Hysteresis Behaviour and Modeling of SMA Actuators

Abstract

In recent years, the use of shape memory alloy (SMA) as a key component in diverse actuation applications has attracted more interests, especially in the field of mechatronics and medical instruments (Wolfe et al, 2005; Wong et al, 2007; Gupta et al, 2009, Okamura et al, 2009, De Sars et al, 2010). The positive features of good reliability, high energy density, design simplicity, compactness in configuration and quiet operation, point to SMA being a promising candidate for actuator. However, great difficulties are always encountered in the precise control of the systems incorporating them, due mainly to the nonlinearities of the complex hysteresis associated with the shape memory effect. These nonlinearities must be considered and dealt with properly, since they may excite unwanted dynamics that lead in the best scenario to a deteriorated system performance and in the worst scenario to an unstable dynamic system. One effective method to compensate for such hysteresis nonlinearities is to involve a model in the control scheme that is able to describe the complex nonlinear behaviour of SMA actuators and accordingly give reliable predictions of the system response. In this case, the crucial part of the development lies in accurate modelling of the actual hysteresis nonlinearity. From the viewpoint of control, such a hysteresis model should characterize the nonlinearities with sufficient accuracy, be amenable to a compensator design for actuator linearization and be well-suited for real-time applications. Therefore, the usual constitutive models (Bhattacharyya & Lagoudas, 1997; Matsuzaki & Naito, 2004; Popov & Lagoudas, 2007; Wang & Dai, 2010), derived from thermodynamical or micromechanical principles, are immediately discarded for this purpose, owing to the mathematical complexity involved and non-availability of the microstructural material parameters. This chapter starts with the description of the hysteresis behaviour of SMA actuators. Following the analysis of its hysteresis characteristics, a phenomenological model based on the theory of hysteresis operator, referred to as MKP model, is proposed and its inverse model is deduced with the aim to provide a more appropriate choice for the modelling of 4