Adaptive Zoom Fractional-Order Control for Liquid Tunable Lens via High-Performance Implicit Inverse Fractional-Order Command Filtering

The giant magnetostrictive actuator (GMA)-driven liquid tunable lens (LTL) offers great potential for rapid and precise focus adjustment, yet its nonlinear dynamics with asymmetric hysteresis and time-delay pose significant control challenges. This article proposes a new fractional-order control framework to address the aforementioned issues. First, a novel adaptive fractional-order control algorithm with command filtering compensation is developed for the first time to precisely realize quick zoom control of GMA-driven LTL, where the asymmetric shifted Prandtl-Ishlinskii model characterizes the inherent hysteresis, a high-performance implicit inverse algorithm based on bisection search effectively eliminates hysteresis effects, and the finite covering lemma combined with radial basis function neural networks compensates for the unknown time-delay functions. Second, an interesting GMA-driven LTL experimental platform is constructed for the first time to identify and validate the fractional-order model, and imaging as well as continuous quick zoom control experiments confirm the effectiveness of the proposed approach. Experimental results demonstrate that the proposed method outperforms other benchmark approaches in terms of root mean square error, mean absolute error, and error 2-norm ($\boldsymbol{||E||_{2}}$), achieving accurate and rapid focus control of GMA-driven LTL, thereby verifying its effectiveness in practical optical focusing and offering a promising solution for high-speed imaging and zooming applications.