Analysis of a self tuning iteration in the presence of noise undermodelling

Self tuning controllers are widespread throughout industry. These controllers use a variety of techniques and algorithms to determine a set of operating parameters for the control system. Research has emphasised the interaction between closed loop experimentation and the closed loop performance. However, an open question exists as to the sensitivity of the resulting control system to these experimental conditions. We examine the sensitivity with respect to the nature of the disturbance. To highlight the issues we examine the case when no external reference signal is applied and analyse stationary points, if they exist, of a simple self tuning algorithm.