End-point tracking control of a class of flexible beams

This paper presents an adaptive robust tracking control approach for a class of Euler-Bernoulli flexible beams with uncertainties. The desired trajectory is specified for the tip displacement of a flexible beam actuated by a linear motor at the base. The modal truncation approach is used to obtain the dynamics of flexible beams, which are subsequently transformed into a standard form having unstable zero dynamics after neglecting high-order modes. Due to the appearance of non-minimum phase zeros, stable dynamical inversion methods have to be used to obtain the desired internal state trajectory needed for perfect output trajectory tracking. A modified adaptive robust controller (ARC) is then designed to ensure a stable output tracking error dynamics with bounded internal states and a guaranteed performance robustness to uncertainties. Simulation results are presented to illustrate the effectiveness of the proposed ARC algorithm.