### CONTROL OF DYNAMIC SYSTEMS

ALGORITHM FOR INCREASING THE SPEED
OF SINUSOIDAL SIGNAL FREQUENCY IDENTIFICATION
Evgenia S. Sevasteeva, Valery A. Chernov, Bobtsov Alexey Alexeevich

767

A new solution to the problem of frequency identification of sinusoidal signal available for mea-surement is proposed. The problem is solved using identification algorithms that ensure the convergence of the adjustable parameter to the true value in a finite time (but not asymptotically).

ADAPTIVE TRACKING OF MULTIHARMONIC SIGNAL IN LINEAR SYSTEM WITH STATE DELAY
Gerasimov Dmitriy N, Milyushin Alexander S., Paramonov Alexey V., Nikiforov Vladimir O

772

The problem of output adaptive tracking of multiharmonic signal in linear time-invariant plant with state delay is considered. The plant state vector is supposed to be unavailable for direct measurement, and reference signal parameters (amplitudes, phases and frequencies of harmonics) are a priori unknown. The solution to the problem is based on internal model principle and adaptation algorithm with augmented error. It is shown that despite the delay, standard scheme of error augmentation preserves the stability properties of the closed-loop system. Results of simulation in the MATLAB / Simulink environment are presented.

ROBUST OUTPUT CONTROL FOR NONLINEAR MULTI-CHANNEL SYSTEMS
Dmitry E. Konovalov, Sergey A. Vrazhevsky, Furtat Igor Borisivich, Kremlev Artem Sergeevich

782

The problem of robust output control for multiple-input multiple-output linear system under unknown mismatched bounded disturbances and parametric uncertainties is considered. The proposed control algorithm is based on a combination of two techniques: the backstepping method and the auxiliary loop method. An iterative procedure is described for synthesis of a decentralized control system with a specialized dynamical subsystem (auxiliary loop) included on each step to provide estimation and compensation of unknown inconsistent perturbations without the use of a strong feedback. Results of practical approbation of the developed algorithm using a real laboratory platform “Twin Rotor MIMO System” are presented.

FORMATION OF CRITERION MATRICES OF MULTI-DIMENSIONAL DYNAMICAL SYSTEMS
USING THE FADDEEV — LEVERRIER ALGORITHM
Vunder Nina A., Dudarenko Natalya Alexandrovna, Melnikov Vitaly G

791

The problem of criterion matrices formation for the multidimensional dynamic systems is considered. The criterion matrices can be used for the properties analysis of a multidimensional system in a stationary state. The procedure of criterion matrices formation is considered in relation to the problem of estimating the tendency of multidimensional dynamic systems to degeneration, which is a measure of the robustness of a multidimensional system. The case of multidimensional continuous-time dynamic systems is considered as an example for criterion matrices construction. The problem is solved using the Faddeev — LeVerrier algorithm, which is supplemented by the Cayley — Hamilton theorem. The obtained real-valued construction for the formation of criterion matrices of the input-output relationship of multidimensional dynamical systems is focused on the problem of a priori express control of the degeneracy of dynamical systems of the multidimensional input — multidimensional output type in static.

### INFORMATION PROCESSING IN ROBOTIC SYSTEMS

AUTOMATED METHOD OF IN-TUBE ULTRASONIC CONTROL
USING PHASED ANTENNA ARRAY
Bazylev Dmitry N, Vitaliy A. Romanovich, Vedyakov Alexei A

805

An analysis of modern methods of pipeline diagnosing based on phased antenna arrays (PAA) using electromagnetic-acoustic converter (EMAC) is presented. A new algorithm of operation for phased arrays using EMAC is proposed. The algorithm can account for the reflections from the bottom surface of the metal and has improved accuracy characteristics as compared to the previously proposed diagnostic method with PAA. Experimental studies using an EMAС-PAA model and a test sample with various types of defects were carried out to test the performance and effectiveness of the developed scanning algorithm. The results show that the new scanning algorithm can significantly reduce the effect of crosstalk and increase the signal-to-noise ratio in the distributions of echo signal amplitudes.

