Ongoing technological advancements demand the need for increasingly fast and precise motion systems, in which piezoelectric nanopositioners play a key role. However, due to their inherent dynamics, achieving open loop bandwidths close to the first resonance has proven to be challenging. An additional limitation arises from linear control, which is constrained by the Bode's phase-gain relationship and the waterbed effect. These limitations make achieving good tracking and disturbance rejection performance while maintaining stability and robustness at high bandwidth challenging.
Given the difficulty of achieving bandwidths close to the first resonance, this thesis investigates the even more challenging problem of extending the open loop bandwidth beyond the first resonance.
To address the challenge, a linear controller with barely positive stability margins is designed to achieve a bandwidth beyond the first resonance. A reset controller is then added on top of the linear controller to achieve stability and robustness without affecting the gain behavior. Unlike previous applications, here the nonlinearity introduced by the reset controller is extremely high, making the handling of higher-order harmonics particularly challenging. To address this, a novel shaping filter is introduced in order to reduce the magnitude of higher-order harmonics, along with pre- and post-filters which smooth the control action signal and keep it within the input saturation constraints.
The controller is fine tuned and validated in simulation using both frequency and time domain tools, and later implemented in an experimental test setup. Simulations show that achieving stable and robust post-resonance control is feasible, however mismatches between simulations and experiments appear during experiments. It is found that these are caused by an excessive amount of nonlinearities in the reset controller, making DF and HOSIDF tools from simulations unreliable. Nonetheless, experiments demonstrate that post-resonance control is feasible, and achievable only with reset control, outperforming the linear controllers currently used in industry.