Replacement of parameter tuning with simple calculation in adaptive control using “Sigmoid generated fixed point transformation”

Lately a systematic method was presented for the generation of whole families of Fixed Point Transformations that can be used in nonlinear adaptive control of Single Input - Single Output (SISO) as well as Multiple Input - Multiple Output (MIMO) systems as alternatives of Lyapunov's direct method. This transformation was called Sigmoid Generated Fixed Point Transformation (SGFPT). This paper introduces new improvements on this alternative approach. It is shown that in contrast to the original Robust Fixed Point Transformation (RFPT), for guaranteeing the global stability of the control, instead of tuning, a simple estimation can be done for one of the adaptive control parameters. The novel method is demonstrated by the adaptive control of a 2 Degree of Freedom (DoF) TORA system. Simulation results validate that the suggested approach is beneficial and ensures satisfactory performance.