Tuning, multitone instabilities, and intrinsic differences in robustness of adaptive control systems

An example is presented of an adaptive system that becomes unstable when a multitone reference input is applied, although it is stable when the spectral components are applied separately. It is further shown that another scheme, based on an input error instead of an output error in the adaptation, does not exhibit the same instability mechanism. The technique of averaging is used to analyze this phenomenon. The equilibrium points of the averaged system, called the tuned values, are investigated. Results are given on the number of tuned values, their locations, and their stability. The analysis is not only valid for a specific plant, but for a large class of systems