcting links into the control system. A new method of solving this problem is proposed, where decoupling is provided by a block of dynamic correction. The desired result of decoupling is represented by a standard model with separate control channels. The mathematical apparatus applied for calculating the correction block is based on the formalism of linear-quadratic optimization, where the optimized integral quadratic criteria serve as a measure of deviation of the transient characteristics of the corrected object from their desired (standard) values.

**Keywords:**controlled multidimensional object; dynamic decoupling of control channels; standard model of separate channels; formalism of linear-quadratic optimization

Architecture of a platform for hardware-in-the-loop simulation of flying vehicle control systems by S. A. Belokon’; Yu. N. Zolotukhin; M. N. Filippov

*(345-350)*. A hardware-software platform is presented, which is designed for the development and hardware-in-the-loop simulation of flying vehicle control systems. This platform ensures the construction of the mathematical model of the plant, development of algorithms and software for onboard radioelectronic equipment and ground control station, and visualization of the three-dimensional model of the vehicle and external environment of the cockpit in the simulator training mode.

**Keywords:**hardware-in-the-loop simulation; mathematical modeling; dynamically scaled free-flight models; navigation equipment; ground control station

Adaptive controller for a strength testbed for aircraft structures by A. I. Laperdin; V. D. Yurkevich

*(351-357)*. The problem of control system design for a strength testbed of aircraft structures is considered. A method for calculating the parameters of a proportional-integral controller (control algorithm) using the time-scale separation method for the testbed taking into account the dead time effect in the control loop is presented. An adaptive control algorithm structure is proposed which limits the amplitude of high-frequency oscillations in the control system with a change in the direction of motion of the rod of the hydraulic cylinders and provides the desired accuracy and quality of transients at all stages of structural loading history. The results of tests of the developed control system with the adaptive control algorithm on an experimental strength testbed for aircraft structures are given.

**Keywords:**structural loading; strength tests; aircraft structures; control system; PI controller; adaptive controller; time-scale separation method

Method of test signal design for estimating the aircraft aerodynamic parameters by S. A. Belokon’; Yu. N. Zolotukhin; M. N. Filippov

*(358-363)*. A method of test signal design is proposed for studying the aircraft aerodynamic characteristics with the use of the technology of dynamically scaled free-flight models. Simultaneous excitation of all input channels in a prescribed frequency band by a set of mutually orthogonal signals is applied to increase the efficiency. A modified method of calculating the set of mutually orthogonal sinusoidal signals with a small normalized peak factor is presented. Results of simulating the aircraft motion in the MATLAB/Simulink environment with the use of the developed method of test signal design are reported.

**Keywords:**aircraft; dynamically scaled free-flight models; aerodynamic characteristics; excitation; orthogonal signals

Synchronization algorithm for three-phase voltages of an inverter and a grid by O. V. Nos

*(364-370)*. This paper presents the results of designing a joint phase-locked loop for adjusting the phase shifts (speed) and Euclidean norm of three-phase voltages of an inverter to the same grid parameters. The design can be used, in particular, to match the potentials of two parallel-connected power sources for the fundamental harmonic at the moments of switching the stator windings of an induction AC motor from a converter to a centralized power-supply system and back. Technical implementation of the developed synchronization algorithm will significantly reduce the inductance of the current-balancing reactor and exclude emergency operation modes in the electric motor power circuit.

**Keywords:**inverter voltage synchronization; phase-locked loop; AC motor vector control

Automation of extrusion of porous cable products based on a digital controller by B. K. Chostkovskii; V. N. Mitroshin

*(371-378)*. This paper presents a new approach to designing an automated system for monitoring and controlling the process of applying porous insulation material on a conductive cable core, which is based on using structurally and parametrically optimized digital controllers of an arbitrary order instead of calculating typical PID controllers using known methods. The digital controller is clocked by signals from the clock length sensor of a measuring wheel, instead of a timer signal, and this provides the robust properties of the system with respect to the changing insulation speed. Digital controller parameters are tuned to provide the operating parameters of the manufactured cable using a simulation model of stochastic extrusion and are minimized by moving a regular simplex in the parameter space of the tuned controller.

