Robust-inversion-based 2DOF-control design for output tracking: Piezoelectric actuator example

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In this article, a novel robust-inversion-based two-degree-of-freedom (2DOF)-control approach for output tracking is proposed. The inversion-based feedforward control techniques have been successfully implemented in various applications. Usually the inverse feedforward input is applied by augmenting it with a feedback controller - to account for adverse effects such as dynamics variations and disturbances. However, currently such an integration, of the feedback control to the inversion-based feedforward control, is ad-hoc, and may not lead to an optimal complementation of the feedback control with the inversion-based feedforward control. The contribution of this article is a systematic development of designing the inversion-based feedforward-feedback 2DOF controller. First, a novel robust system-inversion method is proposed which achieves a guaranteed tracking performance of the feedforward control for bounded dynamics uncertainties. Secondly, the bound of the tracking error of the feedforward control is utilized in the Hinfin robust control framework to design the feedback controller which complements the feedforward control. Based on the concept of Bode's integral, it is shown that the feedback bandwidth can be improved from that by using feedback alone, with no loss of tracking precision and robustness stability. We illustrate the proposed approach through experiments on a piezotube actuator used for precision positioning on an atomic force microscope (AFM).