Adaptive Robust Control of an Air-Floating Positioner Based on Barrier Function

To improve the control performance of an air-floating positioning system, a predefined-precision adaptive terminal sliding mode (PPATSM) control scheme is developed. Explicitly, due to the introduced barrier function (BF), the disturbance's upper bound is not required any longer and the control gain can rapidly adapt itself in accordance with the disturbance variation. This result overcomes the undesired overestimation of the control gain as that in many conventional methods. It also guarantees that the position error of the positioner is enclosed within a frozen bound whose size can be exactly predefined, regardless of the unknown disturbance amplitude. Moreover, to deal with the impacts of input saturation, an auxiliary dynamics is presented in the control design. The introduction of the auxiliary dynamics releases the requirement for selecting an output threshold of the barrier function that is larger than the unknown disturbance. In addition, to improve the positioning speed, a non-singular terminal sliding mode is used for the sliding mode control design rather than the common linear sliding mode, and Lyapunov analysis verifies that finite-time positioning is guaranteed in the presence of input saturation. Simulations and experiments demonstrate that the proposed control benefits in terms of robust control precision against parametric uncertainties and external load variations.