A Two-Time-Scale Model Predictive Control Framework for Precise Strain Control of Shape Memory Alloys

Precise strain control of Shape Memory Alloys (SMAs) is challenging due to their strong nonlinearity, hysteresis, and thermomechanical coupling. To address the needs of real-time control system design, this paper proposes a two-time-scale decoupling control framework based on Model Predictive Control (MPC). First, a transient physics-based model considering one-dimensional heat conduction and latent heat under electrical excitation is established and then reduced to a lumped-parameter model suitable for controller design. To balance prediction accuracy and computational efficiency posed by the model nonlinearity, an innovative two-time-scale MPC strategy is designed: a fast inner-loop temperature MPC is used for efficient thermal management outside the phase transformation plateau, while it switches to an outer-loop strain MPC for precise trajectory tracking and hysteresis compensation during the critical phase transformation period. Simulations demonstrate that this strategy significantly reduces computational burden while maintaining accuracy. Compared to a single-time-scale MPC, the proposed method reduces the settling time by 26%, the root mean square error by 16%, and the single-step computation time by 19.6% for a step reference strain. This work provides an effective and engineering-friendly solution for high-performance, real-time control of SMA-based actuators.