**Keywords:**extrusion process; control; simulation model; digital controllers; optimization

Krill herd and piecewise-linear initialization algorithms for designing Takagi–Sugeno systems by I. A. Hodashinsky; I. V. Filimonenko; K. S. Sarin

*(379-387)*. A method for designing Takagi–Sugeno fuzzy systems is proposed which uses a piecewiselinear initialization algorithm for structure generation and a metaheuristic krill herd algorithm for parameter optimization. The obtained systems are tested against real data sets. The influence of some parameters of this algorithm on the approximation accuracy is analyzed. Estimates of the approximation accuracy and the number of fuzzy rules are compared with four known methods of design.

**Keywords:**initialization; fuzzy systems; metaheuristic algorithms; approximation

Mathematical modeling of fluxgate magnetic gradiometers by D. G. Milovzorov; V. Kh. Yasoveev

*(388-394)*. Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

**Keywords:**fluxgate gradiometer; two-component fluxgate transducers; mathematical model

Analysis of temperature influence on the informative parameters of single-coil eddy current sensors by S. Yu. Borovik; M. M. Kuteynikova; Yu. N. Sekisov; O. P. Skobelev

*(395-401)*. This paper describes the study of temperature in the flowing part of a turbine on the informative parameters (equivalent inductances of primary windings of matching transformers) of single-coil eddy-current sensors with a sensitive element in the form of a conductor section, which are used as part of automation systems for testing gas-turbine engines. In this case, the objects of temperature influences are both sensors and controlled turbine blades. The existing model of electromagnetic interaction of a sensitive element with the end part of a controlled blade is used to obtain quantitative estimates of temperature changes of equivalent inductances of sensitive elements and primary windings of matching transformers. This model is also used to determine the corresponding changes of the informative parameter of the sensor in the process of experimental studies of temperature influences on it (in the absence of blades in the sensitive region). This paper also presents transformations in the form of relationships of informative parameters with radial and axial displacements at normal (20 °C) and nominal (1000 °C) temperatures, and their difference is used to determine the families of dominant functions of temperature, which characterize possible temperature errors for any radial and axial displacements in the ranges of their variation.

**Keywords:**turbine; blades; radial and axial displacements; single-coil eddy-current sensor; sensitive element; temperature effects; family of transformation functions; family of dominant functions of temperature

Estimation of optimal parameters of the multiplicative algorithm of wavelet filtering of images by Yu. E. Voskoboinikov

*(402-407)*. In most widely used wavelet filtering algorithms, the decomposition coefficients are processed with the use of threshold functions, which makes it possible to account for the “energy” feature of each decomposition coefficient. To some extent, this disadvantage is removed in a class of multiplicative algorithms, which account for the energy of decomposition coefficients located in a given proximity from a processed decomposition coefficient. However, the effective error minimization in wavelet filtering of images requires that a parameter, the choice of the optimal value of which remains to be an unsolved problem, is introduced into these processing algorithms. Therefore, the problem solved in this paper is the estimation of the optimal value of this parameter, which minimizes the root-mean-square error of the filtering. The performed studies showed the effectiveness of the proposed estimation algorithm and the possibility of its use in practice.

**Keywords:**wavelet representation of images; multiplicative algorithms of wavelet filtering of images; filtering factors; the choice of the optimal parameter of filtering factors

Filtering of images of small-sized objects in systems with circular microscaning by A. K. Shakenov; D. E. Budeyev

*(408-413)*. This paper describes a model for detection of images obtained in circular microscanning. To detect objects on a low background with the use of an image detection system based on circular microscanning, an approach to image filtering is proposed. The calculation of the noise covariance matrix with respect to the data obtained by the numerical simulation method is used. The calculated matrix is used in filter construction. It is shown that the applied approach makes it possible to increase the signal/noise ratio in image processing with a low background component.

**Keywords:**image simulation; circular microscanning; small-sized objects

Using a stochastic basis in signal and image recovery problems by V. I. Batishchev; I. I. Volkov; A. G. Zolin

*(414-420)*. This paper touches upon the problems of constructing a basis for stochastic functions, which represent samples of random numbers with a given distribution law. The algorithm for constructing an approximation model with the use of this basis is described. The general algorithm for signal recovery using the stochastic basis by the least squares method with a given weight function is given. The approach to solving the problem of recovery of blurred images with a known point scattering function by constructing an inverse filter model is proposed.

**Keywords:**signal recovery; image reconstruction; point scattering function; criterion of adequacy; basis function; least squares method