Almost Disturbance Decoupling for A Class of Underactuated Nonlinear Systems with Unknown Disturbances by Backstepping

In response to the lack of backstepping technology and almost disturbance decoupling (ADD) method in the under-actuated field, this paper proposes a new ADD controller design strategy for a class of underactuated nonlinear systems with unknown disturbances by using backstepping technology. Firstly, an error system is formed via a special state feedback, which is based on a partial differential equation (PDE). It can be deter-mined that this process is essentially the backstepping technique. Then, a novel error transformation is developed for the non-strict feedback problem of the formed error system. An ADD controller for the error system is designed by backstepping technology. Finally, the stability and ADD problem of the proposed strategy are verified according to converse Lyapunov theorem. The inertia wheel pendulum (IWP) with external matched disturbances is utilized to explain the effectiveness of the proposed strategy. From the simulation results, it can be seen that the proposed scheme possesses excellent control performance compared to previous underactuated control methods.