Two-loop self-tuning cascade control

The stability of two single-input/single-output self-tuning controllers, operating in cascade, is considered for the case when the outer-loop design neglects the inner-loop dynamics. It is shown that the stability properties correspond to those of a single-loop controller with neglected system dynamics: appropriate theorems for the single-input/single-output case can be directly invoked and have a frequency locus interpretation. The results are illustrated by simulation.