Stabilization and Tracking of a Quadrotor Using Modified Sigmoid Sliding Mode Control

Abstract

A modified sigmoid sliding mode control (MS-SMC) approach is proposed for stabilizing and tracking a quadrotor system with a nonlinear sliding surface, where the dynamics model is underactuated, highly coupled, and nonlinear. The constructed nonlinear sliding surface is based on the traditional sliding mode surface with a modified sigmoid function, allowing the initial value to quickly reach equilibrium. A new type of nonlinear SMC is applied for performance improvement of the quadrotor using the proposed modified sigmoid sliding surface. To control the quadrotor effectively, a double-loop control method is used to design the control rate, in which the position subsystem is the outer loop, and the attitude subsystem is the inner loop.With the Lyapunov function, the stability of the overall closed-loop system is ensured by stabilizing each subsystem step by step. Moreover, from a practical point of view, the system performance under the model uncertainties and external disturbances are also considered. The simulation results show that the proposed MS-SMC performs better than the conventional sliding mode control (CSMC) and the back-stepping sliding mode control (BS-SMC) in terms of stabilization and tracking against external disturbances.

An Adaptive and Robust Control Strategy for Real-Time Hybrid Simulation

“…Equation ( 19) is approaching Equation (12) as time increases; thus, the error caused by P(0) is gradually eliminated. The first-order derivatives of Ψ(t) and P(t) remain the same as Equations ( 13) and ( 14) with the adoption of Equation (19). The forgetting factor is tuned using…”

“…This assumption is reasonable because the input gain b is normally constant or varying within a small range. Sliding mode controllers have been widely adopted for the tracking control of systems which have bounded model uncertainties like Equation (22) [19,20]. The methodologies of the sliding mode controller are presented below.…”