### CONTROL OF DYNAMIC SYSTEMS

FINITE-TIME STABILITY OF SYSTEM OF SERIES-CONNECTED INTEGRATORS
Zimenko Konstantin A., Polyakov Andrey E., Efimov Denis V., Kremlev Artem Sergeevich

681

The problem of finite-time stability analysis of system of series-connected integrators is considered. An algorithm of the system stabilization is proposed. The algorithm makes use of implicit Lyapunov function technique as well as several properties of homogeneous systems. Evaluation of control parameters is based on solution to a system of linear matrix inequalities. Effectiveness of the proposed method is confirmed by presented results of computer modeling

ADAPTIVE CONTROL ALGORITHM FOR LINEAR OBJECT WITH ARBITRARY RELATIVE DEGREE
Gerasimov Dmitriy N, Lyzlova Mariya V., Milyushin Alexander S., Nikiforov Vladimir O

687

A solution to the problem of adaptive control over linear perturbed object with arbitrary relative degree is proposed. The control is designed on the basis of the method of standard characteristic polynomials and has only one adjustable parameter which is the averaged radius of roots distribution generated by the first order adaptation algorithm. The regulator possesses a simple structure, low dynamic order equal to one, and provides boundedness of all signals in the closed system and exponential decay of output error to zero equilibrium. Results of digital simulation demonstrate the proposed algorithm effectiveness.

DIRECT ADAPTIVE METHOD FOR MULTISINUSOIDAL DISTURBANCE COMPENSATION
Aranovskiy Stanislav V., Losenkov Andrei A

694

The problem of adaptive compensation of multisinusoidal disturbances with unknown parameters is solved for internally stable linear discrete-time plant. The proposed direct approach is based on representation of disturbance as a weighted sum of stable filters. The method does not require an

SYNTHESIS OF CONTROL LAW PARAMETERS FOR NONLINEAR AUTOMATIC CONTROL SYSTEMS AT VARIOUS TYPES OF CHARACTERISTIC APPROXIMATION
Shishlakov Vladislav F., Anisimova Elena V., Shishlakov Andrey V., Shishlakov Dmitry V.

701

A solution to the problem of synthesis of control law parameters for automatic control system is considered when characteristics of nonlinear elements are approximated by analytic and irrational functions. Inversion of direct variational analysis method (the generalized Galerkin method) is applied. Advantages of the viewed methods of nonlinearities approximation for ACS with smooth nonlinearities are demonstrated.

MODIFIED BACKSTEPPING ALGORITHM FOR CONTROL OVER NONLINEAR PLANTS WITH DELAY
Furtat Igor Borisivich, Tupichin Evgeny A.

707

A solution to the robust control problem of nonlinear plants with a state delay is proposed. The plants under control are considered to possess unknown parameters; the plants are subject to external disturbances, and only output signal are measurable. The conditions for such a nonlinear system to be reducible to the normal form are formulated. The modified backstepping algorithm is used for the control algorithm synthesis. It is shown that implementation of the algorithm calls for the use of only one filter by the control signal and simplified control laws, and therefore calculations and implementation of the control system may be simplified. The obtained system is shown to possess a universal structure independent of the plant model – linear, nonlinear, with or without delay.

### APPLIED PROBLEMS OF CONTROL

ROBUST SYSTEM OF DYNAMIC POSITIONING FOR ROBOTIZED MODEL OF SURFACE CRAFT
Vlasov Sergey M., Borisov Oleg I., Gromov Vladislav S., Pyrkin Anton Alexandrovich, Bobtsov Alexey Alexeevich

713

A robotic setup for surface craft movement modeling is presented. The setup is used for testing of algorithms of control over dynamic positioning and external disturbances effects compensation systems. Mathematical model of the robotic system is analyzed; the multi-channel model is decomposed to separate a static function and independent single input — single output dynamic channels. A robust system for dynamic positioning of the craft based on consequent compensation control law is developed. Results of experimental study are demonstrated.

MATHEMATICAL MODEL OF CONTROL SYSTEM FOR TEMPERATURE FIELD OF THE HEAT TREATMENT CHAMBER
Bystrov Sergey V., Grigoriev Valeriy V., Olga K. Mansurova, Ivan M. Pershin, Pershin Maksim I.

720

Application of the method of qualitative distribution of modes determining the process feature parameters in linear systems with distributed parameters is considered. A frequency technique is developed for synthesis of distributed regulators on the base of modified Nyquist criterion allowing for analysis of parameters of the layout areas of spatial mod-related indicators of quality processes.

