Robust control of a class of mechanical systems actuated by shape memory alloys

Abstract

This paper presents a model-based sliding mode control law for interconnected mechanical systems which use shape memory alloys (SMA) as actuators. The systems under consideration are assumed to be fully actuated and represented by unconstrained equations of motion. A system model is developed which combines the equations of motion with SMA heat convection, constitutive law, and phase transformation equations. The sliding mode control law is introduced using asymptotically stable second-order sliding surfaces. Robustness is guaranteed through inclusion of modeling uncertainties in the controller development. The control law is developed assuming only positions are available for measurement. The unmeasured states which include velocities and SMA temperatures and stresses are estimated using an extended Kalman filter. The control law is applied to a three-link planar robot for set point and trajectory tracking problems and shown to be effective despite significant modeling uncertainty and lack of measurements for all states except the joint angles.