Simultaneous quasi-static displacement and force self-sensing of piezoelectric actuators by detecting impedance

An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation

“…Bafumba et al [36] captured the influence of the control voltage v c (amplitude and frequency) on PEAs with an impedance map (see figure 5). Mansour et al [43] has highlighted the effect of an external force on the PEA's impedance. To summarize, to discriminate Q δ from Q d one needs an electrical component in the antiparallel branch that accounts for humidity, ambient temperature, the control voltage (amplitude and frequency) and the external force applied upon the PEA.…”

“…As already mentioned, SSA based on the piezoelectric direct effect cannot provide a good estimate of the PEA's displacement if its initial state is unknown. Whereas one already knows that applying an electric field and/or an external load induces a deformation in the PEA, recent works have shown that the PEA's impedance is also affected by electric field application [36] and external loads [43]. Therefore, instead of voltage/charge-based SSA, many researchers suggested using the change of PEA's electrical properties as a means to estimate its deformation and perceived external force.…”

“…The permittivity feedback control based on this linear relationship has shown its effectiveness for high-precision positioning [67], [68]. Since then, not only the changing relative permittivity [14], but also capacitance [69], or capacitance and resistance at the same time [43] have been used to estimate the PEA's displacement and/or perceived force.…”

“…Although other configurations can be used to produce the same phase shift, the authors opted for a resistor and capacitor in series. The proposed in-situ impedance measurement was used by Mansour et al [43] in a third order polynomial fit to estimate the PEA's generated displacement and the force applied thereto. To the best of our knowledge, the apparatus and method suggested by [73] constitute the most packageable implementation for SSA based on PEA's change of electric properties.…”

“…More recently, Mansour et al [43] proposed a technique for real-time detection of the variation of the capacitance and resistance of the PEA at a resonance frequency and a third order polynomial fit for the simultaneous estimation of the displacement and force. Conducted experiments with this technique have provided estimates of the displacement and force equivalent or better than previously reported displacement-force SSA techniques that use charge and voltage measurements.…”