Odd-harmonic repetitive control for high-speed raster scanning of piezo-actuated nanopositioning stages with hysteresis nonlinearity

In raster scanning applications of atomic force microscopies, precisely tracking periodic triangular trajectories is the major objective of nanopositioning stages. Considering the fact of periodic operations, the repetitive control technique becomes promising and has been recently developed to reduce tracking errors. In our new experiments, it is found that, with triangular reference input, the hysteresis nonlinearity mainly affects the system at the odd harmonics of the input signal. In this sense, an odd-harmonic repetitive control (ORC) strategy is proposed to handle the hysteresis nonlinearity, with the hysteresis treated as the odd-harmonic periodic disturbance. Therefore, it avoids the modeling and inverting of the complex hysteresis nonlinearity. Another benefit of the developed ORC strategy is that it can also account for the tracking errors caused by the linear dynamics effect. To verify the effectiveness of the ORC strategy, real-time experiments are performed on a custom-built piezo-actuated nanopositioning stage. Experimental results show that the developed ORC strategy achieves precise tracking of 1562.5-Hz triangular trajectory with the hysteresis nonlinearity mitigated to a negligible level, which demonstrates the feasibility and effectiveness of the developed ORC strategy on hysteresis compensation during high-speed raster scanning.