Robust QFT control design for a multivariable torsion/bending of rotational nanoscanner

Abstract

This paper proposes a reasonable, practical, and novel method for designing a robust controller for two degrees of freedom nano-electromechanical scanners based on the combination of quantitative feedback theory (QFT) and the Taguchi method. Although the main primary of this paper devotes to rotational control, an investigation of two-degree freedom (rotational/bending) is studied by employing the Taguchi method. A moveable main plate suspended by two nano-beams over a fixed substrate electrode is used to represent the scanner. The nanoscanner is thoroughly analyzed using the most comprehensive modeling design, considering the elastic, electrical, Casimir force and moment, and squeezes film damping. The nanoscanner’s governing equations are initially derived by considering both rotation and deformation. In addition, because the size dependency of materials is significant in ultra-small structures, we developed the constitutive equations within the context of the modified couple stress theory to integrate the effect of scale dependency. Next, system uncertainties have been wholly addressed to achieve an accurate model. As a result, using robust control methods such as quantitative feedback theory to precisely control nano-scanners in the presence of uncertainties is inevitable. The quantitative feedback approach transforms the nonlinear plant into a family of linear uncertain plants in the first part. This is accomplished using a fixed-point theorem, after which appropriate disturbance rejection boundaries are discovered. In this problem, quantitative feedback controllers and checking the system’s stability at any frequency and time are intended to solve the tracking problem and the disturbance rejection issue. Due to the uncertainty associated with the system model’s complexity and accuracy, we employ a QFT controller to control the system. Moreover, because this system has only one input and two outputs, and changing the controller’s gain is complicated, the Taguchi method has been employed to enhance better performance. Nonlinear simulations of the tracking issue are carried out, and the results demonstrate the effectiveness of the developed controllers and prefilters. The findings show that using the suggested approach effectively overcomes the challenges to robust control of a nonlinear rotational nanoscanner, and also the system achieves the best angle and deflection adjustment accuracy.