Model Reference Adaptive Control Using a New Adaptation Law Based on Power-Series Quadratic Lyapunov Functions for the Single Degree of Freedom Wing Rock Phenomenon

In this research, new adaptation law for updating parameters of the model reference adaptive control and the model reference adaptive control with feedback integrators for a specific class of nonlinear systems with additive parametric uncertainty are presented. The innovation presented in this paper is the consideration of a new form for Lyapunov functions candidate to prove the stability of the closed-loop system. In general, Lyapunov functions candidate, which is used to prove stability and to derive rules for updating control parameters, include two sets of quadratic expressions. The first quadratic expression contains the trajectory tracking error and the second category includes the error of estimating the controller parameters. In this research, it is proved that by selecting quadratic expressions including the variable of trajectory tracking error in the form of power series, a new adaptation law is obtained that includes quadratic expressions in terms of the variable of tracking error in the form of power series. This type of adaptation law can be considered as an adaptation law derived from quadratic Lyapunov functions, except that the gain adaptation matrix parameters vary with time. It has been shown that by using an adaptive controller with a feedback integrator, the tracking error tends to zero faster and the flying object roll angle tracks the reference trajectory after a shorter time. In order to evaluate the control performance of the designed controllers, the system of one degree of freedom of the Wing Rock phenomenon has been used.