A novel hysteresis modelling method with improved generalization capability for pneumatic artificial muscles

A pneumatic artificial muscle (PAM) consists mainly of an inner elastomeric bladder surrounded by a braided shell. Due to the special geometric structure, PAMs are subject to the typical drawbacks of a highly-asymmetric hysteresis-based nonlinear system. This paper presents a D-extended un-parallel Prandtl-Ishlinskii model (D-EUPI) model for modelling the asymmetric hysteresis of PAMs, which is a deep learning-based model combining a modified EUPI model and a convolution neural network (CNN). Compared with the existing phenomenological hysteresis models, the proposed model has good generalization capability, meaning that not only can it be suitable for trained data, but also can accurately predict the PAM displacement corresponding to input pressure independent of trained data. We investigate the influences of input frequency and amplitude on the inherent hysteresis characteristics of PAMs via experiments. The experiments reveal that the asymmetric hysteresis of the PAM is quasi-rate independent but dependent on its input amplitude for the low frequency range (<= 1 Hz) in this study. Furthermore, the D-EUPI model is trained and tested based on the experimental data. The results show that the D-EUPI model is effective in predicting the hysteresis of PAMs over a wide range of input amplitudes. And the D-EUPI model has better performance in modelling complex multi-loop hysteresis by comparison with the EUPI model and the CNN model.