Optimal control of an inverted pendulum based on 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 according to the new control performance assessment criterion based on the optimal control theory. The novel control performance index is founded on the method of the Largest Lyapunov Exponent estimation. The detailed description of the new method is provided. Model of the control object is presented. A simple controller is proposed. Parameters of the controller 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 when the regulation time is crucial, whereas somewhat larger overshoot is acceptable.

Słowa kluczowe

EN

inverted pendulum; control; parameters optimization; differential evolution

PL

wahadło odwrócone; sterowanie; optymalizacja parametrów; ewolucja różnicowa

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 1
• Strony: 25--32
• Opis fizyczny: Bibliogr. 10 poz., rys., wykr.

Twórcy

autor

Balcerzak M.

• Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, Łódź, 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] Dąbrowski, A.: Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product, Nonlinear Dynamics, 67, 1, 283–291, 2012.
• [4] Dąbrowski, 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., Dąbrowski, 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., Dąbrowski, A., Balcerzak, M.: New method of multidimensional control simplification and control system optimization, Mechanics and Mechanical Engineering, 19, 2, 127–139, 2015.
• [7] Dąbrowski, 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, 78, 3, 1601–1608, 2014.
• [8] Rao, A. V.: A survey of numerical methods for optimal control, Advances in the Astronautical Sciences, 135, 1, 497–528, 2010.
• [9] 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.
• [10] 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 (2018).