### APPLIED PROBLEMS OF CONTROL

ADAPTIVE ADJUSTMENT OF DISTRIBUTED REGULATORS
Bystrov Sergey V., Grigoriev Valeriy V., Mansurova Olga K., Ivan M. Pershin, Pershin Maksim I.

814

A procedure of synthesis of a control system of the temperature field in a coaxial heating chamber is described and a method of adaptive adjustment of the distributed controller designed with the use of non-standard approximating links is presented. The method employs the principle of modular construction of the heating chamber. The adaptive tuning is implemented as the software product and can be used in design of distributed control systems for complex distributed processes of various physical nature.

ROBUST AUTONOMOUS CONTROL OF A MULTIPLY CONNECTED LINEAR OBJECT
WITH ENTRY DELAYS
Gogol Ivan V., Olga A. Remizova, Vladislav V. Syrokvashin, Alexander L. Fokin

825

A new technique is proposed for compensation for cross-links of a multiply connected control object with delays in direct and cross links. Application of the technique allows one to obtain a physically realizable compensator structure for any correlation between the values of delays in direct and reciprocal relationships and for any transfer functions of inertial elements, and also ensures the robustness of the system to the parametric uncertainty of the object and the values of delay.

### TECHNICAL MEANS OF CONTROL AND INFORMATICS

SYNTHESIS OF NONLINEAR PULSE SYSTEMS WITH POLYNOMIAL APPROXIMATION
Shishlakov Vladislav F., Elizaveta Yu. Vataeva, Natalia V. Reshetnikova, Dmitry V. Shishlakov

834

Solution to the problem of synthesis of the parameters of the control laws for pulsed automatic control systems with polynomial approximation of nonlinearities is considered. As a mathematical apparatus, the inversion of the direct variational method of analysis — the generalized Galerkin method — is applied. This makes it possible to completely algebraize the solution of the problem for the studied class of automated control system, the dynamics of which are described by nonlinear differential equations of arbitrary order.

SYNTHESIS OF THE CONTROL LAW
OF A HIGH-POWER BRIDGE VOLTAGE CONVERTER
Alexandrova Sophia A., Andrey P. Baev, Nikolaev Nikolay A., Slita Olga V.

843

A modified method of phase control is developed for a high-power dc bridge voltage converter is developed. The proposed method is based on variation of power transistors switching frequency. Предложенная методика основана на изменении частоты коммутации силовых ключей. In order to improve dynamic indices characteristics of the designed system and reliability and durability of the converter it is proposed to restrict maximal current switched by transistors and to use an algorithm of PI-control law with adjustable parameters which values depend on supply voltage.

BIOLOGICAL MODEL FOR FINDING SOLUTIONS TO AN INVENTIVE PROBLEM
Bushuev Alexander B., Vladimir Yu. Bazhin, Litvinov Yury V. , Petrov Vadim A., Mansurova Olga K.

851

The process of solving an inventive problem by the known specialized algorithm involves transition from a prototype to technical contradiction between two alternative properties. Therefore, the process is considered as a homeostatic binary division of a biological cell. The mathematical model is the Lorentz attractor, for which it is shown that the energy graphs of both mother-daughter homeostats coincide. An example of solving the inventive problem in the Benard experiment, in which the contradictions between the temperature and the velocity of the particle flow are found, is given. The resolution of the contradiction leads to a violation of symmetry and the appearance of closed convection loops. To estimate the attractor asymmetry, a new numerical method for calculating the structure of a system of nonlinear differential equations is proposed. Based on a system of equations in the basis of physical coordinates, an information-energy scheme of the attractor is constructed, for which the concepts of matrices of input and output signals, as well as transfer matrices of blocks are introduced. The scheme does not depend on the initial and boundary conditions, as well as the numerical values of the attractor coefficients, but only on the physical dimensions of the inputs and outputs of the blocks. The graphical representation of the structure with transfer matrices allows to find the vertical axis of the attractor symmetry and to determine the degree of asymmetry in the relations of resource consumption of the left and the right parts.