MIMO H_μ Feedback Controller With Feedforward Compensator for Scanning Tunneling Microscope Having 3D Cross-Coupled Piezoelectric Actuator

Abstract

Scanning Tunneling Microscope (STM) is used to generate the surface image of any conducting sample surface with an atomic-scale resolution. A multi-axis 3D piezoelectric actuator is attached with the STM tip to move it in horizontal (x and y) and vertical (z) directions. The purpose of control design is to achieve precise reference tracking for horizontal 2D scanning system and to keep the tunneling current constant in the vertical direction in the presence of all possible disturbances. A usual practice is to design independent single-input-single-output (SISO) controllers for individual x, y and z axes by neglecting the cross-coupling dynamics of the multi-axis 3D piezoelectric actuator. In this paper, a complete 3D STM system, without neglecting the cross-coupling dynamics as well as the hysteresis nonlinearity of the actuator, is first mathematically modeled. The parameters of the hysteresis model are identified from the real-time experimental data by using the nonlinear least-squares curve fitting problem. A feedforward compensator is then designed without finding an inverse hysteresis model to avoid any inverse modeling complexity. Then, two control strategies (SISO and multi-input-multi-output (MIMO) $\text{H}_\infty $ feedback controllers cascaded in series with the feedforward compensator) are investigated for an overall 3D system. Three different scanning trajectories (raster, spiral and Lissajous) are considered to analyze and compare the performance of SISO and MIMO control schemes. In the presence of cross-couplings, an average improvement of 83% in reducing the variations of the tunneling current is achieved with the suggested MIMO control scheme as compared to the generally used SISO control scheme for STM.

Keywords

• Cross-coupling
• feedforward compensator
• hysteresis
• MIMO Hμ feedback controller
• scanning tunneling microscope