A Composite Controlled Lagrangian Method for Two-Link Flexible Manipulators

摘要

In this paper, a model-based control design method (i.e., composite controlled Lagrangian method) for a two-link flexible manipulator is proposed. A two-link flexible manipulator is an underactuated Euler-Lagrange system, meaning that there is no control input acting directly on the flexible variables. In general, it is hard to apply the controlled Lagrangian method to this kind of system. But if we take into account the larger stiffness of the links, it is easy to see that the dynamics of this kind of Euler-Lagrange system express two-time-scale characteristics, which means the total Euler-Lagrange system can be considered as a two-time-scale system and can be decomposed into two subsystems: a slow subsystem describing the rigid motion and a fast subsystem describing the flexible vibration. For this two-time-scale Euler-Lagrange system, we explore a new control design idea; that is, an energy-based two-time-scale control design. First, we show a new way to separate the time-scale by using coordinate transformation according to the rigid and flexible modes, which is different from other multi-scale methods such as the singular perturbation approach applied to controlling flexible manipulators, where the separation of time-scale is completed by assuming that the small perturbation parameter is equal to zero. After completing the energy shaping and damping injection for two Euler-Lagrange subsystems of different time-scales, a composite controller is obtained following the idea of composite control. Both the simulation and experimental results are presented to show the effectiveness of this control design method.