Modern H-Infinity Control Design for Ultra-Precise Micro/Nanopositioning with Hysteresis Compensation

Micro/nanopositioning is an important aspect of research in micro/nanotechnology where piezoelectric actuators are widely used for different applications. These actuators generally exhibit nonlinear hysteresis characteristics. The compensation of hysteretic behavior of piezoelectric actuators is mandatory for ultra-precise micro/nanopositioning. This paper proposes a modern H
_∞
feedback controller for ultra-precise micro/nanopositioning with hysteresis compensation. To design the proposed controller, first the dynamics of the considered piezoelectric actuator system is identified experimentally. Then, the mixed-sensitivity H
_∞
control design methodology is adopted in order to achieve the desired performances of the considered system. The performance of the proposed controller is compared with a general approach of using inverse Prandtl-Ishlinskii hysteresis model as a feed-forward controller. The achieved experimental results with H
_∞
feedback controller show improved performances with respect to those obtained with inverse Prandtl-Ishlinskii hysteresis model. The peak to peak tracking error of less than 1% for the desired displacement of 12 μm with tracking frequency of 10 Hz is achieved.