Stability Analysis of a Shape Memory Alloy Adaptive Tuned Vibration Absorber Under PI Control With Anti-Windup

This paper presents a stability analysis of a continuously controlled adaptive tuned vibration absorber (ATVA) incorporating shape memory alloy (SMA) structural elements to realize attenuation of the vibration of a primary system subject to uncertain tonal excitation. The objective is for the SMA ATVA stiffness to be adapted such that a relative phase angle of −90° is achieved between the vibration of the SMA ATVA and the primary mass. The Lyapunov-based stability analysis indicates that the system is stable under proportional-plus-integral control across the operating range of the SMA ATVA when an integral reset is included in the control algorithm. The integral reset also substantially improves the performance of the system when compared to the original PI controller without reset.