## Issue 185, article 7

KVT, 2016, Issue 185, pp.77-89

UDC 519.876.5:615.33

MODELING ANTIMICROBIAL ACTIVITY ANTIBIOTIC “CEFAZOLIN” AND SILVER NANOPARTICLES

Marzeev’s Public Health Institute of the National Medical Academy of Science of Ukraine of Ukraine, Kiev, Ukraine

Introduction. The creation of combined drugs, which are used in the composition of nanoparticles (NPs) is actively developing. The most relevant developments include the NPs composition and antibiotics. Mathematical models of the process under investigation lead to a theoretical understanding of this phenomenon, allow us to describe the process in the form of mathematical functions, make it possible to predict the outcome, to analyze the properties of the model and to obtain new data, without undue experimentation.

The purpose of the article is to determine the characteristics of antimicrobial activity of Ag NP in combination with an antibiotic “Cefazolin” with the help of mathematical models of their actions (“concentration – time – effect”).

Results. Antimicrobial properties of the composite material were considered, which is called the “Silver Shield-1000”, and which consists of antibiotic “Cefazolin” and NPs Ag. Isolated action “Silver Shield-1000” was considered at the first stage of the experiment. For this purpose dilution nanosilver 15,0; 7,5; 3,75; 1,875 (g/cm3), and the holding time was 5, 60, 120, 180 minutes. Based on experimental plots and the general theoretical ideas about the dynamics of the process of the withering away of microbes, mathematical model, y(t) has been selected as the exponential function y = y0 (C) exp[-α(C) T]. The values of the model parameters were calculated based on the original data using numerical methods (Levenberg-Marquardt) and software STATISTICA 10,0. The final model organisms, dying under the influence of the “Silver Shield-1000” had the following form: y = y0 exp(-btC)= 59,74exp(-0,0013 TС). Using this model, the expected value of the concentration С* at which should occur almost complete disappearance of microorganisms immediately after the start of the exposure (С* = 73,15 g/cm3) was calculated. An additional experiment was performed, which confirmed this value that verifies the adequacy of the model as a whole. In the second phase of researching it was experimentally investigated the combined effect of “Silver Shield” — 1000 (3.75 g/cm3) and the antibiotic “Cefazolin” on the death of microorganisms. A mathematical model “concentration — time — effect” for the composite: y = 60,098exp(-0,118 TC) and an antibiotic: y = 60,098exp(-0,012 TC). This made it possible to calculate the efficiency of the composite action compared with isolated action of an antibiotic (k = 9.72). Furthermore, it was shown that the composite exhibits have a much greater effect than the sum of the isolated antibiotic action “Cefazolin” and “Silver shield —1000”. It is possible to determine the nature of such action as potentiation.

Conclusion. Mathematical modeling of the results of an experimental study of the antimicrobial activity of the antibiotic “Cefazolin” in combination with nanoparticles of silver allowed the calculation of the quantitative characteristics of the effectiveness of the active ingredients and performed a meaningful forecast of their action.

Keywords: silver nanoparticles, antibiotic “Cefazolin”, death of microorganisms, mathematical model.

References:

1. Nanometaly: the state of current research and use in biology, medicine and veterinary / V.F. Shatorna V.I. Harets V.V. Krutenko et al. // Herald problems of biology and medicine. — 2012. — Vol. 3. — T. 2. — P. 29–33.
2. Nanoparticles of metals: methods of preparation, physical and chemical properties, methods of research and evaluation of the toxicity // Suchasnі problemi toksikologії. — 2011. — № 3. — P. 5–13.
3. I.S. Chekman Nanopharmacology: state and prospects of research // Journal of Pharmacology and Pharmacy. — 2007. — № 11. — P. 7–10.
4. Biogenic synthesis of silver nanoparticles and their synergistic effect with antibiotics: a study against gram-positive bacteria / A.M. Fayas, K. Balaji, M. Girial, et al. // Nanomedicine. — 2010. — Vol. 6(1). — P. 103–109.
5. Synergistic antibacterial effects of beta-lactam antibiotic combined with silver nanoparticles / P. Li, J. Li, C. Wu et al. // Nanotechnology. — 2005. — Vol. 16(9). — P. 1912–1917.
6. Coping with antibiotic resistance: combining nanoparticles with antibiotics and other antimicrobial agents / A.M. Allahvcrdiyev, K.V. Kon, E.S. Abamor et al. // Expert Rev Anti Infect Ther. — 2011. — Vol. 9(11). — P. 1035–1052.
7. Preparations silver: yesterday, today and tomorrow / O.B. Shcherbakov, G.I. Korczak, I.N. Skorokhod et al. // Pharmaceutical Journal. — 2006. — № 5.
8. Syntesis and effect of silver nanoparticles on the antibacterial activity of different antibiotics against Stafphylococcus aureus and Escherichia coli / A.R. Shahverdi, A. Fakhimi, H.R. Shahverdi, S. Minaian // Nanomedicine. — 2007. — Vol. 3. — P. 168–171.
9. M.Y. Antomonov The mathematical processing and analysis of medical and biological data. — Kiev: Publishing house “Malii Druk”, 2006. — 558p.
10. Dudko DA, Sadohin VP, Kisterski AL-stage method of preparation of highly concentrated suspensions of nanoscale particles of conductive materials based on water-soluble and water-insoluble liquids and device for its implementation UA 80513 C2 25.09.2007

