Diagonalizing controller for a superconducting six-axis accelerometer

Abstract

A relatively simple MIMO (multiple input, multiple output) controller which converts an instrument with a nondiagonally dominant transfer function matrix into a strongly diagonally dominant device is developed. The instrument, which uses inductance bridges to sense the position of a magnetically levitated superconducting mass, has very lightly damped resonances and fairly strong cross coupling. By taking advantage of the particular structure of the instrument's transfer function matrix, it is possible to develop a relatively simple controller which achieves the desired decoupling. This controller consists of two parts. The first part cancels the nondiagonal terms of the open-loop transfer function matrix, while the second part is simply a set of SISO (single input, single output) controllers. The stability of the closed-loop system is studied using Rosenbrock's inverse Nyquist array technique which produces a simple set of conditions guaranteeing stability. Simulation of the closed-loop system indicates that it should easily achieve its performance goals.<>