On the Control of Two-link Flexible Robot Arm with Nonuniform Cross Section

We consider the motion of a two-link flexible arm with nonuniform cross section. We obtain the equations of motion by using the extended Hamilton's principle. These equations consist of coupled partial differential equations and (nonlinear) ordinary differential equations with appropriate boundary conditions. Our control problem is to achieve the given desired link angles and suppress the link vibrations. To solve this problem, we propose a novel control scheme which consists of a dominant control law together with a parallel controller. We show that with the proposed controller, the control objectives are satisfied. Our stability analysis is based on the Lyapunov approach and LaSalle's invariance principle extended to infinite-dimensional systems. We also present some simulation results, which indicate that large parameter uncertainties such as tip and hub mass changes are also handled effectively by the proposed controller.