Non-overshooting sliding mode for UAV control

Abstract

For a class of uncertain systems, a non-overshooting sliding mode control is presented to make them globally exponentially stable and without overshoot. Even when the unknown stochastic disturbance exists, and the time-variant reference trajectory is required, the strict non-overshooting stabilization is still achieved. The control law design is based on a desired second-order sliding mode (2-sliding mode), which successively includes two bounded-gain subsystems. Non-overshooting stability requires that the system gains depend on the initial values of system variables. In order to obtain the global non-overshooting stability, the first subsystem with non-overshooting reachability compresses the initial values of the second subsystem to a given bounded range. By partitioning these initial values, the bounded system gains are determined to satisfy the robust non-overshooting stability. In order to reject the chattering in the controller output, a tanh-function-based sliding mode is developed for the design of smoothed non-overshooting controller. The proposed method is applied to a UAV trajectory tracking when the disturbances and uncertainties exist. The control laws are designed to implement the non-overshooting stabilization in position and attitude. Finally, the effectiveness of the proposed method is demonstrated by the flying tests.

Figures (17)

• Figure 1: Configuration of globally non-overshooting 2-sliding mode. (a) Flow chart of 2-sliding mode. (b) Convergence process of sliding variables.
• Figure 2: Example 4.1 Sliding variables $e_{1}\left( t\right)$ and $e_{2}\left( t\right)$ of sliding mode (18).
• Figure 3: Example 4.2 Sliding variables $e_{1}\left( t\right)$ and $e_{2}\left( t\right)$ of sliding mode (24).
• Figure 4: Flow chart of non-overshooting controller design.
• Figure 5: Example 6.1 Non-overshooting sliding mode control. (a) $x_{1}$. (b) $x_{2}$. (c) Controller $u\left( t\right)$.