Identification of Hammerstein Systems with Rate-Dependent Hysteresis Nonlinearities in a Class of Smart Material-Based Actuators

In [1], we introduced an algorithm to identify rate-independent hysteresis nonlinearities of a class of smart material-based actuators, which is modeled as a Hammerstein system, that is, a cascade of a Prandtl-Ishlinskii (PI) hysteresis nonlinearity with a linear dynamic system. In this paper, we extend the results in [1] to Hammerstein systems with rate-dependent hysteresis nonlinearities. We consider a rate-dependent PI model, which has been used to model rate-dependent hysteresis nonlinearities in smart micro-positioning actuators such as piezoceramic actuators and magnetostrictive actuators. The rate-dependent hysteresis nonlinearity, the linear dynamic system, and the intermediate signal between them are assumed to be unknown. Least squares is used with a finite impulse response (FIR) model structure to identify the linear part of the Hammerstein system. Then, the output of the Hammerstein system is used along with the identified model of the linear plant to reconstruct the unknown intermediate signal. A nonparametric model of the rate-dependent hysteresis loop is obtained by plotting the reconstructed intermediate signal versus the input signal.