Projection and Barrier Lyapunov-Based Controller Update Laws in MRAC Structure for Flexible Satellite Launch Vehicles

Abstract

This paper investigates adaptive flight control design strategies which are robust to a wide range of both parametric and non-parametric uncertainties for a highly non-linear, time-varying and under-actuated launch vehicle system. In general, scheduled PID controllers are designed for the rigid body dynamics of the launch vehicle and structural filters/compensators are used to stabilize underactuated dynamics such as slosh and flexibility. In this work, two stable Lyapunov-based adaptive controllers are designed with full-state feedback. In the first controller, adapted gains are constrained to be within the limits defined by the user using a rectangular projection operator. In the second controller, tracking error is also constrained using a barrier Lyapunov function. States of the under-actuated dynamics and rigid body dynamics are estimated from the noisy attitude and attitude rate measurements using an extended Kalman filter. Tracking and regulation control studies are conducted to show the efficiency of the proposed controller update laws using different command signals.