Comparison of actuator placement criteria for control of structures

The performance of a controlled system depends on the location of the control actuator, in addition to the controller itself. Thus actuator placement is part of controller design for these systems. In this paper, a number of different actuator placement criteria are compared in the context of controlling vibrations on a simply supported beam. Maximizing a measure of the controllability is very common actuator placement criteria. It is shown here that this approach yields predictions that depend on the order of the model used for the calculations. Furthermore, this criteria does not always lead to locations that also minimize the control objective. The control objectives considered here are the minimization of linear-quadratic, H2H2 and H∞H∞ costs. The effect of different weights in the linear-quadratic, H2H2 and H∞H∞ cost functions on the optimal actuator location is also examined. The control signal is calculated for a number of different cases. Linear-quadratic, H2H2 or H∞H∞ optimal location of the actuator typically leads to better performance with control effort comparable to that at sub-optimal points.