Fine tuning with sigmoid functions in robust fixed point transformation

Abstract

In this paper a novel implementation of the adaptive controllers designed by the use of Robust Fixed Point Transformation is studied. Instead guaranteeing global stability the so designed controllers work smoothly in a bounded region of operation. Both the limits of this region as well as the performance of the controller depends on the basic component of the RFPT-based design, i.e. on the properties of a sigmoid function that can be defined in various manners. In this case a special, easily parameterizable sigmoid was chosen that is widely used in the daily engineering practice, a truncated linear function. This function has a single parameter, its slope, that in the same time determines the width of the window within which the adaptive nature of the controller is guaranteed. It was found that by varying this parameter either the precision of the controller or the frequency of the necessary adaptive tuning can be improved. This statement is substantiated by simulations.