Passivity-based stability and control of hysteresis in smart actuators

The past decade has seen an increase in the use of smart materials in actua tor design, notably for inclusion in active structures such as noise-reduci ng paneling or vibration-controlled buildings. Materials such as shape memo ry alloys (SMAs), piezoceramics, magnetostrictives and others all offer exc iting new actuation possibilities. However, all of these materials present an interesting control challenge due to their nonlinear hysteretic behavior in some regimes. In this paper, we look at the energy properties of the Pr eisach hysteresis model, widely regarded as the most general hysteresis mod el available for the representation of classes of hysteretic systems. We co nsider the ideas of energy storage and minimum energy states of the Preisac h model, and derive a passivity property of the model. Passivity is useful in controller design, and experimental results are included showing control of a differential shape memory alloy actuator using a passivity-based rate controller.