Passivity-based stability and control of hysteresis in smart actuators

The past decade has seen an increase in the use of smart materials in actuator design, notably for inclusion in active structures such as noise-reducing paneling or vibration-controlled buildings. Materials such as shape memory alloys (SMAs), piezoceramics, magnetostrictives and others all offer exciting new actuation possibilities. However, all of these materials present an interesting control challenge due to their nonlinear hysteretic behavior in some régimes. In this paper, we look at the energy properties of the Preisach hysteresis model, widely regarded as the most general hysteresis model available for the representation of classes of hysteretic systems. We consider the ideas of energy storage and minimum energy states of the Preisach 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.