###### Abstract
On the other hand, the disadvantages are that the displacement change of PAM is time-varying and non-linear compared to the input pressure, and there is some friction between the inner elastic rubber tube and the outer fiber mesh of PAM when the displacement change occurs due to the internal pressure change, thus causing a hysteresis phenomenon [13; 14]. In recent years, the German Festo team has been developing the application of PAM in robotics. The ZAR5, developed by the Festo team, uses PAM as an actuator, and its mechanism consists of a rotatable base, two upper limb arms, and a total of ten fingers on both hands. By controlling the flow valve to change the air flow in the pneumatic artificial muscles, it can perform the action of bending the fingers with the arms together and can track the action of simulated human hands [15]. A UK-based shadow company also designed a bionic arm using PAMs, with each group of PAMs installed in the same position as the corresponding muscles of the human arm, which can realize the same bending elbow and arm forward and extension movements as human hands [16]. [PERSON] et al. [17] published a seven-degrees-of-freedom humanoid robotic arm with PAM as the actuator to drive each axis of the arm in remote control mode, allowing the arm to perform the task of picking up and dropping objects. [PERSON] et al. [18] designed an exoskeleton device for upper limb and lower limb rehabilitation with seven degrees of freedom for the upper limb exoskeleton and five degrees of freedom for the lower limb exoskeleton, which is driven by a PAM. The upper limb exoskeleton is equipped with a torque sensor at the end of the hand, which can sense the force signal applied at the end of the hand and use the force signal to achieve the desired movement position of the patient through control. PAMs are applied to control robotic arms, which can be generally classified as single PAM control or dual PAMs operating in linear or rotary motion; the use of pneumatic control valves is also different from pressure control valves or flow-control flow servo valves. [PERSON] et al. [19] used a proportional flow-control PAM, but because the PAM produced hysteresis during operation, the hysteresis was modeled by isometric, isobaric, and isotropic experiments to perform feed-forward compensation so that the system could achieve better control results. [PERSON] [20] proposed using sliding mode control (SMC) to control the linear motion of a proportional flow servo valve with dual PAMs, and established a nonlinear model of the PAMs, with ideal gas equation and air flow equation to derive the relationship between the control command parameters and the dual PAMs, and designed the sliding plane to calculate the control commands through the equivalent control law and switching control law to control the system. [PERSON] et al. [21] used a nonlinear proportional-integral-derivative (PID) structure to simplify the modeling process and provide pneumatic artificial muscles to compensate for nonlinear hysteresis phenomena and increase the robustness of the system. In order to improve the control accuracy of the trajectory tracking, this study uses iterative learning control. The initial idea of iterative learning control was to make a relevant correction to the control of mechanical motion through the implementation error in the mechanical system, but the analysis of learning control was still insufficient at that time [22]. [PERSON] et al. [23] proposed a learning algorithm called the PID-type, which can guarantee the convergence of the system without initial error and specially defined norm limits. Since then, different definitions of iterative learning control and modified learning algorithms have been proposed; these learning algorithms require several iterations to achieve a certain control accuracy [24; 25]. [PERSON] and [PERSON] [26] proposed a theoretical algorithm that can adjust the control error to zero in just one learning session, but this method is obtained from the system state generated by the new control input.