Variable Structure Control of Shape

A novel Shape Memory Alloy (SMA) actuator consisting of several thin NiTi bers woven in a counter rotating helical pattern around supporting disks is rst described. This structure accomplishes a highly eecient transformation between force and displacement overcoming the main mechanical drawback of shape memory alloys, that being limited strain. Time domain open loop experiments were then conducted to determine the intrinsic properties of the actuator. From these experiments and from the knowledge of the underlying physics of SMA's, a multi-term model, including linear and nonlinear elements, was proposed. After further investigation and simulation, it was found that most of these complexities did not need to be considered in order to explain the reported results, and that the model could be reduced to that of a single integrator. A variable structure controller was then applied to a pair of antagonist actuators. The feedback switches between the two actuators according to the sign of the displacement error. A further improvement was added to compensate for known gross nonlinearities by modulating the current magnitude in a discrete manner as a function of the state space position. It was therefore possible to realize smooth and robust control with very little cost in complexity. 1 INTRODUCTION With the continued miniaturisation of robotic systems comes the need for powerful, compact, lightweight actuators. Conventional techniques such as electric, hydraulic, and pneumatic actuators, suuer from a drastic reduction of the amount of power they can deliver as they scale down in size and weight. 8] To overcome this limitation, diierent actuator technologies have been investigated, in particular Shape Memory Alloys (SMA). Shape Memory Alloys have a high strength to weight ratio which makes them ideal for miniature applications. A SMA ber can achieve a maximum pulling force of 180 MPa. Comparing this to an electromagnetic actuator, which can only achieve .002 MPa 7], this represents an almost 10 5 increase in strength per cross sectional area. Thin bers of shape memory alloy can accomplish ac-tuation by being pretreated to contract upon heating. The contraction is a result of the ber undergoing a phase transition between its Martensitic and Austenitic phases. When in the cool phase (martensitic) the alloy is malleable and can easily be deformed by applying external stress. The original pretrained shape can then be recovered by simply heating the ber above its phase transition temperature. Since the alloy is resistive it can easily be heated …