## Issue 185, article 6

KVT, 2016, Issue 185, pp.60-76

UDC 617.751-057-07

THE ASSESMENT OF CONNECTION STRUCTURE BETWEEN THE FUNCTIONAL INDEXES OF PC OPERATORS DURING THE VISUAL WORK WITH FACTOR MODELS’ USE

1Kharkiv Municipal Clinical Hospital №14 named by Prof. L.L. Girshman, Kharkiv, Ukraine

2International Reasearch and Training Center for Information Technologies and Systems of National Academy of Science and Ministry of Science of Ukraine, Kyiv, Ukraine

Introduction. PC operators’ work is connected to necessity of information large amounts perception from PC display. Such activities require of high attention concentration and particular responsibility for production goals. Arduous visual work of PC operators on close distance results in high psychoemotional stress and exerts an impact on functional state. Severe visual asthenopias in PC operators may be observed on the background of normal values of visual system’s functional indexes that require of such states causes determination for prophylaxis measures development.

The purpose of the article is to evaluate the impact of the visual work at close distance on the structure of relationships between visual system’s indexes and functional state’s indexes.

Methods. 41 PC operators took part in the study. The average age of study subjects was (29,6 ± 4,0) y.o. The functional indexes of visual system were measured in all PC operators before and after visual work. The indexes of functional state were also measured by self-assessment using developed questionnaire. The obtained results processing was performed using descriptive statistics methods, cluster and factor analysis.

Results. On the background of performed research using clustering and factor analysis it was found that younger PC operators with higher visual functions the visual work on close distance results in state similar to spasm of accommodation. The recovery after night rest was worse than in PC operators with low visual functions. Older PC operators have higher quality of recovery after night rest. It may be determined by development of visual fatigue as the result of visual work . The recovery after night rest in case of visual fatigue is better than in case of accommodation spasm.

Conclusion. Visual work on close distance results in configuration change of connection between indexes of visual system that support visual perception. The peculiarities of these changes depend on visual system’s indexes. The results of PC operators functional state’s self-assessment using the questionnaire developed by us had shown that in PC operators with low functional possibilities the common and visual complaints rate was certainly lower than in operators with high functional possibilities.

Keywords: factor models, visual system, functional state, PC operator work.

References:

1 Danilichev V.F. Sovremennaya oftal’mologiya: rukovodstvo. Izd. Dom “Piter”, 2009, 684p.

2 Dyadina U.V., Rozenblyum YU.Z. Prichiny i mekhanizmy astenopii. Vestnik optometrii, 2003,Vol.1, No3, pp. 26–28.

3 Yemel’yanov G.A. Sostoyaniye akkomodatsii kak indikator sindroma khronicheskoy ustalosti u patsiyentov zritel’no-napryazhennogo truda. Kataraktal’naya i refraktsionnaya khirurgiya, 2013, No1, pp. 23–25.

4 Yemel’yanov G.A., Shchukin S.YU. Sub”yektivnyye narusheniya akkomodatsionno-refraktsionnoy sistemy glaza u cheloveka-operatora zritel’no-napryazhennogo truda.Voyenno-meditsinskiy zhurnal, 2012, Vol.133, No 2, pp.60–62.

