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Adaptive robust tip tracking control of a class of flexible beams

This paper presents a novel tip tracking control of a class of Euler-Bernoulli flexible beams, which are actuated by a linear motor driven stage. The dynamic model is obtained by the finite-dimensional truncation approach, and transformed into the standard form with unknown parameters. The least square estimation algorithm is designed for on-line parameter adaptation. For the use of adaptive backstepping control design later, the beam dynamics is also transformed into the strict feedback form with the unstable zero dynamics. The desired internal state trajectory is found by dynamical inversion methods based on the on-line estimated parameters. Due to the appearance of non-minimum phase zeros, this stable solution is unique and non-causal. A modified adaptive robust controller is then designed to ensure bounded internal states and a guaranteed output tracking performance with model uncertainties. Comparative experiments are subsequently implemented on a HIWIN linear motor driven flexible beam system, and the results show the excellent tracking performance of the proposed control algorithm.