Force control of a piezoelectric actuator based on a statistical system model and dynamic compensation

Piezoelectric actuators present a promising option if actuation of small-sized robot joints is considered. They develop forces of several newtons at velocities in the cm/s range while their dimensions and weight remain small as compared to electric motors. This work presents an approach for modelling a class of contemporary, non-resonant translatory piezoelectric actuators. The proposed modelling approach results in three motor models of increasing complexity independently of the low-level piezoelectric properties of the driving elements. The basic model establishes a static relation between motor velocity and drive frequency for a free-moving motor. The second model is a non-linear extension of the first model which introduces external load forces. The final model introduces time-dependent aspects by employing system identification techniques. The final model is used to develop a force compensation mechanism which restores linearity in the motor operation even in the loaded case. Based on the linearised model, standard control design techniques are applicable to design an explicit force controller. Limits on the performance of the controller are derived. The actual performance of the controller is evaluated both in simulations and experiments by pulling on tendons of different elasticity.

Research highlights
► Three control theoretical models of a non-resonant piezoelectric motor are introduced.
► The models are based on high-level least-squares data analysis.
► Linearity in motor operation under load is maintained through compensation technique.
► Explicit force controller is developed and limits on its performance derived.
► The linearised motor system is evaluated in a force control scenario.