Flatness-based tracking control of a piezoactuated Euler–Bernoulli beam with non-collocated output feedback: theory and experiments†

Abstract

This paper considers the combination of flatness-based motion planning and feedforward control with output feedback to achieve robust tracking of prescribed trajectories for the tip displacement of a multi-layered piezoelectric cantilever beam. Thereby, the flatness property of the distributed-parameter beam model is exploited to derive the infinite-dimensional tracking error system, which serves as the basis for the design of the output error feedback control. The stability of the resulting closed-loop system involving the infinite-dimensional beam model is proven in an input/output sense by utilizing a Nyquist-type stability criterion. Experimental results illustrate the high tracking performance in view of exogenous disturbances. The presented approach provides a systematic extension of the two-degrees-of-freedom control concept to distributed-parameter systems. †This paper is dedicated to Prof. Michel Fliess on the occasion of his 60th birthday.