Nonlinearity Effects Reduction of an AFM Piezoelectric Tube Scanner Using MIMO MPC

The design of a controller which compensates for the effects of creep, hysteresis, vibration, and cross-coupling in a piezoelectric tube scanner (PTS) is presented in this paper. The PTS is a key nanopositioning component installed in a commercial atomic force microscope (AFM) to perform scanning. The impediments to fast scanning due to PTS dynamics are: 1) the presence of mechanical resonances; 2) nonlinearities due to the piezoelectric characteristics; and 3) the cross-coupling effect between
${x}$
- and
${y}$
-axes in the PTS. In this paper, a multi-input multi-output model predictive control (MPC) scheme is designed to counteract the effects of creep, hysteresis, vibration, and cross-coupling in a PTS. Also, a damping compensator is included to suppress the vibration effect at its resonance frequency. The proposed controller achieves a high closed-loop bandwidth and significant damping of the resonant mode. To evaluate the performance improvement using the proposed control scheme, an experimental comparison with the existing AFM proportional-integral (PI) controller and a single-input single-output (SISO) MPC is conducted. Enhancement in the scanning speed up to 125 Hz is observed with the proposed controller.