Tracking Control of a Linear Motor Positioner Based on Barrier Function Adaptive Sliding Mode

The tracking performance of linear motor (LM) positioners is subject to payload uncertainty and external time-varying disturbances. Conventional robust controllers typically employ a high control gain that is substantially greater than the known a priori upper bound of the disturbance to ensure tracking error convergence. The main disadvantage of those controllers lies in that when the disturbance decreases, the control input is often overly generated, which then results in undesired control chattering effect or even actuator saturation. To overcome this problem, this article develops a robust tracking controller based on barrier function adaptive sliding mode (BFASM) for the LM positioners. The main benefits of BFASM are twofold: first, the controller is designed without the need for any disturbance information; second, its control gain is adaptively adjusted in terms of the amplitude of disturbance and, thus, leads to decreased control input when the disturbance becomes small. Furthermore, a modified barrier function (MBF) is proposed for applications with actuator saturation. It is proved that both the BFASM and MBF-based controllers can ensure the convergence of the tracking error into a prespecified neighborhood of zero in finite time. Experimental results on a real LM positioner demonstrate the superior properties of the developed controllers in comparison with two existing robust control schemes.