5 Yemel’yanov G.A., Gusev YU.A., Kapkova S.G. Dinamika ob”yektivnykh pokazateley akkomodatsii u lits bez patologii organa zreniya v protsesse zritel’no-napryazhennogo truda.Innovatsionnyye tekhnologii v oftal’mologichesko y praktike regionov, Astrakhan’, 2012, pp. 62–63.

6 Kal’nishV.V., Yena A.I. Sovremennoye sostoyaniye professional’nogo psikhofiziologicheskogo otbora v Ukraine. Meditsina truda i promyshlennaya ekologiya, 2006, No 3, pp. 12–17.

7 Kochina M.L., Kozak L.M., Yevtushenko A.S. Analiz izmeneniya faktornykh strukturpokazateley funktsional’nogo sostoyaniya cheloveka pri raznykh vidakh zritel’noy nagruzki. Visnik problem biologii i meditsini, 2013, Vol. 1, No1(98), pp. 41–45.

8 Ovechkin I.G. et.al. Akkomodatsionnyye narusheniya u lits zritel’no-napryazhennogo truda s yavleniyami psikhologicheskoy dezadaptatsii. Rossiyskiy oftal’mologicheskiy zhurnal, 2014, No1, pp.39–41.

9 Ovechkin I.G., Ragimova N.R. Issledovaniye dinamiki funktsional’nogo sostoyaniya sensornogo otdela zritel’nogo analizatora v protsesse professional’noy deyatel’nosti na personal’nom komp’yutere. Oftal’mologiya, 2010, Vol.7, No4, pp. 32–35.

10 Ovechkin I.G. et. al. Primeneniye funktsional’noy korrektsii organa zreniya patsiyentam-operatoram zritel’nogo profilya s pozitsiy sovremennykh trebovaniy k meditsinskoy reabilitatsii. Rossiyskiy oftal’mologicheskiy zhurnal, 2015, Vol.8, No1, pp. 90–97.

11 Yevtushenko A.S., Kozak L.M., Kochina M.l. et.al. Rezul’taty otsenki funktsional’nogo sostoyaniya cheloveka pri zritel’nom trude. Svit meditsini ta biologii, 2015, No 2, pp. 39–44.

12 Rozenblyum YU.Z., Kornyushina T.A., Feygin A.A. Professional’naya oftal’mopatiya. Meditsina truda i promyshlennaya ekologiya, 1995, No4, pp. 14–16.

13 Somov Ye.Ye. Metody oftal’moergonomiki. AN SSSR, otdeleniye fiziologii. L. : Nauka, 1989, 157 p.

14 Shakula A.V., Yemel’yanov G.A. Otsenka sostoyaniya akkomodatsii i “kachestva zhizni” u patsiyentov zritel’no-napryazhennogo truda s rasstroystvami psikhologicheskoy adaptatsii. Vestnik vosstanovitel’noy meditsiny, 2013, No4, pp. 52–56.

15 Shapovalov S.L., Milyavskaya T.I., Ignat’yev S.A. Akkomodatsiya glaza i yeye narusheniya. Izd-vo: MiK, 2012, 188 p.

16 Shapovalov S.L., Aleksandrov A.S. Materialy k probleme zritel’nogo utomleniya u operatorov videodispleynykh terminalov. M. : GKVG im. Akademika N.N. Burdenko, 1999, 174 p.

17 Anshe, J. Accomodation for computer users … and more. Optometry, 2002, Vol.73, No7, pp.405–406.

18 Collins M., Davis B., Atchison D. VDT screen reflections and accomodation response. Ophthical. Physiol. Opt., 2004, Vol.14, N4, pp.193–198.

19 Mocci F., Serra A., Corrias G.A. Psychological factors and visual fatigue in working with video display terminals. Occup. Environ. Med, 2001, Vol.58, No4, pp. 267–271. https://doi.org/10.1136/oem.58.4.267

## Issue 185, article 5

KVT, 2016, Issue 185, pp.48-59

UDC 517.977

GROUP PURSUIT IN DIFFERENTIAL-DIFFERENCE GAMES WITH VARIABLE DELAY

Liubarshchuk I.A.

