Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding mode (ARTSM) controller is proposed in this paper. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experiment results also demonstrate the effectiveness of the controller in term of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding mode (FNTSM) controller for the LM positioner.

As one type of unmanned aerial vehicles, the quadrotor typically suffers from payload variations, system uncertainties, and environmental wind disturbances, which significantly deteriorate its attitude control performance. To provide high-speed, accurate, and robust attitude tracking performance for the quadrotor, an adaptive fast nonsingular terminal sliding mode (AFNTSM) controller is proposed in this article. The proposed AFNTSM controller combines the advantages of fast nonsingular terminal sliding mode (FNTSM), integral sliding mode, and adaptive estimation techniques, which are effective to achieve the desired tracking performance and suppress control signal chattering. Furthermore, unlike conventional methods, the adaptive estimation removes the requirements for the upper bound information of the disturbances. It is proved that the proposed AFNTSM can guarantee finite-time convergence and zero tracking error for the quadrotor attitude control. Finally, comparative study with the FNTSM control only and conventional sliding mode control is conducted through experiments and the results demonstrate that the proposed AFNTSM can achieve faster convergence and stronger robustness in line with theoretical analysis.

This article aims to present a barrier function based adaptive sliding mode (BFASM) control scheme for a class of uncertain nonlinear systems with actuator saturation. In conventional adaptive sliding mode control for saturated systems, the adaptive gain is often monotonically increasing with respect to the persistent disturbance, which results in aggressive control input with severe chattering that is often giving rise to system instability. In order to solve this problem, this article proposes a BFASM controller with explicit consideration of actuator saturation and uncertainties. The proposed method contains a reaching control input that can adapt to the time-varying disturbances. In addition, the proposed method does not require the upper bound information of disturbance that is commonly requested in conventional sliding mode control and thus removes the conservative assumption on a sufficiently large control gain. Stability analysis proves that the tracking error under the proposed control can asymptotically converge into a prespecified region in the presence of actuator saturation, parameter uncertainties, and external disturbances. The proposed method is also applied to an air-floating positioning system with input saturation, and experimental results demonstrate its efficacy.

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.