Resistive-inductive piezoelectric shunts with negative capacitances and positive position feedback - a comparative study

By drawing a parallel between the controller parameters of a piezoelectric inductive-resistive (RL) shunt with a negative capacitance (NC) and the active control method positive position feedback (PPF), we prove that there exists an equivalence between the controller parameters and their receptance functions. Based on these findings, exact H∞ tuning rules for RL shunts are extended to the use of a NC to eventually find optimal values for the design of a PPF controller. In addition, a closed-form expression of the maximum amplitude of the frequency responses is provided. Using these rules, a thorough comparison in terms of performance
and stability margins between the RL shunt with NC and the PPF is performed and discussed.