An improved generalized Prandtl–Ishlinskii model for the hysteresis modeling of pneumatic artificial muscles

Due to the merits of high flexibility, large driving force, and light weight, the pneumatic artificial muscle (PAM) has been widely applied in robot. However, the inherent asymmetric hysteresis nonlinear characteristics affect the control performance of PAM seriously. This paper presents an improved generalized Prandtl–Ishlinskii (GPI-M) model for the asymmetric hysteresis characterization of PAM, which adopts the simplified Magic Formula (SMF) as the envelop function instead of hyperbolic tangent function (GPI) or arc tangent function (GPI-A). With regard to the effect of parameters identification, the Levenberg-Marquardt (LM) algorithm, genetic algorithm (GA), particle swarm optimization (PSO) algorithm, and differential evolution (DE) algorithm are studied, which shows the LM algorithm is far superior to the other three intelligent algorithms in terms of computational efficiency and identification accuracy. Furthermore, a crosswise comparative study on three models and two envelop functions investigating modeling accuracy reveals that the newly introduced GPI-M model exhibits better performance than the modified symmetric generalized Prandtl-Ishlinskii (MSGPI) model and the GPI-A model presented previously. Meanwhile, the influence of the operator numbers on the modeling accuracy of three models is discussed, which finds that the GPI-M model possess the best accuracy with the least operator numbers.