Dynamical Systems at Queen Mary

This talk covers 2 systems where industry has a strong interest in the application of nonlinear dynamics techniques. The first is the stepper motor, a low-dimensional system which exhibits high periodic, quasiperiodic, and chaotic behaviour. A robust control method is sought which would force  period 1 behaviour over the entire range of dynamics. This system is also interesting because it is low-dimensional, relatively noise free and stationary, and has a well understood and accurate model, yet still exhibits unusual and unexplained phenomena.

The second half of the talk covers an investigation into the nonlinear dynamics of sigma delta modulators (SDMs). SDMs, which are used as A/D and D/A converters, may be described as low dimensional, nonlinear and possibly chaotic, iterative maps. Of critical importance is the prevention of periodic behaviour while at the same time ensuring global stability for a wide range of input signals. Industry is interested in theoretical advances in this area since at present they have little justification for, or ways to improve, the ad-hoc methods they use for limit cycle prevention.