Stability and operating constraints of adaptive LMS-based feedback control. (Q1868072)

Filtered-E control (Eriksson, 1991; Eriksson and Allie, 1993; Elliot and Nelson, 1993) and filtered-U control have enjoyed widespread usage in both feedforward and feedback controller architectures (Kuo and Morgan, 1996). But, while some systems have stable convergence, others diverge. Here, the authors study two distinct reasons to explain these unstable behaviours: feedback loop instabilities and LMS algorithm divergence. Both are examined analytically in terms of the plant estimate for stable systems. The authors show that for an inaccurate plant estimation in the control of a stable plant, the controller can become unstable. On the other hand, if the controlled plant is unstable, no choice of the plant estimate can guarantee stability during adaptation. These analytical results are illustrated by two simulations. While the majority of the discussion in the paper focuses on filtered-E control the conclusions are extended to the more general version of filtered-U forms as well as to the control of unstable self-excited plants.