Robust actuator placement in flexible plates subject to worst-case spatial distribution of disturbances

In this study, we consider the problem of actuator placement in the vibration control of flexible plates. Unlike earlier approaches based on enhanced controllability and/or improved performance measures, we consider the case of actuator placement based on robustness-with-respect to spatial variability of disturbances. As predicted from our extensive numerical investigation, when the spatial distribution of disturbances is known, then the resulting optimal location differs from the one predicted from controllability/LQR approaches. When the distribution is not known, then one may introduce an element of spatial robustness by considering the worst-case spatial distribution. Extensive numerical results are reported here which provide an insight on the judicious actuator placement when spatial distributions of disturbances are taken into consideration for actuator placement and controller design.