On the control design and robustness analysis for high-density microcantilever arrays

In this paper we present a basic model and control design of an array of electrostatically actuated microcantilevers. Part of the main focus of this paper is to study the feasibility and compare the performance of the centralized, decentralized and distributed schemes on a microcantilever array system. Since the implementation of a centralized controller for such systems is impractical, we consider the following two control schemes with localized architecture: (a) a H_∞ decentralized controller that completely ignores the dynamics contributed by the neighbors hence treating them as an external disturbance; and (b) a H_∞ distributed controller that makes use of information only from its immediate neighbors. In order to have some benchmark performance index, we first design a H_∞ centralized controller for an array of eight microcantilevers. The performance of these controllers are tested via simulations on a finite nonlinear model of the system, and compared with the benchmark performance delivered by the centralized controller. It is seen that the performance delivered by a distributed controller is quite comparable to the performance delivered by the benchmark scheme of a centralized controller. In comparison, the performance of the decentralized controller degrades by more than 100% in terms of resolution. Another main contribution of this paper is the robustness analysis with respect to the modeling uncertainties. This is important, especially in the view of the fabrication errors which result in deviation of actual dynamics of each microcantilever from its model, as well as since the control designs are derived from a linearized model of the cantilever array. In this direction, analysis and simulations of control implementations on perturbed linear as well as nonlinear models of system with finite microcantilever arrays are presented.