Liapunov stability analysis for PDS control of flexible multi-link manipulators

For flexible multilink manipulators, a nonlinear lumped-parameter model including centrifugal and Coriolis forces is derived on the basis of Hamilton´s principle and Galerkin´s modal expansion method. A control scheme called PDS (proportional-derivative-strain) control is proposed, which is composed of a conventional PD control and feedback of strain detected at the root of each link. Stability conditions of the closed-loop system are obtained by using the moment equilibrium equation for the root of each link and the direct method of Liapunov. Effects of stabilization of this PDS control scheme are discussed for a linearized model. Experimental results are provided to illustrate the effectiveness of the proposed PDS control