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Application of the Lyapunov Exponent Based on Current Vibration Control Parameter (CVC) in Control of an Industrial Robot

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Controlling dynamics of industrial robots is one of the most important and complicated tasks in robotics. In some works[3,7], there are algorithms of the manipulators steering with flexible joints or arms. However, introducing them to calculation of trajectory results in complicated equations and a longer time of counting. On the other hand, works [4,5,6]show that improvement of the tool path is possible thanks to the previousidentification of the robot errors and their compensation. This text covers application of Largest Lyapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a real control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [9–11] is presented in the article.
Rocznik
Strony
51--61
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
  • Department of Dynamics Lodz University of Technology Stefanowskiego 1/15, 90-924 Lódź, Poland
  • Department of Dynamics Lodz University of Technology Stefanowskiego 1/15, 90-924 Lódź, Poland
autor
  • Department of Dynamics Lodz University of Technology Stefanowskiego 1/15, 90-924 Lódź, Poland
autor
  • Institute of Machine Tools and Manufacturing Technology Lodz University of Technology Stefanowskiego 1/15, 90-924 Lódź, Poland
Bibliografia
  • [1] Alban, T. and Janocha, H.: Dynamic calibration of industrial robots with inertial measurement systems, Laboratory for Process Automation, 1999.
  • [2] Shiakolas, P. S., Conrad, K. L. and Yih, T. C.: On the accuracy, repeatability, and degree of influence of kinematics parameters for industrial robots, International Journal of Modelling and Simulation, V. 202, No. 3, 2002.
  • [3] Tchoń,Mazur, K. A., Dulba, I., Hossa, R. and Muszyski, R.: Manipulatory i roboty mobilne. Modele, planowanie ruchu, sterowanie, Akademicka Oficyna Wydawnicza PLJ, Warsaw, 2000.
  • [4] Abele, E., Bauer, J., Pischan, M., v. Stryk, O., Friedmann, M. and Hemker, T.: Prediction of the tool displacement for robot milling applications using coupled models of an industrial robot and removal simulation, Proceedings of the CIRP 2nd International Conference Process Machine Interactions, Vancouver, Canada, 2010.
  • [5] Klimchik, A., Wu, Y., Caro, S., Furet, B. and Pashkevich, A.: Accuracy Improvement of Robot-Based Milling Using an Enhanced Manipulator Model, Advances on Theory and Practice of Robots and Manipulators, 73–81, 2014.
  • [6] Slamani, M., Nubiola, A. and Bonev, I.: Assessment of the positioning performance of an industrial robot, Industrial Robot: An International Journal , 39(1), 57–68, 2012.
  • [7] Moberg, S.: Modeling and Control of Flexible Manipulators, Linkping, 2010.
  • [8] Dfiebowski, A.: Automatyka podstawy teorii, Industrial Robot: An International Journal , 39(1), 57–68, 2012.
  • [9] Dfiabrowski, A.: Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product, Nonlinear Dynamics, 67, 283–291, 2012.
  • [10] Balcerzak, M., Dfiabrowski, A., Kapitaniak, T. and Jach, A.: Optimization of the Control System Parameters with Use of the New Simple Method of the Largest Lyapunov Exponent Estimation, Mechanics and Mechanical Engineering, 17(4), 325–339, 2013.
  • [11] Dfiabrowski, A.: Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product, Nonlinear Dynamics, NODY-D-13-01203R3, 2014.
  • [12] Eckmann, J. P., Kamphorst, S.O., Ruelle, D. and Ciliberto, S.: Lyapunov- Exponents from a time series, Phys. Rev. Lett., 34(9), 4971–9, 1986.
  • [13] Rosenstein, M. T., Collins, J. J. and De Luca, C. J.: A practical method for calculating largest Lyapunov exponents from small data sets, Physica D, 65(1,2), 117–34, 1993.
  • [14] Parlitz, U.: Identification of true and spurious Lyapunov exponents from time series, Int. J. Bifurcat. Chaos , 2(1), 155–65, 1992.
  • [15] Young, L.: Entropy, Lyapunov exponents, and Hausdorff dimension in differentiable dynamical systems, IEEE Trans. Circuits Syst., 30, 599–607, 1983.
  • [16] Kantz, H.: A robust method to estimate the maximal Lyapunov exponent of a time series, Phys. Lett. A, 185, 77–87, 1994.
  • [17] Kim, B. J. and Choe, G. H.: High precision numerical estimation of the largest Lyapunov exponent, Commun Nonlinear Sci.Numer.Simulat., 15, 1378–1384, 2010.
  • [18] Stefański, A.: Estimation of the largest Lyapunov exponent in systems with impacts, Chaos Solitons Fractals, 11(15), 2443–2451, 2000.
  • [19] Stefański, A. and Kapitaniak, T.: Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization, Chaos Solitons Fractals, 15, 233–244, 2003.
  • [20] Stefański, A.,Dfiabrowski, A. and Kapitaniak, T.: Evaluation of the largest Lyapunov exponent in dynamical systems with time delay, Chaos, Solitons and Fractals, 23, 1651–1659, 2005.
  • [21] Stefański, A.: Lyapunov exponents of the systems with noise and fluctuating parameters, Journal of Theoretical and Applied Mechanics, 46(3), 665–678, 2008.
  • [22] Yilmaz, D. and Gulerb, N. F.: Analysis of the Doppler signals using largest Lyapunovexponentand correlation dimension in healthy and stenosed internal carotid artery patients, Digital Signal Processing, 20, 401–409, 2010.
  • [23] Gharavia, R. and Anantharamb, V.: An upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices, Theoretical Computer Science, 332, 543–557, 2005.
  • [24] Ronga, H. W., Mengb, G., Wanga, X. D., Xuc, W. and Fangc, T.: Largest Lyapunov exponent for second-order linear systems under combined harmonic and random parametric excitations, Journal of Sound and Vibration, 283, 1250–1256, 2005.
  • [25] Vallejos, R. O. and Anteneodo, C.: Largest Lyapunov exponent of long-range XY systems, Physica A, 340, 178–186, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-879c056e-6b49-4e67-beaf-234570a022ca
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