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

In this paper, a novel robust inversion-based 2-DOF control approach for output tracking is proposed. Inversion-based feedforward control techniques have been successfully implemented in various applications. Usually, to account for adverse effects such as dynamics variations and disturbances, the inverse feedforward control is applied by augmenting it with a feedback control. However, such effects have not been directly addressed in existing system-inversion methods, and the integration of the feedback control with the inversion-based feedforward control is performed in an ad hoc manner, which may not lead to an optimal complement of the inversion-based feedforward control with the feedback control. The contribution of this paper is the development of the following: 1) a robust system-inversion approach to directly account for and then minimize the dynamics-uncertainty effect when finding the inversion-based feedforward controller, and 2) a systematic integration (of such a feedforward controller) with a robust feedback controller. The proposed robust inversion method achieves a guaranteed tracking performance of the feedforward control for bounded dynamics uncertainties. Then, the quantified bound of the feedforward control tracking error is utilized in designing an H_∞ robust feedback controller to complement the feedforward control. Based on the concept of Bode's integral, it is shown that the feedback bandwidth can be improved from that obtained by using feedback alone. We illustrated the proposed approach by implementing it in experiments on a piezotube actuator of an atomic force microscope for precision positioning.