Robust Control of Flexible Structures Using Multiple Shape Memory Alloy Actuators

Abstract

The design and implementation of control strategies for large, flexible smart struc tures presents challenging problems. To demonstrate the capabilities of shape-memory-alloy (SMA) actuators, we have designed and fabricated a three-mass test article with multiple shape-memory- alloy, NiTiNOL, actuators. Both force and moment actuators were implemented on the structure to examine the effects of control structure interaction and to increase actuation force. These SMA actu ators exhibit nonlinear effects due to dead band and saturation. The first step in the modeling process was the experimental determination of the transfer function matrix derived from frequency response data. A minimal state space representation was determined based on this transfer function matrix. Finally, a reduced order state space model was derived from the minimal state space representation. The simplified analytical models were compared with models developed by structural identification techniques based on vibration test data. From the reduced order model, a controller was designed to dampen vibrations in the test bed. To minimize the effects of uncertainties on the closed-loop system performance of smart structures, a linear quadratic Gaussian loop transfer recovery, LQG / LTR, control methodology was utilized. A standard LQG/LTR controller was designed; however, this controller could not achieve the desired performance robustness due to saturation effects. Therefore, a modified LQG / LTR design methodology was implemented to accommodate for the limited control force provided by the actua tors. The closed-loop system response of the multiple input multiple output (MIMO) test article with robustness verification was experimentally obtained and is presented in this paper. The modified LQG / LTR controller demonstrated performance and stability robustness to both sensor noise and parameter variations.