Global Stability Analysis of an Adaptively-Controlled Mixing Tank Experiment

An adaptive controller for a mixing tank is developed and experimentally implemented, and the effects of plant/reference-model mismatch are studied. The ranges of mismatch where the desired operating point is locally, but not globally, stable are predicted with numerical bifurcation analysis techniques and verified experimentally. In the cases of multistability, finite perturbations which destabilize the set point are quantified by computing the boundaries separating the sets of initial conditions which asymptotically approach each attractor. These basins of attraction are found to sometimes consist of disconnected and distorted structures. This results from the nonunique inverse-time dynamics of the controlled system and can be studied by considering the behavior of the reverse-time map along the basin boundaries.