Optimization of the inverted pendulum controller with friction compensation by means of the new method of Lyapunov exponents estimation

• Autorzy: Balcerzak M.
• Języki publikacji: EN

Abstrakty

EN

This text covers optimization of an inverted pendulum control system with friction compensator. The control system is tuned with respect to a performance index based on the novel method of the Largest Lyapunov Exponent estimation. The detailed description of the method is provided. Model of the control object is presented. A simple controller is proposed. Two control systems are compared: the one with compensator and the one without. Parameters of both controllers are optimized with respect to the novel criterion by means of the Differential Evolution method. Results of numerical simulations are presented. It is shown that the new criterion can be successfully applied to both: typical linear regulators and controllers with compensators.

Słowa kluczowe

EN

inverted pendulum; control; friction compensator; parameters optimization; differential evolution

PL

wahadło odwrócone; sterowanie; kompensator tarcia; optymalizacja parametrów; ewolucja różnicowa

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 4
• Strony: 959--965
• Opis fizyczny: Bibliogr. 9 poz., 1 rys., wykr.

Twórcy

autor

Balcerzak M.

• Division of Dynamics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-924 Lodz, Poland

Bibliografia

• [1] Oseledec, V.I.: A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Mosc. Math. Soc., 19, 197-231, 1968.
• [2] Henon, M., Heiles, C.: The applicability of the third integral of the motion: some numerical results, Astron. J., 69, 77, 1964.
• [3] Dabrowski, A.: Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product, Nonlinear Dynamics, 67(1), 283-291, 2012.
• [4] Dabrowski, A.: The largest transversal Lyapunov exponent and master stability function from the perturbation vector and its derivative dot product (TLEVDP), Nonlinear Dynamics, 69(3), 1225-1235, 2012.
• [5] Balcerzak, M., Dabrowski, A., Kapitaniak, T., 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(3), 225-239, 2013.
• [6] Pijanowski, K., Dabrowski, A., Balcerzak, M.: New method of multidimensional control simplification and control system optimization, Mechanics and Mechanical Engineering, 19(2), 127-139, 2015.
• [7] Dabrowski, A.: Estimation of the the Largest Lyapunov exponent-like (LLEL) stability measure parameter from the perturbation vector and its derivative dot product (Part 2) Experiment simulation, Nonlinear Dynamics, bf 78(3), 1601-1608, 2014.
• [8] Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11, 341-359, 1997.
• [9] Taylor, J. R.: Classical Mechanics, University Science Books, 2005.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).