Control two-link flexible manipulators using controlled Lagrangian method

In this paper, we propose a control method for two-link flexible manipulators using controlled Lagrangian method. Since the two-link flexible manipulators are underactuated Euler-lagrange systems, which means there is no control input acting on the flexible variables directly. In general, it is hard to use the controlled lagrangian method to this kind of systems. 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 systems express two-time-scale characteristics which means the total Euler-lagrange system can be decomposed into two subsystems: a slow subsystem describing the rigid motion and a fast one describing the flexible vibration. For this two-time-scale Euler-lagrange system, we explore a new control design idea that is energy-based two-time-scale control design. First we separate the time-scale only using coordinate transformation according to the rigid mode and the flexible mode. Then after completing the energy reshaping and damping injection for two Euler-lagrange subsystems of different time-scales, a composite controller is obtained following the idea of composite control. The experimental results are presented to show the effectiveness of this control design method.