Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems

On the basis of sliding-mode control, two sliding-mode controller models based on incremental hierarchical structure and aggregated hierarchical structure for a class of under-actuated systems are presented. The design steps of the two types of sliding-mode controllers and the principle of choosing parameters are given. At the same time, to guarantee the system's stability, two determinant theorems are presented. Then, by theoretical analysis, the two types of sliding-mode controllers are proved to be globally stable in the sense that all signals involved are bounded. The simulation results show the validity of the methods. Therefore an academic foundation for the development of high-dimension under-actuated mechanical systems is provided.