Swing-up problem of an inverted pendulum - energy space approach

• Autorzy: Balcerzak M.
• Języki publikacji: EN

Abstrakty

EN

This paper describes a novel, energy space based approach to the swing-up of an inverted pendulum. The details of the swing-up problem have been described. Equations of the velocity-controlled have been presented. Design of the controller based on energy space notion has been elaborated. The control algorithm takes into account state constraints and control signal constraints. Parameters of the controller have been optimized by means of the Differential Evolution method. A numerical simulation of the inverted pendulum driven by the proposed controller has been conducted, its results have been presented and elaborated. The paper confirms that the proposed method results in a simple and effective swing-up algorithm for a velocity-controlled inverted pendulum with state constraints and control signal constraints.

Słowa kluczowe

EN

swing-up; inverted pendulum; controller; state constraints; control constraints; energy space

PL

swing-up; wahadło odwrócone; sterownik; ograniczenia zmiennych stanu; przestrzeń energetyczna

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 1
• Strony: 33--40
• Opis fizyczny: Bibliogr. 8 poz., 1 rys., wykr.

Twórcy

autor

Balcerzak M.

• Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, Łódź, Poland

Bibliografia

• [1] Ogata, K.: Modern control engineering, Prentice Hall, Upper Saddle River, 2002.
• [2] Chung, C. C., Hauser, J.: Nonlinear control of a swinging pendulum, Automatica, 31, 6, 851–862, 1995.
• [3] Rao, A. V.: A survey of numerical methods for optimal control, Advances in the Astronautical Sciences, 135, 1, 497–528, 2010.
• [4] Dabrowski, A.: The construction of the energy space, Chaos, Solitons & Fractals, 26, 5,1277–1292, 2005.
• [5] Dabrowski, A.: Energy–vector method in mechanical oscillations, Chaos, Solitons & Fractals, 39, 4, 1684–1697, 2009.
• [6] 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.
• [7] Taylor, J. R.: Classical mechanics, University Science Books, 2005.
• [8] McQuarrie, D. A.: Mathematical methods for scientists and engineers, University Science Books, 2003.

Uwagi

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