Sliding mode control based on an inverse compensator design for hysteretic smart systems

Ferroelectric (e.g., PZT), ferromagnetic (e.g., Terfenol-D) and ferroelastic (e.g., shape memory alloy (SMA)) materials offer unique design and control capabilities for a range of present and emerging control applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in model-based control designs to achieve stringent tracking requirements. In this paper, we employ a recently-developed extension of the homogenized energy model (HEM) to characterize rate-dependent hysteresis behavior and construct an approximate model inverse for sliding mode control design. 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.