An adaptive control system with sinusoidal parameter perturbation

An adaptive control system is analyzed in order to investigate system behavior. The system consists of a model system in parallel with a system whose parameters are adjusted or dithered sinus-oidally. The difference in output (error) of the two systems is squared and used as a performance criterion in optimizing the parameters of the adjusted system. It is shown that the deviation from the optimum parameter value is a linear function of the component of error squared at the dither frequency if initial error is not too large. If the initial error is large, the deviation may be independent of error squared in which case the system will not adapt.