"TII-26-1146"

"To enhance the hysteresis modeling accuracy of piezoelectric positioning stages, this study proposes an integrated adaptive identification method for the Hammerstein model. First, guided by frequency characteristic analysis, the system is modeled as a Hammerstein structure comprising a static hysteresis nonlinearity cascaded with a dynamic linear subsystem. Second, to address the unmeasurability nature of the intermediate variable, a filtering operation combined with auxiliary variable construction is employed to formulate the parameter estimation error using solely input-output data. Subsequently, an adaptive parameter estimation law incorporating an improved barrier function is developed, and the prescribed time and bound convergence of the estimation error is rigorously proven via Lyapunov stability analysis. Finally, experimental results demonstrate that the proposed method outperforms comparative recursive and two-step methods in both convergence rate and steady-state accuracy of parameter estimation, providing a reliable modeling foundation for high-performance adaptive control."