Nonlinear Control of a Shape Memory Alloy Actuator via Mu-Synthesis

Miniature, low mass actuators play an important role for practical applications in developing technologies. Having the responsive behavior to the applied current, Shape Memory Alloy (SMA) wire actuators provide cost effective solutions to many actuation problems. However there are still challenging problems need to be solved for the SMA actuators to be used efficiently, especially in applications that require precise positioning tasks. This work presents an experimental positioning application of an SMA wire actuator using μ-Synthesis controller along with a Feed-Forward (FF) compensator. The feed-forward compensator is designed as a piecewise function and used to reduce the nonlinearity of the most problematic are of the hysteresis where the steepest response change occurs. The remaining hysteretic behavior of the SMA wire actuator is modeled as a parametric uncertainty. Controller synthesis problem is defined as an S-KS mixed sensitivity problem. By minimizing the requirement of fast actuator movement using FF compensator, the overall control strategy yields good results in terms of tracking performance both at low and higher frequencies.