Adaptive control of plants that are practically impossible to control by fixed-gain control laws

Some LTI plants are practically impossible to control due to extremely small gain and phase margins. These plants tend to be either unstable or nonminimum phase or both. Since practical control of these plants using fixed-gain controllers is not feasible, it is of interest to determine whether adaptive control can overcome these difficulties. To investigate this question, we apply retrospective cost adaptive control (RCAC) to a collection of plants that are practically impossible to control from an LTI perspective. For each plant, we introduce a destabilizing perturbation in order to determine whether or not RCAC can re-adapt in such a way as to compensate for the loss of margin and restabilize the closed-loop system without manual retuning. Since these plants are inherently difficult to control, it is of interest to determine whether or not restabilization is possible and, if so, assess the severity of the transient response.