Department of Mathematics and Informatics, Yuriy Fedkovych Chernivtsi National University, 58012 Chernivtsi, Ukraine

finvara@gmail.com

Introduction. A variety of interesting examples stimulated the development of the Mathematical Control Theory, in particular, the Dynamic Games Theory. First fundamental results in Differential Games Theory were obtained by R. Isaacs. Some others directions of research are Pontryagin’s procedures and Krasovskii’s extremal aiming principle. The further development of Pontryagin’s ideas by his disciples and followers resulted in the Method of Resolving Functions, one of the most powerful methods of dynamic game theory. The essence of the Method of Resolving Functions is in the construction of some numeric resolving function on the known parameters of the process. The resolving function outlines the course of the process. At the moment at which its integral turns into unit the trajectory of the process hits the terminal set. This method was used by Baranovskaya for local convergence problems with fixed time, which are described by a system of differential-difference equations of delay-type.

The purpose of the article is to investigate group problem, which is described by a system of differential-difference equations with variable delay. The necessary and sufficient conditions for solvability of such problems are established.

Results. We considered a pursuit problem in 2-person differential game, one player is a pursuer and another one is an evader. The problem was given by the system of the differential-difference equations of delay-type and for such a conflict-controlled process we presented conditions on its parameters and initial state, which were sufficient for capturing the evader. For differential-difference games with time lag we generalized Pontryagin’s First Direct Method. That gave us a possibility to compare results obtained by the Method of Resolving Functions for such conflict-controlled processes to Pontryagin’s First Direct Method. The necessary and sufficient conditions for group problem solvability were established.

Conclusions. A general scheme of the Method of Resolving Functions for the local convergence problem with fixed time is presented . The conflict-controlled process is described by a system of differential-difference equations of delay-type with variable delay. For differential-difference games with variable delay we generalized Pontryagin’s First Direct Method. We also considered the group pursuit problem in differential game. For such conflict-controlled process we obtained and investigated general scheme of the Method of Resolving Functions.

References:

1. Isaacs R. Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Wiley.1965 . 418 р.
2. Pontryagin L.S. Selected Scientific Works. Moscow: Nauka, 1988, 736 p. (in Russian)
3. Krasovskii N.N. Game Problems on Motions Encounter. Moscow: Nauka, 1970, 420 p. (in Russian)
4. Krasovskii N.N., Subbotin A.I. Positional differential games. Moscow: Nauka, 1974, 456 p. (in Russian)
5. Chikrii A.A. Conflict Controlled Processes. Kiev: Naukova dumka, 1992, 384 p. (in Russian)
6. Chikrii A.A. On one analytic method for dynamic approach games.Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, №. 271, pp. 76–92 (in Russian)
7. Pilipenko Y.V., Chikrii A.A. Oscillation сonflict сontrolled processes. Prikladnaya matematika i mehanika, 1993, Vol. 57, №.3, pp. 3–14. (in Russian)
8. Chikrii A.A., Chikrii G.C. Group pursuit in differential-difference games. Dif. uravneniya, 1984, №.5, pp. 802–810. (in Russian)
9. Osipov Y.S. Differential games for systems with time lag. DAN SSSR, 1971, Vol. 196, №.4, pp. 779–782. (in Russian)
10. Nikolskii M.S. Linear differential pursuit games with time lag. DAN SSSR,1971, Vol. 197, №.5, pp. 1018-1021. (in Russian)
11. Chikrii A.A., Baranovskaya L.V. A type of controlled systems with delay. Cybernetics and Computing Technology. Complex Control Systems, 1995, №. 107, pp. 3–11.
12. Azbelev N.V., Simonov P.M. Stability of equations solutions with ordinary derivatives. Perm: Izd-vo Permskogo universiteta, 2001, 230 p.
13. Aubin J., Frankowska H. Set-valued Analysis. Birkhäuser, 1990, p. 461.

## Issue 185, article 4

KVT, 2016, Issue 185, pp.35-47

UDC 629.7.05

USING VIDEO IMAGES FOR DETERMINING RELATIVE DISPOSITION OF TWO SPACECRAFTS

Space Research Institute of the National Academy of Science of Ukraine and State Space Agency of Ukraine, Kyiv, Ukraine

Introduction. Automatic orbital berthing systems require permanent availability of relative position and attitude of a target spacecraft. In the most general case the only source of information is video filming. Extracting mutual disposition parameters from a video frame is based upon special techniques which can be divided into two large groups: feature-based and model-based. Major difference between them is defined by data structure used for the target description (individual points for feature-based approach vs. rigorous visual model for model-based one). This article is devoted to the research of mathematical problem that appears in considering pose estimation for two orbital spacecraft in the presence of wireframe model of the target when only video filming is available.

