An Operator-Based Controller Concept for Smart Piezo-Electric Stack Actuators

Abstract

Solid-state actuators based on piezoelectric materials are characterized by forces reaching the kilonewton range and reaction times on the order of microseconds. However, the displacements are low because the maximum strain amounts to 1.5.. 2 ‰ If they are used in micropositioning drives, the piezoelectric stack actuators are mainly driven with high voltages vt) to achieve the largest possible displacements st). In large-signal operation the actuator characteristic shows strong hysteresis and creep effects which can be regarded as undesired internal disturbances for the micropositioning process. Normally piezoelectric actuators are subsystems in an overlying mechanical structure. During the micropositioning process the mechanical structure reacts with a force f(t) against the piezoelectric transducer. This reaction force has a strong influence on the displacement and can therefore be regarded as an undesired external disturbance for the micropositioning process. Under normal operating conditions the displacement of the piezoelectric stack transducer can be seperated, at least in a first order approximation, into a creep and hysteretic voltage-dependent part described here by a scalar operator rΓ _a and a linear force-dependent part characterised by the small-signal elasticity S

$$ s(t) = \Gamma _a [v](t) + S \cdot f(t). $$

((1))

Equation (1) is the so-called operator-based actuator model of the piezoelectric stack transducer [6].