Model-based L1 adaptive control of hysteresis in smart materials

Undesired hysteresis and constitutive nonlinearities are present to varying degrees in all smart material based transducers when they are driven at high levels. This motivates the development of adaptive inverse compensation techniques that can approximately linearize the transducer response and also are sufficiently efficient to accommodate model uncertainties and the error introduced by inexact inverse algorithms. In this paper, we employ the homogenized energy model for describing hysteresis, and we incorporate the corresponding inverse filter in L₁ control design to develop a robust adaptive inverse control approach. Asymptotic tracking properties of the proposed algorithm are established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.