A modified asymmetric generalized Prandtl–Ishlinskii model for characterizing the irregular asymmetric hysteresis of self-made pneumatic muscle actuators

Abstract Reducing the errors of hysteresis models is of great significance for improving the accuracy of controlling pneumatic muscle actuators (PMAs). However, the irregularity and asymmetry of the hysteresis loops of PMAs limit the modeling accuracy of existing models. This paper proposes a modified asymmetric generalized Prandtl–Ishlinskii (MAGPI) model for the irregular asymmetric hysteresis characterization of PMAs, which adopts cascading operators. The first element in the cascade is the superposition of two weighted generalized play operators with different parameters; the second element is the superposition of weighted dead-zone operators. The effectiveness of the proposed approach is validated by experimental testing using Festo commercial and self-made PMAs, where its capacity to capture the irregular asymmetric hysteresis relationship between length and pressure parameters has been examined by generating different input pressure signals. The experimental results prove that the modeling capacity of the MAGPI model is better to characterize the complex hysteresis loops of PMAs, and this strength is more apparent when the hysteresis loops become irregular. Meanwhile, a crosswise comparative study on three envelope functions investigating modeling accuracy reveals that the newly introduced arc tangent function exhibits better performance than the traditional exponential and hyperbolic tangent functions.