High precision structured H∞ control of a piezoelectric nanopositioning platform.

The inherent weakly damped resonant modes of the piezoelectric nanopositioning platform and the presence of model uncertainty seriously affect the performance of the system. A structured H∞ design is used in this paper to solve the accuracy and robustness problems respectively using a two-loop control structure. The multiple performance requirements of the system are constituted into an H∞ optimization matrix containing multi-dimensional performance diagonal decoupling outputs, and an inner damping controller d is set according to the damping of the resonant modes; the second-order robust feedback controller is preset in the inner loop to improve the robustness of the system; the tracking controller is connected in series in the outer loop to achieve high accuracy scanning; finally, the structured H∞ controller is designed to meet the multiple performance requirements. To verify the effectiveness of the proposed structured H∞ control, simulation comparison experiments are done with the integral resonant control (IRC) and H∞ controller. The results demonstrate that the designed structured H∞ controller achieves higher tracking accuracy compared to the IRC and H∞ controllers under grating input signals of 5, 10, and 20 Hz. Moreover, it has good robustness under 600g and 1000g loads and high frequency disturbances close to the resonant frequency of the system, meeting multiple performance requirements. Compared with the traditional H∞ control, yet with lower complexity and transparency, which is more suitable for engineering practice applications.