A comprehensive dynamic model for pneumatic artificial muscles considering different input frequencies and mechanical loads

•A load-dependent dynamic hysteresis model for PAMs is proposed.•The model is developed based on UPI operators and a NARMAX structure.•The inverse model is designed to predict the mechanical load exerted to the PAM. The pneumatic artificial muscle (PAM) actuated with different input frequencies and mechanical loads suffers from complex dynamic asymmetric hysteresis behaviors, leading to inaccurate positioning performance of the PAM. In order to predict the dynamic hysteresis behaviors with both rate-dependent and load-dependent effects, a comprehensive dynamic model is developed which includes two components: the first component is used to describe the rate-independent hysteresis nonlinearity with un-parallel Prandtl-Ishlinskii operators, and the cascaded second component is applied to represent the load-dependent dynamic behavior of the PAM using a nonlinear autoregressive moving average with exogenous input model implemented by recurrent fuzzy neural networks. To validate the proposed model, experiments are conducted with different input frequencies and mechanical loads. The experimental results demonstrate that the dynamic model shows a good agreement with the dynamic behaviors of the PAM under input conditions with different mechanical loads and input frequencies. In addition, the inverse model is designed to predict the mechanical load exerted to the PAM, and shows good prediction ability.