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

Didier Henrion (1) , Michael Overton (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 CIMS - Courant Institute of Mathematical Sciences [New York]

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.

Mots clés: linear systems; polynomials; decay-rate; fixed-order controller design; nonsmooth analysis

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion, Michael Overton. Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem. 2006. ⟨hal-00021929⟩