CONTROL OVER TEMPERATURE FIELD OF THE HEAT TREATMENT CHAMBER ON THE BASE OF QUALITATIVE MODE DISTRIBUTION
Bystrov Sergey V., Grigoriev Valeriy V., Olga K. Mansurova, Ivan M. Pershin, Pershin Maksim I.

725

A method for development of regulators for control over systems with distributed parameters is presented using control system of temperature field of the heat treatment chamber as an example. The method is based on the use of qualitative distribution of modes and ensures desirable quality of transient processes in the closed system.

DYNAMIC MODELS OF THE CONTROLLED BIOCHEMICAL PROCESSES OF WASTEWATER TREATMENT
Grudyaeva Elizaveta K., Dushin Sergey E., Kuzmin Nikolay N.

732

Nonlinear dynamic models of nitrification and denitrification processes in the bioreactor with the corresponding zones and the controlled recirculation contour are presented. The models are based on ASM1 model proposed by Henze to describe the microbiological processes in active sludge that involve removal of nitrogen compounds from wastewater, change of alkalinity, concentration of soluble substratum and inert compounds, as well as bacteria populations. Graphs of transient processes obtained with computer modeling are demonstrated.

ALGORITHMS OF CONTROL OVER FOUR-WHEEL ROBOT MOVING OVER ROUGH TERRAIN
Yury V. Litvinov, Evstigneev Maksim I., Mazulina Veronika V., Мishchenko Galina M.

738

An algorithm of control over mobile robot is considered for the case of unknown obstacles on the route. Identification of an obstacle is carried out with the use of a technical vision system. A model based on four-wheel motorcar-type chassis is used as an example of mobile robot.

### INFORMATICS IN TECHNICAL SYSTEMS

STATE ESTIMATION OF THE MULTIPENDULUM SETUP UNDER COMMUNICATION CONSTRAINTS
Fradkov Alexander L., Andrievsky Boris R., Andrievsky Alexey B.

742

Application of the coding-decoding procedure based on a plant dynamics model for implementation of embedded observer with low-bitrate data transmission channel is demonstrated for computer-controlled mechanical system — a multipendulum setup. Experimental results show efficiency of the proposed method in the case of corrupted measurements and plant model uncertainty.

CAPACITY OF COMMUNICATION CHANNEL AS A GUARANTEE OF QUALITY OF DIGITAL REMOTE CONTROL OVER CONTINUOUS TECHNICAL PLANT
Nuyya Olga S, Peshcherov Ruslan O, Ushakov Anatoly Vladimirovich, Liholetova Elena S.

751

Using the problem of digital remote control over a continuous technical plant as an example, it is shown that restriction on the communication channel capacity provided by the channel environment may be a major limitation on the control quality. Illustrations are provided.

APPLICATION OF GRAM METHOD FOR RANGING OF PARAMETRIC UNCERTAINTIES
Alexandrova Sophia A., Slita Olga V., Ushakov Anatoly Vladimirovich

759

The problem of output invariance of a closed-loop system with respect to uncertain parameters of the initial plant state matrix is considered. Two methods of uncertainties ranging by levels of influence on the closed-loop system output are proposed. The both methods use Gramians of the channels “control signal — plant output” and “parametric influence — plant output” controllability. An algorithm for parametric uncertainties ranging based on the methods is developed. An example demonstrating application of the methods is presented.

MODIFICATION OF STEEL LADLES LABELS IN THE PROBLEM OF AUTOMATION OF THE LADLES TURNOVER
Blinnikov Andrey A., Glebova Ekaterina S.

765

The system of steel ladles marking used in a number of domestic plants is described. The system shortcomings within the task of automation turnover buckets are identified and illustrated. A typical scheme of movement of the steel ladle in the workshop is considered. A review of existing technical solutions is presented; advantages and disadvantages of the approaches are discussed. The use of traditional graphic labels as well as RFID labels is shown to be unacceptable. A mechanism of alphabet labels is proposed, requirements to the alphabet symbols are defined. The proposed method of marking steel is illustrated by the example of the character set made up of oblique lines; the corresponding values of one bit are used as the ladles numbers. The lines of further research are determined.

STUDY OF OPTIMIZATION METHODS FOR TECHNICAL EQUIPMENT OF AGRICULTURAL ENTERPRISES
Sergey A. Vrazhevsky, Salikhov Vladimir I.

770

Multi-objective optimization methods for technical equipping control systems in the agricultural business area are reviewed. Economic and tangible optimality criteria for agricultural enterprises are considered. The control system of technical equipping is treated as a multi-level system with marked vertical and horizontal communication. Methods of multi-criteria optimization are formulated for agronomic production systems with the account for character of relations between subsystems under optimization. Attention is paid to the gradient descent method for organization of vertical communications. External effects are accounted for in solving the problem of optimization of technical equipment.