Boundary Torque Control of a Flexible Two-Link Manipulator and Its Experimental Investigation

This article focuses on a two-dimensional flexible two-link manipulator that moves in a plane. The two links are simplified into Euler-Bernoulli beams and the coupled partial differential equation-ordinary differential equation dynamic model is established via Hamiltonian's principle. Two torque controllers acting on two motors, respectively, are designed for the simultaneous angular position control of two motors and suppression of the elastic vibrations of the links. The Lyapunov direct method and extended LaSalle invariance principle are used to prove the asymptotic stability of the system. In addition, numerical simulations illustrate the correctness and reasonability of the theoretical proof for the stability analysis and boundary control design, and the experimental verification on the platform of the Quanser laboratory also reaches the same conclusion.