Adaptive PPF Control Using a Modified EKF Observer

This thesis presents an approach for suppressing parasitic vibrations in flexure-based structures with varying resonance frequencies by integrating an indirect adaptive Positive Position Feedback controller with an Extended Kalman Filter estimator. Flexure-based systems experience changes in resonance frequency due to elasto-kinematic effects, which require real-time adaptation of the PPF controller parameters to maintain optimal performance. The focus of this study is on the low-frequency vibration mode, therefore a reduced single-degreeof- freedom model is used to represent the system, specifically a cantilever beam. However, to account for the effects of higher resonance modes on the first vibration mode, a direct feed-through term is added to the system model. An EKF algorithm is developed to estimate the system’s resonance frequency by treating stiffness as an additional state variable. The estimated resonance frequency is used to adaptively update the PPF controller parameters, improving vibration suppression, and maintaining robustness. The presence of the direct feed-through term in the system model equations leads to unconventional correlations in the EKF formulation. Therefore, the EKF algorithm is re derived to account for these correlations. Finally, the proposed method is validated through numerical simulations, demonstrating its ability to maintain system stability and effectively suppress parasitic vibrations compared to traditional PPF controllers with fixed parameters.