Mean square error versus parameter curves for model reference adaptive systems with sinusoidal input

Abstract

The nature of performance index versus parameter curves determines the applicability of perturbation method. Mean square error (MSE) is taken as the PI in this paper. It is shown that with sinusoidal input there exists one maximum and one minimum for the MSE versus parameter curve irrespective of the order of the transfer function and irrespective of the model being an exact replica of the system or not. The location and value of the parameter corresponding to extremum performance index are found to be dependent on the adjustments made in the other adaptive loops (i.e. interaction between the adaptive loops) and the frequency of input. It is therefore concluded that the perturbation method in its simplest form cannot be applied without suitable modifications, and the necessary modifications are suggested. Three typical examples arc included to give a better understanding of the nature of adjustment to be done when two parameters are varying.