Least square based sliding mode control for a quad-rotor helicopter and energy saving by chattering reduction

Abstract

In this paper, a new control structure for a quad-rotor helicopter that employs the least squares method is introduced. This proposed algorithm solves the overdetermined problem of the control input for the translational motion of a quad-rotor helicopter. The algorithm allows all six degrees of freedom to be considered to calculate the control input. The sliding mode controller is applied to achieve robust tracking and stabilization. A saturation function is designed around a boundary layer to reduce the chattering phenomenon that is a common problem in sliding mode control. In order to improve the tracking performance, an integral sliding surface is designed. An energy saving effect because of chattering reduction is also evaluated. First, the dynamics of the quad-rotor helicopter is derived by the Newton–Euler formulation for a rigid body. Second, a constant plus proportional reaching law is introduced to increase the reaching rate of the sliding mode controller. Global stability of the proposed control strategy is guaranteed based on the Lyapunov׳s stability theory. Finally, the robustness and effectiveness of the proposed control system are demonstrated experimentally under wind gusts, and are compared with a regular sliding mode controller, a proportional–differential controller, and a proportional–integral–differential controller.