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 …