Observer based incremental backstepping terminal sliding-mode control with learning rate for a multi-vectored propeller airship

The problem of finite-time trajectory tracking control for a multivectored propeller airship with model parameter uncertainties and unknown disturbances is addressed in the paper. In order to obtain a fast transient response and finite time convergence without singularity, an incremental backstepping nonsingular terminal sliding mode controller is designed to track desired trajectory within finite time. To overcome the limitation of backstepping terminal sliding-mode control design being dependant on prior knowledge, a nonlinear disturbance-observer is designed to estimate the external observable disturbances. Meanwhile, to reduce system chattering when the tracking error reaches the sliding mode surface, an adaptive learning rate design is proposed for the terminal sliding mode controller such that the tracking error approaches the sliding mode surface at a low speed and so the system chattering is restrained. The closed-loop trajectory tracking control system is proved to be stable and finite time convergence by using Lyapunov theory. The results are compared with traditional backstepping sliding mode control and different learning rate based control design, and they demonstrate the averaged tracking error in altitude and pitch motion is reduced more than 30% by using the disturbance-observer based incremental backstepping terminal sliding mode controller for the multivectored propeller airship to execute a realistic trajectory tracking mission, even in the presence of aerodynamic coefficient uncertainties, unknown disturbances.