Optimal control of arrays of microcantilevers

We present a model for an array of microcantilevers that are used in atomic force microscopy and nano-scale manufacturing. The microcantilevers are connected to each other through a common base, and are individually actuated. The sensors are also integrated on each microcantilever. This system is an example of a spatially-invariant system with a distributed array of sensors and actuators. We exploit the spatial invariance of the problem to design optimal H₂ controllers for this array. An analytic expression for the optimal controller is derived in the transformed domain, and estimates of the coupling range of the controller is obtained