H∞ Control of a Planar 3-DOF Flexible-Cable Manipulator

Abstract

This paper deals with the dynamic modeling and the H∞ control of a cable-driven parallel robot with flexible cables. The modeling of planar 3-DOF (two translation and one rotation) robot pulled by four-cables has been performed using the assumed modes approach and the Euler-Lagrange equation, leading to a differential-algebraic equations model (DAE model). This model has been then transformed into an ordinary-differential equations model (ODE model) whose linearization is observable and controllable. An H∞ controller has been synthesized, considering a four-bloc synthesis scheme, in order to control the translation and the rotation of the platform and the mean tension of the cables. An original tuning strategy of the weighting functions is proposed, in order to ensure different performances on the different DOF, that suits to the physical nature of the process. The approach is evaluated in simulation on the nonlinear model and shows good disturbance rejection and reference tracking.