Sliding Mode Control for Inverse Compensated Hysteretic Smart Systems

Ferroelectric (e.g., PZT), ferromagnetic (e.g., Terfenol-D) and ferroelastic (e.g., shape memory alloy (SMA)) materials offer unique capabilities for a range of present and emerging control applications. To fully realize the capabilities these materials offer, model-based control designs must account for the nonideal effects (e.g., creep, rate-dependent hysteresis, and constitutive nonlinearities) that the materials exhibit. In this paper, we employ the homogenized energy model (HEM) to characterize rate-dependent hysteresis behavior, construct an approximate inverse algorithm to compensate the material nonlinearities, and combine this with a sliding mode controller to accommodate uncertainties in the model. We illustrate this in the context of an actuator employing the ferroelectric material PZT but note that the general framework is also applicable to magnetic and shape memory alloy transducers. Through numerical examples, we illustrate the effectiveness of the HEM inverse-based sliding mode design for tracking a reference trajectory in the presence of modeling and inversion errors.