Improving Positioning Performance of Positive Position Feedback Scheme with Delay Compensation

Piezoelectric stack-actuated serial kinematic nanopositioning stages are widely utilized in nanopositioning applications but are plagued by challenges such as hysteresis, creep, and mechanical resonance, which degrade system performance. Closed-loop control, particularly positive position feedback (PPF) control, has shown the potential in mitigating these issues and achieving robust nanopositioning. This study focuses on evaluating the performance of PPF control in nanopositioning, specifically considering closed-loop stability. To address the inherent time delay effects in piezoelectric stack actuated nanopositioners, a PPF controller is designed to achieve stable and robust operation. The impact of time delay in flexure nanopositioners is analyzed through simulation-based frequency response analysis, revealing the relationship between the period of the peak-to-peak of the error signal simulation and the performance of the PPF controller. The study demonstrates that a gain of 7.84 dB is required for the PPF controller with delay to become unstable. The design methodology incorporates second-order Padé approximations, allowing the system to be represented by eight poles. Among these poles, five are determined by the controller's parameter design, while the remaining three are influenced by the system's delay. To ensure desirable system behavior, the five designed poles are positioned closer to the imaginary axis compared to the three poles introduced by the delay. The analysis identifies an upper limit of
$\tau=342us$
for the permissible delay, beyond which the poles introduced by the delay surpass some of the designed poles' proximity to the imaginary axis. This situation undermines the dominance of the designed poles and compromises system performance. The findings emphasize the critical relationship between the error signal simulation and the performance of the PPF controller. This study provides valuable insights for improving controller design and ensuring stable nanopositioning systems. The results also highlight the importance of addressing time delay effects in flexure nanopositioners to achieve robust and reliable performance.