SVD-based control of a beam figure

This paper addresses a beam figure control problem. A slender beam (thin round bar), simply supported at both ends, is deformed by a distributed dynamic load, which produces a distributed displacement (figure distortion). The load is norm-bounded, and a feedback control is required to maintain a desired shape or figure accuracy, i.e. a specified frequency-dependent norm bound, using only a finite number of control forces. To construct an efficient and realistic control a simple feedback configuration is needed with a finite and small number of sensors and actuators, limited only by the desired figure accuracy. Three main points are considered: a discrete-parameter finite-dimensional dynamic model, compatible with original continuous parameter infinite-dimensional I/O model; a control strategy, which enables the control of continuous shapes by means of discrete forces; optimization of actuator/sensor positions, to produce a minimal closed-loop displacement/load ratio