Hysteresis Modeling and Direct Inverse Compensation Based on Dynamic Time Warping

Actuators based on smart materials often exhibit severe hysteresis nonlinearity. This paper proposes a hysteresis modeling method and a direct inverse model based on the Dynamic Time Warping (DTW) algorithm by analyzing the time-domain characteristics of the input and output signals of actuators with hysteresis. Unlike traditional methods that involve modeling hysteresis loops and solving their inverse models, this study uses DTW to align the input and output signals in the time domain, capturing their temporal discrepancies. An index matrix is introduced to quantify the delay of the output signal relative to the input signal, enabling highly efficient and convenient modeling of hysteresis. The proposed hysteresis model eliminates the need for inverse model computation. Instead, inverse compensation can be achieved simply by using one row of the index matrix obtained during the identification process. Experimental results validate the proposed methods, demonstrating their high accuracy and convenience for modeling asymmetric hysteresis and feedforward compensation.