High Order Sliding Mode Decoupling Control of Two-dimensional Linear Motor Based on Proportional Integral Model Free Adaptive Control

Two-dimensional linear motor motion systems are nonlinear, multivariate, uncertain and strongly coupled, and easy to be affected by external disturbances. Based on the characteristics of the model free adaptive control (MFAC) does not depend on the controlled system accurate mathematical model and that sliding mode control (SMC) can suppress external disturbances and is insensitive to bounded disturbances, a composite control scheme combining proportional integral model free adaptive control (PIMFAC) and high order sliding mode control (HOSMC) is proposed. A proportional control term is added to the model free adaptive control to further improve the response speed of the two-dimensional linear motor. High-order sliding mode controller compensates for system errors, and the two methods are closely combined to improve the position tracking accuracy of the two-dimensional linear motor and improve the system robustness. An adaptive decoupling control strategy is also used to further decouple the system by designing a discrete expansion state observer (DESO) to estimate and compensate for the coupling between the two axes, unmodelled dynamics and unknown external disturbances. The simulation experimental results show that the proposed scheme can effectively improve the position control accuracy of the two-dimensional linear motor.