Loop-shaping is widely used in precision motion control, but conventional approaches — focused on phase margin and open-loop gain — are inadequate for piezo positioning systems where open-loop phase critically affects performance. This paper proposes generalized loop-shaping guidelines tailored for nonlinear piezo-actuated stages. A constant-in-gain lead-in-phase reset controller is developed to implement the guidelines by overcoming waterbed effect in linear control. An intuitive methodology for shaping filter design is presented to ensure reliable reset control implementation. Using (higher-order) sinusoidal input describing functions, nonlinear motion control is designed. Experiments demonstrate closed-loop bandwidth flatness (±[jls-end-space/]1 dB) and enhanced sensitivity function.

In this paper, a robust nonlinear control scheme is designed for the motion control of a class of piezo-actuated nano-positioning systems using frequency-domain analysis. The hysteresis, the nonlinearity in the piezoelectric material, degrades the precision in tracking references with high frequency contents and different travel ranges. The hysteresis compensation by the inverse model, as the state-of-the-art solution, is not reliable alone. Therefore, a control framework with robustness against the remaining nonlinearity is needed. It is shown that there is an unavoidable limitation in robust linear control design to improve the performance. A robust control methodology based on a complex-order element is established to relax the limitation. Then, a constant-in-gain-lead-in-phase (CgLp) reset controller is utilized to realize the complex-order control. The control design is based on the sinusoidal input describing function (SIDF) and the higher-order SIDF (HOSIDF) tools. A constrained optimization problem is provided to tune the control parameters. The achieved improvements by the CgLp control is validated by the simulation.