Fully-actuated Robust Predictive Control for Cascaded Under-actuated Systems

This study focuses on robust predictive control for cascaded under-actuated systems (UASs) based on fully-actuated system (FAS) approaches. Rooted in the fundamental principles of model mechanics, the dynamic model for a cascade UAS is derived from the Lagrangian equation. A global coordinate transformation is given for the cascaded UAS, which kinetic and potential energy are in general forms, such that the cascade UAS is converted into an equivalent FAS. Meanwhile, considering discretization errors inevitably introduced during the model discretization process, the FAS-RPC control scheme is proposed. The predictive controller is solved through linear matrix inequalities (LMI) and the asymptotical stability of the closed-loop system and minimum of robust performance index can be guaranteed simultaneously. Finally, the effectiveness of the proposed algorithm is verified by the simulation of a cascaded under-actuated dual rotational translational actuator (RTAC) system.