Abstract
Given in this paper is a design method of parameter adjusting systems. Parameter optimization is essential for the adaptive systems and also is applicable to the identification problems. The identifying system considered in this paper employs the method of the steepest descent. Parameters are adjusted at the speed proportional to the gradient of the penalty function. Although this method is essentially equivalent in value to the parameter perturbation method, it does not require the perturbation signals but utilizes the partial derivatives concerning the parameters of the model in the system. Thus, a simpler system can be obtained even if there are many parameters to be adjusted. In this paper, a construction method of the parameter adjusting identification system is developed and then an investigation is carried out about the dynamic characteristics of the parameter adjusting processes. Approach to the dynamics is conducted through differential equations. The Hill's differential equations play an important role in this investigation. Noteworthy results are as follows: The parameter adjustment can be done as rapidly as the order of e-t/2T, where T is the time constant of the averaging element in the parameter adjusting loop. The time constant T can be taken as small as a quarter of the period of the lowest frequency component passing through the system to be measured. A simple design procedure is also given to assure this extremely rapid parameter adjustment.
