In this paper a nonlinear model-based controller is designed to globally asymptotically stabilize a single-degree-of-freedom shape memory alloy (SMA) actuated manipulator. A three part model was constructed based on the dynamics/kinematics of the arm, the thermomechanical behavior of SMA’s, and an assumed heat transfer model consisting of electrical heating and natural convection. The backstepping control is used to calculate the applied voltage to the SMA wire. Initially, the SMA’s wire stress is assumed to be the control input of the system. The stress is then chosen to asymptotically stabilize the desired position. The applied voltage to the SMA wire is the actual control input. This voltage is calculated based on the desired stress and the SMA’s thermomechanical and heat transfer models. It is shown that the calculated voltage can globally asymptotically stabilize the system. Numerical simulations are performed to investigate stabilizing performance as well as other issues such as robustness. The results demonstrate that the backstepping controller designs is highly accurate in stabilization.
Backstepping Control of an SMA-Actuated Manipulator
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Elahinia, MH, Koo, J, Woolsey, C, & Ahmadian, M. "Backstepping Control of an SMA-Actuated Manipulator." Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition. Dynamic Systems and Control, Parts A and B. Anaheim, California, USA. November 13–19, 2004. pp. 45-54. ASME. https://doi.org/10.1115/IMECE2004-60009
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