Piezoelectric nanopositioning systems are indispensable in high-precision applications such as Atomic Force Microscopy (AFM), wafer metrology, and medical applications. Enhancing their throughput while maintaining precision presents significant challenges due to lightly damped resonant modes and substantial dynamic variations associated with payload changes. Contemporary approaches, involve the tuning of motion controllers in a dual-closed-loop architecture that incorporates active damping to achieve higher bandwidths. Although these methods function adequately for nominal systems, they fail to meet performance requirements under system variations in resonance modes caused by payload changes and often overlook higher-order dynamics and delays. This research introduces a robust control framework that synthesises H-infinity and Mu synthesis-based controllers by shaping sensitivities within a dual-closed-loop, considering payload variations and prominent higher-order system dynamics. Systematic design guidelines for weighting functions are established to synthesise robust controllers that meet specified performance criteria. The proposed framework is experimentally validated on an industrial nanopositioning system, demonstrating robust performance despite dynamic variations induced by varying payloads.

Piezoelectric nanopositioning systems are widely used in applications demanding high-speed and high-precision motion. Their closed-loop performance is often constrained by lightly damped modes and strong inherent nonlinearity which limit achievable bandwidth and tracking accuracy. Conventional approaches such as notch filters can mitigate resonances but struggle to provide robust damping without sacrificing bandwidth.

This thesis investigates the combination of active damping control and nonlinear reset control to overcome the limitations of linear time-invariant (LTI) feedback methods. A dual-loop control architecture is proposed, employing an active damping controller to suppress dominant modes and enable higher bandwidths, together with a nonlinear CgLp reset controller to recover the phase lag introduced by the damping control. Unlike typical applications, the high nonlinearity of piezoelectric systems makes introducing additional nonlinearity from reset control challenging, particularly when aiming for large phase lead. To address this, a dedicated shaping filter is designed to limit higher-order harmonics and prevent multiple resets, enabling effective phase compensation of up to 20°.

The control architecture is optimized in the frequency domain and validated through simulation and experiments on a piezoelectric nanopositioning platform. Results demonstrate significant improvements in both open- and closed-loop bandwidth and tracking performance compared to conventional LTI controllers, while maintaining stability and robustness. The shaping filter effectively reduces harmonic distortion, ensuring the practical viability of combining reset control with active damping in highly nonlinear, lightly damped systems.

This work shows that the integration of reset control with shaping filter, within a dual-loop active damping framework, can push the performance of nanopositioning systems beyond the traditional LTI control limits.