MIMO $$H_{\infty }$$ H ∞ Integral Control Design for 2D Tunneling Current Measurement System: STM Application

Abstract

Ultrahigh measurement precision of the tunneling current (which is a quantum mechanical phenomenon and of the order of nano-amperes) is one of the key requirements in many of its applications like in STM (Scanning Tunneling Microscope). STM is used to generate the image of any conducting sample surface with atomic scale resolution, and the image quality highly depends on the precision of the tunneling current. Multi-axis piezoelectric actuator is attached with the tip of STM to move it precisely over the sample surface in vertical as well as in horizontal directions. The desired precision of the tunneling current is adversely affected not only because of the sample surface variations and the measurement noise, but also because of the cross-couplings of multi-axis piezoelectric actuator. In this paper, a dynamic modeling of MIMO (multi-input-multi-output) plant having vertical tunneling current measurement system with horizontal scanning system in the presence of cross-coupling phenomenon is proposed. Then, a robust MIMO \(H_{\infty }\) integral controller is analyzed in order to achieve the desired measurement precision of the tunneling current. Results are compared with SISO (single-input-single-output) \(H_{\infty }\) integral controller and the conventionally used classical PI (proportional-integral) controller. The simulation results achieved with proposed MIMO \(H_{\infty }\) integral controller show improved performances than those obtained with SISO \(H_{\infty }\) integral controller and classical PI controller.