Robust Control of a Two-Degree-of-Freedom Flexure-Based Nanopositioner for Planar Scanning Tasks

A two-degree-of-freedom (2-DoF) flexure-based nanopositioner is investigated for the planar scanning tasks, and a robust controller design scheme based on the convex inner approximation method is proposed. In practice, a flexure-based mechanism is usually represented by a second-order dynamic model. However, the second-order dynamic model cannot precisely fit the real system dynamics, and the model mismatch renders it difficult to achieve satisfying system performance in applications. Such a mismatch includes the parameter uncertainties caused by inaccurate model identification, different motion conditions, as well as high-order resonances. Note that if the controller is not well designed, the high-order resonances can be frequently activated, especially when the system input variation is significant. Therefore, to deal with the above impediments, a novel scheme for the robust controller design is proposed, with the variation of system input considered. In the proposed scheme, a subset of gains that can stabilize the closed-loop system is characterized elegantly via an inner approximation method considering the model uncertainties, and the formulated optimization problem regarding the determination of the controller parameters can be efficiently solved. Furthermore, the proposed scheme guarantees the performance regarding the H
2
-norm level and limits the H
∞
-norm level in a designated range. Finally, numerical optimization and comparative experiments are carried out, and the results evidently show the effectiveness of the proposed method.