Chaos patterns in a 3 Degree of Freedom control with Robust Fixed Point Transformation

The controllers designed by Lypunov's 2nd method normally have global stability but do not concentrate on the details of the primary intent of the designer: the details of the tracking error relaxation. They have a huge number of arbitrary adaptive control parameters that -from the engineering point of view- are hard to design for prescribed detailed behavior of the controlled system. In the past few years a new method that concentrates on the design intent, easy to produce and has only a few adaptive control parameters was invented: the Robust Fixed Point Transformation (RFPT). According to ample simulations it is seems to be a good choice, but it has only local stability yet. Though its present form can be satisfactory for solving most of the cases, sometimes ancillary methods are needed for maintaining or restoring its convergence. It was recently discovered for one and two degree of freedom systems that when the controller quits the region of stability it still guarantees good tracking at the price of huge chattering that also was reduced and stopped. In this paper it will be shown that in the adaptive control of the 3Degree Of Freedom (DOF) system similar phenomena happen and the controller can be stabilized by similar methods.