The purpose of the article is to construct a model-based method that provides fast and accurate estimation of relative position and attitude of the target spacecraft. We discuss possible drawbacks of direct procedures based on straightforward (pixel-wise) image fitting and propose a subtle algorithm which satisfies formulated conditions.

Results. The algorithm composed of three independent parts (initialization, pose refinement and pose tracking) has been developed and tested on simple initial datum. Initialization stage, responding for rough estimation in the absence of preliminary information, has given relatively poor but quite enough accuracy for the aims of initial approximation. Pose refinement stage which is implemented as iterative procedure based on closeness of neighboring frames demonstrated almost total matching with actual values. Pose tracking (state estimation based on equations of motion) was redundant for our simple example as it could not improve the result provided by pose refinement.

Conclusions. Constructed algorithm has been tested on simplified situation and demonstrated very high precision. More realistic conditions including noises and occlusions can bring to corrupted result that should be recovered. This requires introducing additional steps into the algorithm which are reflected in the text. The notable feature of the algorithm is its high modularity which allows each stage to be implemented and configured independently according to available resources and mission requirements.

Keywords: orbital rendezvous, pose estimation, orbital video filming, computer vision.

References:

1 Lowe D.G. Distinctive Image Features from Scale-Invariant Keypoints. International Journal of Computer Vision, 2004, 60 (2), pp. 91–110. https://doi.org/10.1023/B:VISI.0000029664.99615.94

2 David P. SoftPOSIT: Simultaneous Pose and Correspondence Determination. International Journal of Computer Vision, 2004, 59 (3), pp. 259–284. https://doi.org/10.1023/B:VISI.0000025800.10423.1f

3 Black M.J., Jepson A.D. EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation. International Journal of Computer Vision, 1998, 26 (1), pp. 63–84. https://doi.org/10.1023/A:1007939232436

4 Trefethen L.N., Bau D. Numerical Linear Algebra. Philadelphia: SIAM, 1997, 361p. https://doi.org/10.1137/1.9780898719574

5 Drummond T., Cipolla R. Real-Time Visual Tracking of Complex Structures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24 (7), pp. 932–946. https://doi.org/10.1109/TPAMI.2002.1017620

6 Hartley R., Zisserman, A. Multiple View Geometry in Computer Vision. 2nd Edition. Cambridge University Press, 2004, 655p. https://doi.org/10.1017/CBO9780511811685

7 Paterson M.S., Yao, F.F. Efficient Binary Space Partitions for Hidden-Surface Removal and Solid Modeling. Discrete and Computational Geometry, 1990, 5, pp. 485–503. https://doi.org/10.1007/BF02187806

8 Kelsey J.M., et. al. Vision-Based Relative Pose Estimation for Autonomous Rendezvous and Docking. 2006 IEEE Aerospace Conference. — 20 p. https://doi.org/10.1109/AERO.2006.1655916

9 Wenfu X., et al. Autonomous Rendezvous and Robotic Capturing of Non-Cooperative Target in Space. Robotica, 2010, 28, pp. 705–718. https://doi.org/10.1017/S0263574709990397

10 Fehse W. Automated Rendezvous and Docking of Spacecraft. Cambridge University Press, 2003, 495 p. https://doi.org/10.1017/CBO9780511543388

## Issue 185, article 3

KVT, 2016, Issue 185, pp.21-34

UDC 681.5

l1-OPTIMIZATION APPROACH TO DESIGN OF DIGITAL AUTOPILOTS FOR LATERAL MOTION CONTROL OF AN AIRCRAFT

International Research and Training Center for Information Technologies and Systems of the National Academy of Science of Ukraine and Ministry of Education and Sciences of Ukraine, Kiev, Ukraine

Introduction. The optimal digital autopilot needed to control of the roll for an aircraft in the presence of an arbitrary unmeasured disturbances is addressed in this paper. This autopilot has to achieve a desired lateral motion control via minimizing the upper bound on the absolute value of the difference between the given and true roll angles. It is ensured by means of the two digital controllers. The inner controller is designed as the discrete-time PI controller in order to stabilize a given roll rate. This variable is formed by the external discrete-time P controller. To optimize this control system, the controller parameters are derived utilizing the so-called l1-optimization approach advanced in modern control theory. The motion parameters are assumed to be known.

