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Vol: 57(71) No: 2 / June 2012 Probability Estimation of Defined Properties of the Real Technical Systems with Stochastic Parameters Dragan Antić Department of Control Systems, University of Niš, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, P.O. Box 73 18000 Niš, Serbia, phone: (381) 18 529-363, e-mail: dragan.antic@elfak.ni.ac.rs, web: http://www.elfak.ni.ac.rs Zoran Jovanović Department of Control Systems, University of Niš, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, P.O. Box 73 18000 Niš, Serbia, e-mail: zoran.jovanovic@elfak.ni.ac.rs Nikola Danković Department of Control Systems, University of Niš, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, P.O. Box 73 18000 Niš, Serbia, e-mail: nikola.dankovic@elfak.ni.ac.rs Miodrag Spasić Department of Control Systems, University of Niš, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, P.O. Box 73 18000 Niš, Serbia, e-mail: miodrag.spasic@elfak.ni.ac.rs Stanko Stankov Department of Control Systems, University of Niš, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, P.O. Box 73 18000 Niš, Serbia, e-mail: stanko.stankov@elfak.ni.ac.rs Keywords: probability estimation, oscillations, stability, imperfect systems, stochastic parameter, normal distribution Abstract This paper presents one method for probability estimation of some property of imperfect system (stability, oscillations appearance, controllability, reliability, observability, etc.). That is significant improvement compared to papers where considered property is always stability. All real technical systems are imperfect and they have stochastic parameters. Normal distribution is the most frequent distribution and the method described in this paper is applied to this distribution. The region of certain system property is approximated in parameter space and relations for probability of defined properties are obtained. The approximation can be performed by straight line or circular arches. Proposed algorithm for both approximations is given. The method is especially efficient for the imperfect systems with three or four parameters, of which two have large standard deviations. Application of this approximate method is given in the real technical system such as the system for rubber transportation in tyre industry. The method was verified for the case of determining the probability of oscillations appearance and asymptotic stability. Proofs of theorems used in the paper are given in Appendix. References [1] V. G. Suhorebrij, Dynamics and Stability of Control Systems, Science Academy of Ukraine, Kiev, 1977, (in Russian). [2] O. U. Komarnickaja and K. B. Starobin, Application of Probability Theory at Engineering and Economic Calculations, Leningrad, 1984, (in Russian). [3] B. Danković, “Stability probability estimation of the system with more random parameters”, Proc. of HIPNEF, Niš, 1988, pp. 300-307, (in Serbian). [4] B. Danković and Z. Jovanović, “On the oscillations of the automatic control cascade connected systems for strip material transportation”, Elektrotehnika vol. 43, no. 10-11, pp. E1-E3, 1994, (in Serbian). [5] Z. Jovanović, N. Danković, M. Spasić, S. Stankov and Z. Icić, “Practical testing of the probability of stability of the discrete system with random parameters”, Proc. of 10th International Conference on Applied Electromagnetics, ПЕС 2011, Niš, Serbia, September 25.-29., 2011. [6] D. Antić, S. Nikolić, M. Milojković, N. Danković, Z. Jovanović and S. Perić, \'\'Sensitivity Analysis of Imperfect Systems Using Almost Orthogonal Filters\'\', Acta Polytechnika Hungarica, vol. 8, no. 6,, pp. 79-94, 2011. [7] B. Danković, S. Nikolić, M. Milojković and Z. Jovanović, “A class of almost orthogonal filters”, Journal of Circuits, Systems, and Computers, vol. 18, no. 5, pp. 923-931, 2009. [8] M. Milojković, S. Nikolić, B. Danković, D. Antić and Z. Jovanović, “Modelling of dynamical systems based on almost orthogonal polynomials”, Mathematical and Computer Modelling of Dynamical Systems, vol. 16, no. 2, pp. 133-144, 2010. [9] D. Antić, Z. Jovanović, V. Nikolić, M. Milojković, S. Nikolić and N. Danković, “Modeling of cascade-connected systems using quasi-orthogonal functions”, Electronics and Electrical Engineering, vol. 10(126), 2012, in press. [10] Z. Jovanović, N. Danković, M. Spasić, S. Stankov and Z. Icić, “Adaptive control of system for rubber transportation”, Proc. of the XLVI ICEST 2011, Niš, Serbia, June 29. - July 01., vol. 2, pp. 383-386, 2011. [11] B. Danković, B. Vidojković and Z. Jovanović, “Dynamical analysis of the protector cooling system in tyre industry”, Proc. XVII International Conference on Material Flow, Machines and Devices in Industry, ICMFMDI 2002, Belgrade, pp. 56-59, 2002. [12] B. Samardžić and B. M. Zlatković, “Simulation of bifurcation and escape-time diagrams of cascade-connected nonlinear systems for rubber strip transportation”, Nonlinear Dynamics, vol. 67, pp. 1105-1113, 2012. [13] D. Antić, Z. Jovanović, N. Danković, M. Spasić and S. Stankov, \'\'Probability estimation of certain properties of the imperfect systems\'\', Proc. of the 7th International Symposium on Applied Computational Intelligence and Informatics, SACI 2012, Timisoara, Romania, May 24.-26., 2012., pp. 213-216. |