Nonlinear control of a shape memory alloy adaptive tuned vibration absorber

The adaptive-passive approach to vibration control shows potential for achieving superior performance when compared to classical passive solutions. On-line adaptation of passive elements is central to the adaptive-passive approach and a great deal of research has focused on determining methods to realize the physical adaptation of the vibration control system. However, very little effort has been put into designing feedback laws to close the loop and control on-line adaptation to achieve desired performance. This paper discusses the design and analysis of a controller to tune an adaptive-passive vibration control system, in this case a shape memory alloy (SMA) adaptive-tuned vibration absorber (ATVA). Tuning of the SMA ATVA is achieved through appropriate heating and cooling of SMA beam elements. The SMA ATVA controller is designed using a model developed in a previous study. A Lyapunov analysis is presented to demonstrate stability of the system under proportional-integral (PI) control when saturation of the control effort is neglected. However, severe control saturations can occur in response to excitation profiles that call for rapid cooling of the SMA beam elements. Without active cooling, integrator windup results, particularly if high gains are used. To deal with the windup, a nonlinear PI controller with integrator reset was developed. A second Lyapunov analysis is used to demonstrate stability of the modified system. Experimental results are included that demonstrate the improved performance of the system with the nonlinear controller.