A Port-Controlled Hamiltonian Approach to Control of an Electrostatic MEMS Actuator
Authors
D. H. S. Maithripala, Jordan M. Berg, W. P. Dayawansa
Abstract
While mechanical, electrical and electromechanical systems may exhibit complex nonlinear dynamics, their behavior is typically governed by relatively simple underlying principles of energy transfer. Modeling methodologies that seek to capture this underlying order give rise to a special form of the equations of motion, called a port controlled Hamiltonian structure with damping (PCHD). Often the natural behavior of a system is unacceptable for a desired application, and must be modified. A body of work on passivity-based control exists that shows how to use Casimir functions—certain invariant quantities of the open-loop PCHD—to reshape the natural dynamics in a desired way. We seek to apply this approach to an electrostatically-actuated MEMS device subject to the saddle-node bifurcation known as snap-through. We show that the equations describing this system do not have an appropriate Casimir function, but that they can be suitably modified through an implementable output feedback. We fully characterize the Casimirs of the modified system, and show how they may be used to eliminate snap-through. Unfortunately the transient behavior of the resulting closed-loop system is governed by the damping of the mechanical subsystem, which may or may not provide adequate performance.
Citation
- Journal: Microelectromechanical Systems
- Year: 2003
- Volume:
- Issue:
- Pages: 687–692
- Publisher: ASMEDC
- DOI: 10.1115/imece2003-42461
BibTeX
@inproceedings{Maithripala_2003,
series={IMECE2003},
title={{A Port-Controlled Hamiltonian Approach to Control of an Electrostatic MEMS Actuator}},
DOI={10.1115/imece2003-42461},
booktitle={{Microelectromechanical Systems}},
publisher={ASMEDC},
author={Maithripala, D. H. S. and Berg, Jordan M. and Dayawansa, W. P.},
year={2003},
pages={687--692},
collection={IMECE2003}
}