Transient analysis of an adaptive system for optimization of design parameters

Averaging methods are applied to analyzing and optimizing the transient response associated with the direct adaptive control of an oscillatory second-order minimum-phase system. In order to implement the optimal adaptive design, it is necessary to have knowledge of certain parameters well beyond what needs to be known for adaptive stability, and this may or may not be feasible, depending on the application. However, even if the optimal design cannot by implemented exactly, partial knowledge of the system dominant mode may suffice to improve performance in practical implementations