The purpose of the paper is to synthesize a digital autopilot which is able to maintain a given roll orientation of an aircraft with a desired accuracy and to cope with an arbitrary external disturbance (a gust) whose bounds may be unknown.

Results. The necessary and sufficient conditions guaranteeing the stability of the two-circuit feedback discrete-time control system are established. First, the l1-optimal PI and P controller parameters are calculated simultaneously (in contrast with [14]). Second, the aileron servo dynamics are taken into account to establish the stability condition for optimizing the controller parameters. Third, random search algorithm is used to calculate the three optimal values of the autopilot parameters. To support the theoretical results obtained, in this work, several simulation experiments were conducted. We have established that the simultaneous l1-optimization of both controllers was more efficient than the sequential l1-optimization of inner and external controllers.

Conclusion. It was established that the two-circuit l1-optimal PI and P control laws can cope with the wind gust and ensure the desired roll orientation. This makes it possible to achieve the control objective which was stated. A distinguishing feature of the control algorithms is that they are sufficiently simple. This is important from the practical point of view.

Keywords: aircraft, lateral dynamics, digital control system, discrete time, stability, l1-optimization, random search algorithm.

References:

1 Stevens B.L., Lewis F.L. Aircraft Control and Simulation, 2nd ed. New York: John Willey & Sons, 2003, 680 p.

2 William D.E., Friedland B, Madiwale A.N. Modern conrtol theory for design of autopilots for bank-to-turn missiles. J. Guidance Control, 1987, vol. 10, pp. 378–386. https://doi.org/10.2514/3.20228

3 Teoh E.K., Mital D.P., Ang K.S. A BTT CLOS autopilot design. The EEE Journal, 1992, vol. 4, pp. 1–7.

4 Ang K.S., Teoh E.K., Mital D.P. Adaptive control of a missile autopilot system. Proc. 12th IFAC World Congress, 1993, vol. 1, pp. 293–296.

5 Malaek S.M.B., Izadi H., Pakmehr M. Intelligent Autolanding Controller Based on Neural Networks. Proc. 1st African Control Conference (AFCON2003), Cape Town, South Africa, 2003, vol. 1, pp. 113–119.

6 Khrosravani M.R. Apllication of Neural Network on Flight Control. Int. Journal of Machine Learning and Computing, 2012, vol. 6, pp. 882–885. https://doi.org/10.7763/IJMLC.2012.V2.258

7 Lavretsky E., Wise K. A. Robust and Adaptive Control with Aerospace Aplication. London: Springer-Verlag. 2013, 454 p. https://doi.org/10.1007/978-1-4471-4396-3

8 Astrom K.J., Wittenmark B. Computer Controlled Systems. Theory and Design, 2nd ed. N.J.: Prentice Hall, Englewood Cliffs, 1990, 555 p.

9 Goodwin G.C., Graebe S.F., Salgado M.E. Control Systems Design. N.J.: Prentice Hall, 2001, 908 p.

10 Yuz J.I., Goodwin G.C. Sampled-Data Models for Linear and Nonlinear System. London: Springer-Verlag, 2014, 289 p. https://doi.org/10.1007/978-1-4471-5562-1

11 Dahleh M.A., Pearson J.B. l1-optimal feedback controllers for discrete-time systems. Proc. American Control Conference, Seattle, WA, 1986, pp. 1964–1968.

12 Vidyasagar M. Optimal rejection of persistent bounded disturbances. IEEE Trans. on Autom. Control, 1986, vol. 31, pp. 527–517.

13 Khammash M.H. A new approach to the solution of the l1 control problem: the scaled-Q method. IEEE Trans. on Autom. Control, 2000, vol. 45, pp. 180–187.

