A simulator study of a two-parameter adaptive system

The use of sinusoidal parameter perturbation applied to a feedback control system to obtain an adaptive scheme which optimizes the system for changes in inputs and/or system parameters is discussed. It is shown that if a parameter perturbation signal is cross-correlated with the system error squared, the correlator output can be used to adjust the parameter to minimize the mean-square error. Other error measures may also be used. Two or more parameters may be simultaneously adjusted if they are perturbed at different frequencies, and each provided with an independent adaptive loop. A computer simulation of a third-order system having two adjustable parameters was examined for a variety of inputs including random signals. It is shown that the scheme minimizes the mean-square error in all cases.