Adaptive fixed-time prescribed performance control for macro-micro composite positioning stage with input saturation

In this paper, the adaptive tracking control problem for macro-micro composite positioning stage (MMCPS) with error constraints and input saturation is considered. The MMCPS has important applications in realizing high-speed macromotion and high-precision micromotion, which can be regarded as a non-strict feedback interconnected nonlinear system. A fixed-time prescribed performance (FTPP) function is proposed to restrict the tracking error and virtual errors. Based on the designed barrier Lyapunov function, the transform errors can also be constrainted in the prescribed constant bounds. Furthermore, an auxiliary system is constructed to compensate adverse effect of the saturation nonlinearity. By integrating the nonlinear filtering technique into the backstepping control framework, the problem of computational complexity explosion can be effectively avoided. For the purpose of achieving better transient performance and improving control precision, an adaptive FTPP tracking control method is presented. According to the Lyapunov stability theory, the proposed control method guarantees that all dynamic errors can converge to the prescribed bounds within fixed time. Finally, a simulation example is given to indicate the effectiveness of the designed controller.