Diagonalizing controller for a superconducting six-axis accelerometer

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