Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity. In this paper, a Hammerstein-like model based on the support vector machines (SVM) is proposed to capture the rate-dependent hysteresis nonlinearity. We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model. Subsequently, a two-degree-of-freedom (2DOF) H robust control scheme for the rate-dependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator (PEA) for real-time precision trajectory tracking. Simulations and experiments on the structure verify both the effectiveness and the practicality of the proposed modeling and control methods.