Controlling dynamics of an SMA structure with thermomechanical couplings using time-delayed feedback control method

Morphing structures which are currently employed in different applications typically suffer from slow actuation rates for most of the built in actuators. Shape memory alloy elements are commonly used as actuators due to their ability to produce large forces and displacements. A common practice when dealing with shape memory alloys actuation in smart structures is to perform quasi-static analyses to evaluate morphing capabilities, neglecting temperature dynamics and its constraints on the actuation. This oversight becomes critical when dynamical forces can perturb the structure from its intended configuration. In these scenarios, the application of nonlinear control methods, such as the extended time-delayed feedback control, and the dynamical analysis of SMA behaviour can ensure the stability of a desired configuration or be used to rapidly change configurations. This work investigates stabilization of unstable periodic orbits exhibited by a shape memory alloy two-bar truss system. The considered thermomechanical model describes the internal hysteresis and energy dissipation due to phase transformations. The heat transfer constraints on actuation and the effectiveness of the control in stabilizing unstable periodic orbits are evaluated. Results show that the extended time-delayed feedback method can successfully stabilize a target orbit in a range of convective heat dissipation coefficients and reveal the mechanisms that prevent the controller to succeed outside that region. In addition the constrained thermal actuation demonstrates that heat dissipation limits the maximum stability that can be achieved by the controller.