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Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem

Didier Henrion·Michael L. Overton
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Abstract

We consider the following problem: find a fixed-order linear controller that maximizes the closed-loop asymptotic decay rate for the classical two-mass-spring system. This can be formulated as the problem of minimizing the abscissa (maximum of the real parts of the roots) of a polynomial whose coefficients depend linearly on the controller parameters. We show that the only order for which there is a non-trivial solution is 2. In this case, we derive a controller that we prove locally maximizes the asymptotic decay rate, using recently developed techniques from nonsmooth analysis.

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Didier Henrion, Michael L. Overton. 2006-03-29. Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem. https://arxiv.org/abs/math/0603681

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