A Robustness Approach for Handling Modeling Errors in Parallel-Plate Electrostatic MEMS Control

This paper addresses the control of electrostatic parallel-plate microactuators in the presence of such modeling errors as unmodeled fringing field effect and deformations. In general, accurate descriptions of these phenomena often lead to very complicated mathematical models, while ignoring them may result in significant performance degradation. In this paper, it is shown by finite-element-method-based simulations that the capacitance due to fringing field effect and deformations can be compensated by introducing a variable serial capacitor. When a suitable robust controller is used, the full knowledge of the introduced serial capacitor is not required, but merely its boundaries of variation. Based on this model, a robust control scheme is derived using the theory of input-to-state stability combined with backstepping state feedback design. Since the full state measurement may not be available under practical operational conditions, an output feedback control scheme is developed. The stability and performance of the system using the proposed control schemes are demonstrated through both stability analysis and numerical simulation. The present approach allows the loosening of the stringent requirements on modeling accuracy without compromising the performance of control systems.