Convex control design for vibration induced by uncertain excitations

This paper presents an introduction to convex control methods suitable for suppressing vibrations induced in flexible structures by wind or other uncertain excitations. Results on controlling linear systems subject to uncertain inputs using deterministic methods are presented. The results are general, but are illustrated by application to a tuned-mass damper system as an example. Rather than using traditional probabilistic information, the approach presented here treats uncertain loads as members of a convex set defined by bounds on the maximum values of the load. A feedback control law is then defined over this set. In particular, this work addresses the control of flexible structures against transient wind loads of known, bounded magnitude. Results are compared to a standard linear quadratic Gaussian (LQG) approach.