Stochastic Optimal Control to Minimize the Impact of Manufacturing Variations on Nanomechanical Systems

Abstract

This paper presents a control method intended to suppress the effects of manufacturing variations on nanomechanical systems. Often, the resonance characteristics of nanoscale devices are inconsistent, due to unavoidable variations in the fabrication process. This is important because resonant vibrations enhance the sensitivities of the devices. As such, the sensitivities of these systems can be degraded if the device characteristics are not identified. To address this fundamental problem, this paper presents a multidisciplinary method based on control theory, nanotechnology, and communication technology. A stochastic optimal feedback controller is employed to enhance an average sensitivity by regarding the variations as stochastic parameters. This method is applied to nanoscale receivers that detect transmitted binary data based on binary phase-shift keying in communication systems. The proposed method controls the vibrations of carbon nanotubes (CNTs) that serve as the antennas of the receiver. The proposed method is demonstrated via a numerical simulation using nanoscale receivers with the manufacturing variation. The simulation based on experimental data obtained from CNTs shows that the average performance of the devices is enhanced. INDEX TERMS Nanoelectromechanical systems, optimal control, stochastic systems.

High-Sensitivity Thermal Sensing Based on a Single Strain-Assisted Resonator

“…Residual stresses in the fabricated devices are inevitable and can differ from one batch to another due to fabrication variations, which affects the fundamental resonance mode. Minimizing these variations can be done through stochastic optimal control [26], or through different stress engineering techniques such as surface micromachining with properly designed boron diffusion [27] and high temperature rapid thermal annealing processes [28]. In addition, calibration of the devices and using different operating conditions (e.g.…”

Simple Design on Nanoscale Receivers Using CNT Cantilevers

“…Considering a sufficiently large symbol duration T s , x(t) is close to x(t), which justifies the approximation. This approximation has been exploited in our relevant work; the details are provided in [41,Appendix].…”

“…The values of the external voltage V and the CNT length L are set according to the existing work [29]. The gap h 0 between the anode and CNT is set to a designed value that was previously used in a fabrication process [41]. The angular frequency ω in is set to the resonant angular frequency of the CNT such that it is well oscillated.…”

“…Note that the values of the CNT length and gap h 0 are set based on our fabrication process [44], [45], which allows us to control these physical properties. The other parameters m, γ, k, q, and I 1 are set according to those of the existing work [41], which describes the detailed derivation of these settings. In the proposed method, the functions/parameters E r (t), f c (t), θ + in , θ − in , and η are designed using Theorems 1 and 2.…”

“…Through both theoretical and numerical approaches, we demonstrate that the receiver structure is successfully simplified. The results of this study have been applied in our relevant work that focuses on the control of nanomechanical systems [41]. The remainder of this paper is organized as follows.…”