Modeling and observer design for an array of electrostatically actuated microcantilevers

We present a mathematical model for the dynamics of an array of capacitively actuated microcantilevers. We propose a system where the current measured at each cantilever is used as the sensing signal of the cantilever state through an observer. We show that such an array is a spatially invariant system with distributed control and sensing. For the common case of periodically excited cantilevers, we show that the underlying dynamics are those of a periodic system described by a Mathieu equation. We exploit the spatial invariance of the problem to design an optimal distributed observer, where the temporal periodicity is handled using the lifting technique.