Though the effect of fringing field in electrostatic parallel-plate actuators is a well-understood phenomenon, the existing formulations often result in complicated mathematical models from which it is difficult to determine the deflection of the moving plate for given voltages and hence, they are not suitable for accurate actuation control. This work presents a new formulation for tackling the fringing field, in which the effect of fringing field is modeled as a variable serial capacitor. Based on this model, a robust control scheme is constructed using the theory of input-to-state stabilization (ISS) and backstepping state feedback design. This method allows loosening the stringent requirements on modeling accuracy without compromising the performance. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation.Keywords Fringing field effect Á Modeling of electrostatic MEMS Á FEM based simulation Á Input-to-state stabilization Á Robust nonlinear control 1 Introduction

This work aims at developing control algorithms for an electrostatically actuated torsional micromirror, extending the operational range of the device to a full 90 • tilt angle. The analytical model of the micromirror equipped with an additional vertical electrode is established. Since the geometrical extent of the device is comparable to the air gap, the effect of the fringing field is also incorporated into the model. It is shown that the considered system is differentially flat and, based on this property, a closed-loop control scheme is constructed for both scanning control and set-point control. In addition, the desired performance can be specified through reference trajectories, allowing the control system tuning to be performed in a systematic way. The simulation results demonstrate the advantage of the developed control scheme over the constant voltage control.

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The purpose of this work is to develop a systematic approach towards synchronisation of two micro-mechanical oscillators inside one optical cavity using feedback control. We first obtain the linear quantum stochastic state space model for the optomechanical system considered in this paper. Then we design a measurement-based optimal controller, aimed at achieving complete quantum synchronisation of the two mechanical oscillators with different natural frequencies, in the linear quadratic Gaussian setting. In addition, simulation results are provided, which show how system parameters impact on the control effect. These findings shed light on the synchronised network of oscillators that can be used for memory and quantum state transfer.