Hysteresis Modeling of Pneumatic Artificial Muscles using a Modified Fractional-Order Bouc-Wen Model

Pneumatic artificial muscles (PAMs) serve as flexible actuators widely employed in robotics. However, the severe asymmetric hysteresis of PAMs significantly impedes their application in high-precision robotic control. To characterize the hysteresis phenomenon in PAMs with asymmetric properties, a modified Fractional-Order Bouc-Wen (MFOBW) model is proposed. Based on the Modified Bouc-Wen (MBW) model, this method replaces integer-order input terms with their fractional-order counterparts. This enables more accurate description of the hysteretic behavior with memory effects in PAMs and provides the model with greater degrees of freedom. Simultaneously, the introduction of state variable coefficient terms in the model’s auxiliary terms effectively enhances the fitting capability for the asymmetric hysteretic loop of PAMs. To validate the effectiveness of the proposed MFOBW model, parameters for both MBW and MFOBW models were identified based on typical open-loop voltage-displacement hysteresis data at different frequencies. Modeling errors between the two models were compared. Simulation results demonstrate that the proposed MFOBW model achieves higher accuracy in describing the asymmetric hysteresis of PAM, reducing MaxAE by $\mathbf{4 5. 6 \%} \boldsymbol{(} \mathbf{0. 0 5 H z} \boldsymbol{)}$ and $\mathbf{3 4. 1 \%} \boldsymbol{(} \mathbf{0. 1 H z} \boldsymbol{)}$, RMSE by 52.2% and 35.2%, and MAE by 51% and 34.4% compared to the MBW model.