# Stable dynamics of micro-machined inductive contactless suspensions

## TL;DR

This paper introduces a generalized linear model for micro-machined inductive contactless suspensions, analyzing their stability and demonstrating design guidelines through theoretical and applied studies.

## Contribution

It develops a comprehensive linear differential equation model for MIS and establishes stability criteria, including the impossibility of stable levitation without damping.

## Key findings

- Stable levitation without damping is impossible.
- The model applies to symmetric and axially symmetric MIS designs.
- Guidelines for designing stable MIS are provided.

## Abstract

In this article, we present a qualitative approach to study the dynamics and stability of micro-machined inductive contactless suspensions (MIS). In the framework of this approach, the induced eddy current into a levitated micro-object is considered as a collection of m-eddy current circuits. Assuming small displacements and the quasi- static behaviour of the levitated micro-object, a generalized model of MIS is obtained and represented as a set of six linear differential equations corresponding to six degrees of freedom in a rigid body by using Lagrange-Maxwell formalism. The linear model allows us to investigate the general stability properties of the MIS as a dynamic system, and these properties are synthesized in three major theorems. In particular, we prove that the stable levitation in the MIS without damping is impossible. Based on the approach presented herewith, we give general guidelines for MIS designing. In addition to we demonstrate the successful application of this technique to study the dynamics and stability of the symmetric and axially symmetric MIS designs both based on 3D micro-coil technology.