H∞ tuning rules for positive position feedback controllers: The single-degree-of-freedom case and beyond

This paper presents an exact H ∞ tuning methodology for a positive position feedback (PPF) controller applied to a single-degree-of-freedom (SDOF) system. To this end, an equivalence between the closed-loop receptances of a PPF controller and a resistive–inductive shunt with a negative capacitance is put forward, which, in turn, enables us to adopt the existing shunt tuning rule in the active control case. The resulting tuning procedure is demonstrated using two numerical examples, namely, an SDOF system and a finite element model of a cantilever beam. Based on the results obtained on the cantilever beam, it is shown that the influence of higher-frequency modes cannot be neglected to obtain effective vibration damping. The design procedure proposed for the PPF controller is then extended to this case and validated using an experimental cantilever beam.