Hysteresis Model of Magnetically Controlled Shape Memory Alloy Based on a PID Neural Network

Magnetically controlled shape memory alloys are a new kind of smart material that can be used in microdisplacement and micropositioning applications. However, the hysteresis nonlinearity of this material is an obstacle in achieving high precision accuracy. To describe the hysteresis nonlinearity, a modeling method based on a proportional-integral-differential (PID) neural network is proposed. Using backpropagation training algorithms to train weights, this model can better approximate the main and minor hysteresis loops by adding a nonlinear function in the input layer. The simulation results show that the maximum prediction error of the PID neural network model is 0.0073 mm when the given input signal results in a major hysteresis loop, and the maximum prediction error of the PID neural network model is 0.0101 mm when the given input signal results in both major and minor hysteresis loops. Error calculations further demonstrate the effectiveness of this modeling method.