H ∞ controller design for high sensitivity fringe tracking

The next generation of fringe tracker (FT) is intended to allow continuous fringe observation and to improve significantly the sensitivity of the interferometer. A promising control approach is presented to cope with contradictory requirements. The FT system must be accurate and stable, which implies high frequency sampling of the optical path differences introduced by the atmosphere and the interferometer vibrations. It must also be as sensitive as possible, which needs to minimize the sampling frequency. The optimum between these concurrent requirements must be maintained through atmospheric and instrument conditions that change very rapidly. We consider a discrete time feedback system where the controller design is based on the frequency domain method. Performance is considered through the use of the H∞ norm. This approach provides the best tradeoff between the largest sampling time and the validity of the discrete time feedback system. The effectiveness of the presented approach is illustrated through dedicated simulations involving a realistic case study.