Hysteresis model of magnetically controlled shape memory alloy based on a PID neural network

Abstract

Magnetically controlled shape memory alloys(MSMA) are a new kind of smart material that can be used in micro-displacement and micro-positioning applications. However, the hysteresis nonlinearity of this material is an obstacle to achieve high precision accuracy [1]. The hysteresis nonlinearity of MSMA can be described by the relationship between the input and output signal which is called hysteresis loop [2]. As shown in figure 1(a), hysteresis loops can be divided into major and minor hysteresis loops. The input and output signals have the same phase at the extrema and the phase of the output signal lags behind the input signal at all other times. A major hysteresis loop takes shape when the input signal rises from an initial value to a maximum value before decreasing to a minimum value (which is same as the initial value). Minor hysteresis loops occur when the input signal rises from a local minimum value (which is different from the overall minimum value) to a local maximum value (which is different from the overall maximum value) before decreasing to a local minimum value.