[Paper Review] A New Model of Fringing Capacitance and its Application to the Control of Parallel-Plate Electrostatic Micro Actuators

Maryam Hosseini, Zhu, G.+1 more|PolyPublie (École Polytechnique de Montréal)|Nov 21, 2007

Advanced MEMS and NEMS Technologies8 citations

TL;DR

This paper proposes a simplified model of fringing capacitance in parallel-plate electrostatic micro actuators by representing its effect as a series capacitor, enabling more tractable control design. Using input-to-state stabilization (ISS) and back-stepping, the authors develop a robust control scheme that ensures stability and performance, validated through numerical simulation and a new analytical formulation that improves predictability of actuator deflection under voltage input.

ABSTRACT

Fringing field has to be taken into account in the formulation of electrostatic parallel-plate actuators when the gap separating the electrodes is comparable to the geometrical dimensions of the moving plate. Even in this case, 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 therefore to predict the necessary applied voltages for actuation control. This work presents a new method for the modeling of fringing field, in which the effect of fringing field is modeled as a serial capacitor. Numerical simulation demonstrates the suitability of this formulation. Based on this model, a robust control scheme is constructed using the theory of input-to-state stabilization (ISS) and back-stepping state feedback design. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation.

Motivation & Objective

• To address the challenge of modeling fringing fields in parallel-plate electrostatic micro actuators when the gap is comparable to plate dimensions.
• To simplify existing complex mathematical models of fringing capacitance for easier deflection prediction and control design.
• To develop a robust control scheme that ensures system stability under uncertain dynamics and input variations.
• To validate the effectiveness of the proposed model and control strategy through numerical simulation and stability analysis.

Proposed method

• Model the fringing field effect as an equivalent series capacitor, simplifying the overall capacitance formulation.
• Integrate the new fringing capacitance model into the electrostatic actuator dynamics to derive a tractable system model.
• Apply input-to-state stabilization (ISS) theory to ensure robustness against disturbances and uncertainties.
• Use back-stepping state feedback design to construct a stabilizing control law for the actuator system.
• Formulate the control law based on Lyapunov-based stability analysis to guarantee asymptotic stability.
• Validate the control performance and stability through numerical simulation of the closed-loop system.

Experimental results

Research questions

• RQ1 How can fringing capacitance be modeled in a way that simplifies the control design of electrostatic micro actuators?
• RQ2 What control strategy ensures robust stability when the actuator dynamics are nonlinear and subject to uncertainties?
• RQ3 Can a simplified capacitance model maintain accuracy while enabling practical control implementation?
• RQ4 How does the proposed control scheme perform under varying voltage inputs and system disturbances?

Key findings

• The proposed fringing capacitance model effectively captures the field distortion effect using a series capacitor representation, simplifying system modeling.
• The control scheme based on ISS and back-stepping ensures asymptotic stability of the actuator system under bounded disturbances.
• Numerical simulations confirm that the control law achieves desired deflection tracking with improved robustness and convergence.
• The model enables accurate prediction of actuator deflection for given applied voltages, enhancing control design predictability.