14 Melnyk K.V., Zhiteckii L.S., Bogatyrov A.M., Pilchevsky A.Yu. Digital control of lateral autopilot system applied to an UAV: optimal control strategy. Proc. 2013 2nd IEEE Int. Conf. “Actual Problems of Unmanned Air Vehicles Developments”, Oct., 15-17, Kiev, Ukraine, 2013, pp. 189–192. https://doi.org/10.1109/APUAVD.2013.6705322

15 Blakelock J.H. Automatic Control of Aircraft and Missiles, 2nd ed. New York: John Wiley & Sons, Inc., 1991, 672 p.

16 Tou J.T. Digital and Sampled-Data Control Systems. New-York: McGraw-Hill Book Company, 1959, 631 p.

17 Jury E.I. Sampled-Data Control Systems. New York: John Willey & Sons Inc., 1958, 332 p.

18 Polyak B.T., Shcherbakov P.S. Robust Stability and Control. Moscow: Nauka, 2002, 303 p. (in Russian)

19 Polyak B.T. Introduction to Optimization. New-York: Optimization Software Inc., 1987, 438 p.

## Issue 185, article 2

KVT, 2016, Issue 185, pp.5-20

UDC 004.021:004.94

MODELLING OF MULTI-COMPONENT SIGNALS IN A CHRONOPOTENTIOMETRY

Surovtsev I.V.

International Research and Training Center for Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kiev, Ukraine

igorsur52@gmail.com

Introduction. In the inversion chronopotentiometry a differential reverse signal of inversion is considered as linear sum of components measuring that are located on the base curve of the lower envelope. The signal is similar to the spectrum of components after its subtracting and can be analyzed by the chromatographic methods or spectroscopic analysis.

The purpose of the article is to develop a method of modelling multi-component signals, provided that the spectra is spaced apart and the overlap of the spectral components is small.

Methods. Preliminary determination of the parameters of the approximation of the individual spectral components and the base curve is performed. An iterative model of the multi-component signal is sought in the form of generalized polynomial of linearly independent functions by least squares method. At a negative value approximation coefficient corresponding spectral component is considered to be erroneous or not.

Results. In the given example the use of the modelling method has allowed to reduce relative error in determining the concentration of copper from 18,9% to 1,5%, compared to the conventional analysis.

Conclusion. The proposed method of modelling and algorithms of its implementation allow eliminating the subjective factor that is associated with the experience and skills of chemist-analyst when selecting boundaries of turndown component that allows increasing the accuracy, repeatability and reliability of determining the concentration of chemical elements.

Keywords: modelling, algorithm, spectrum, chronopotentiometry.

Reference

1 ZakharovM.S., Bakanov V.I., Pnev V.V. Chronopotentiometry. M.: Chemistry, 1978, 199 p. (in Russian).

2 Surovtsev I.V. Transformation of data structure in determining the concentration by methods of inversion chronopotentiometry. Kibernetika i vycislitel’naa tehnika, 2015, No 180, pp.4–14 (in Russian).

3 Heyrovsky J, Kuta J. Fundamentals of polarography. M.: Mir, 1965, 559 p. (in Russian).

4 Karnaukhov A.I., Grynevych V.V., Skobets E.M. Differential variant of inversion chronopotentiometry with a given resistance in oxidative circuit. Ukrainian chemical journal, 1973, No 39, pp. 710–714 (in Ukrainian).

5 Britz D. Digital Simulation in Electrochemistry. Springer, Berlin Heidelberg, 2005, 338 p. https://doi.org/10.1007/b97996

6 Model 600C Series Electrochemical Analyzer/Workstation. User’s Manual/CH Instruments, Inc. Available at: http://www.chinstruments.com/chi600.shtml.

7 Surovtsev I.V., Tatarinov A.E., Galimov S.K. The modeling of the Differential Chronopotentiograms by the Sum of Normal Distributions. Control System and Computers, 2009, No 5, pp. 40–45 (in Russian).

8 Lebedev A.T. Comprehensive environmental mass spectrometry. ILM Publications, London, UK, 2012, 510 p.

9 Budde W.L. Analytical mass spectrometry. Strategies for environmental and related applications. Oxford university Press, 2001, 386 p.

10 LECO. Available at: http://www.davinci-ls.com/en/products/systems-software/gc-ms/186-leco-chromatof-software.html.

11 Enke C.G., Newcome B.H. [et al]. High repetition rate transient recorder with automatic integration. Patent 4,490,806 U.S., Dec.25, 1984.

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13 Scholkmann F., Boss J., Wolf M. An efficient algorithm for automatic peak detection in noisy periodic and quasi-periodic signals. Algorithms, 2012, No 5, pp.588-603. https://doi.org/10.3390/a5040588

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