Comprehensive Dynamic Model of Vertical Pneumatic Bellows Actuator System Considering Bidirectional Asymmetric Hysteresis

The complex nonlinear characteristics of pneumatic soft actuators, such as asymmetric hysteresis, rate-dependence, and mechanical load-dependence, pose a challenge in accurately modeling their dynamics. To address this challenge, this paper proposes a comprehensive dynamic model aimed at describing bidirectional asymmetric hysteresis, rate-dependent, and mechanical load-dependent characteristics of a vertical pneu-matic bellows actuator (PBA) system. The dynamic model contains a hysteresis submodel and a load-dependent dynamic sub-model. The hysteresis submodel consists of several sets of weighted double-side play (DSP) and weighted dead-zone (DZ) operators connected in series, and it is used to model the bidirectional asymmetric hysteresis of the system. The load-dependent dynamic submodel is built based on the gated recurrent unit (GRU) neural network, and it is used to fit the nonlinear relationship between the displacement of the system and the frequency of the input air pressure as well as the mechanical load. The model parameters of the hysteresis submodel and the load-dependent dynamic submodel are determined by intelligent optimization method and neural network training method, resepa-rately. The fitness value (FV) between the output of the dynamic model and the experimental data is calculated to be 96.1736%, demonstrating that the parameters of the dynamic model are valid. We conduct six set of experiments to compare the model output with the experimental data, and calculate the root-mean-square errors and the maximum error, respectively. The experimental results show that, the root-mean-square error remains consistently below 2.7700%, while the maximum error remains below 8.4000% across all experiments, thereby substantiating the validity and generality of the proposed model.