Total energy-shaping control for mechanical systems via Control-by-Interconnection

Joel Ferguson

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arXiv · 2301.03746

Total energy-shaping control for mechanical systems via Control-by-Interconnection

Joel Ferguson

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Abstract

Application of IDA-PBC to mechanical systems has received much attention in recent decades, but its application is still limited by the solvability of the so-called matching conditions. In this work, it is shown that total energy-shaping control of under-actuated mechanical systems has a control-by-interconnection interpretation. Using this interpretation, alternate matching conditions are formulated that defines constraints on the added energy, rather then the total closed-loop energy. It is additionally shown that, for systems that are under-actuated degree one with the mass matrix depending on a single coordinate, the kinetic energy matching conditions resolve to ODEs which can be evaluated numerically. Using this approach controllers are proposed for the benchmark cart-pole and acrobot systems.

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Joel Ferguson. 2023-01-16. Total energy-shaping control for mechanical systems via Control-by-Interconnection. https://arxiv.org/abs/2301.03746

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