Backstepping based Actuator Failure Compensation of Rigid-Flexible Coupled Systems

This paper develops an actuator fault compensation scheme for a class of rigid-flexible coupled systems, using a model transform based backstepping control design. A new actuator dynamics is studied in this paper, modeled by a fourth-order partial differential equation (PDE), i.e., Euler-Bernoulli beam (EBB) equation. An invertible model transformation is introduced to transform the EBB PDE-ODE cascade system into a heat-like PDE-ODE cascade system, and a new target system is constructed from a two-step backstepping procedure. A novel fault-tolerant control scheme is proposed for the heat-like PDE-ODE cascade system and the well-posedness of the system solutions is analyzed. The closed-loop system stability and the well-posedness property of the original EBB PDE-ODE cascade system are ensured.