A Memristive-System-Based Hysteresis Model for a Compact Pneumatic Artificial Muscle

Pneumatic artificial muscles exhibit pronounced hysteresis in the force-contraction domain, which complicates accurate force modeling under pressure-dependent operation. This work presents a discrete-time quasi-static hysteresis model for a compact pneumatic artificial muscle using a memristive system-based branch-memory formulation. The model combines separate loading and unloading force surfaces through a bounded internal state and is evaluated on experimental data acquired at a force-change rate of 4N/s. Measurements were performed at 13 pressure levels from 0 to 0.6 MPa in 0.05 MPa increments, with 32 unloading points and 32 loading points per pressure level and five repetitions for each operating condition. Representative branch curves were obtained by median reduction in the repeated measurements, and the loading and unloading surfaces were identified with the five-parameter Sárosi–Fabulya exponential-bilinear function. The state update parameter was evaluated over a fixed grid, and the best loop reconstruction on the present dataset was obtained for the hard-switching case α=1. Benchmark comparisons with Prandtl–Ishlinskii, discrete Preisach, Maxwell-slip, and sampled Bouc–Wen-type models show that Preisach and Bouc–Wen provide higher loop-reconstruction accuracy. The proposed memristive formulation should not be interpreted as a best-fit benchmark model, but as a low-order global branch-memory representation that preserves pressure dependence and branch asymmetry within a single analytical framework over the investigated quasi-static operating range.