Thermo-Mechanical Modeling and Iterative Learning Control for Electrothermal Microgrippers with Integrated Compliant Rotary Joints

This study presents the modeling, control design, and simulation of a MEMS-based V-shaped electrothermal microgripper integrated with compliant rotary joints as a novel mechanical enhancement to achieve both displacement amplification and stress reduction. A comprehensive thermo–mechanical model was developed, including heat conduction, thermo-elastic deformation, and kinematic transmission; the modeling assumptions are explicitly stated (neglecting convection and radiation, assuming small angular deflections), yielding an amplification ratio of approximately 3.33. The main contributions include developing a tractable thermo-mechanical model, integrating compliant rotary joints, and evaluating PD/PID-ILC for high-precision trajectory tracking. Two iterative learning control (ILC) schemes, namely PD-ILC and PID-ILC, were implemented in MATLAB/Simulink for trajectory tracking of a trapezoidal reference signal with a peak jaw displacement of 40 µm. Simulation results show that both controllers achieve convergence within finite iterations, with PID-ILC exhibiting faster convergence and smaller tracking errors. The steady-state error was about 0.21 µm (0.52% of 40 µm), while the maximum post-convergence error was 1.73 µm (4.33%). The results highlight the advantages of iterative learning control, which can progressively reduce tracking errors over repeated tasks while maintaining a simple structure suitable for MEMS implementation. These findings confirm the effectiveness of the proposed control strategies in compensating for thermal delays and nonlinearities, enabling high-precision micromanipulation in biomedical handling, micro-assembly, and precision optics. Nevertheless, this paper acknowledges its limitations (lack of experimental validation and sensitivity to parameter variations) and outlines future research directions, including real-time implementation, robustness testing under disturbances, and the development of adaptive ILC variants.