Adaptive Hysteresis Compensation Using Reduced Memory Sequences

Hysteresis in sensors and actuators can often be effectively compensated for by implementing an inverse hysteresis model in series with the sensor or the actuator. However, an apparent problem enters when the hysteresis characteristics vary over time in an unpredicted manner. Here, we derive an adaptive hysteresis compensation method for the case when we only have observations that are very sparse in time and magnitude. Contrary to previous methods it is based on reduced memory sequences and a preidentified initial model, which makes it possible to use only a few adaption parameters. In particular, we investigate the Preisach model (PM). Using a Bernstein polynomial basis for the PM, it is shown that invertibility translates into linear constraints, which ensures that the overall identification problem for the initial PM is convex. The dependence on PM initial conditions may have negative effects on hysteresis compensation and model adaptation. We give general conditions for losing this dependence and also an upper bound for the maximum error it may cause. The method is experimentally applied to a sensor for measurement of torque in a shaft. At times, the shaft is unloaded and consequently the torque can then be independently observed as being zero. This kind of problem leads to a nonlinear parameterization, but with very few parameters to update, which is successfully achieved using an extended Kalman filter. The method essentially removes the effects of hysteresis, fatigue, and aging for the intended use of the sensor.