Guess-Free Pseudospectral Solution for Time Optimal Swing-Up of a Rotary Inverted Pendulum
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Authors
Frontera, Paul J.
Feemster, Matthew
Hurni, Michael
Karpenko, Mark
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Date of Issue
2017
Date
2017
Publisher
American Society of Mechanical Engineers (ASME)
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Abstract
Control of the inverted pendulum is a canonical problem in nonlinear and optimal control. Over the years, many workers have developed solutions for inverting the pendulum link (swingup phase) and for maintaining the pendulum link upright (stabilization/disturbance rejection). In this paper, the time-optimal swing-up of a rotary inverted pendulum is studied. Previous solutions to this problem have required that the original time-optimal problem formulation be transformed to a more computationally tractable form. For example, one transformation is to a fixedtime problem with bounds on the control. Other approaches involve guessing the switching structure in order to construct a candidate solution. Advances in computational optimal control theory, particularly pseudospectral optimal control, allow the original time-optimal problem to be solved directly, and without the need for a guess. One such solution is presented in this paper. It is shown that the result adheres to the conditions of Pontryagin’s minimum principle. An experimental implementation of the solution illustrates its feasibility in practice.
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Article
Description
Proceedings of the ASME 2017 Dynamic Systems and Control Conference DSCC2017 October 11-13, 2017, Tysons, Virginia, USA
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Mechanical and Aerospace Engineering (MAE)
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9 p.
Citation
Frontera, Paul J., et al. "Guess-Free Pseudospectral Solution for Time Optimal Swing-Up of a Rotary Inverted Pendulum." Dynamic Systems and Control Conference. Vol. 58271. American Society of Mechanical Engineers, 2017.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.