Lpv Modeling and Control of a 2-dof Robotic Manipulator Based on Descriptor Representation

This paper deals with the practical applicability of the control design methods that are based on the descriptor representation for robotic manipulators. The nonlinear model of a manipulator can be reformulated as a linear parameter varying (LPV) model with rational parametric dependence. The statespace LPV model can then be converted into a LPV descriptor model with affine parametric dependence by using a linear fractional representation (LFR). In this paper, a two degrees of freedom (2-DOF) robotic planar manipulator is considered. The affine dependence allows to derive analysis and design procedures that consist in a finite set of LMI conditions. Such an approach is used for the design of an output-feedback LPV controller which guarantees the stability and the H∞ performance of the closed-loop system. The validity of the H∞ control scheme is evaluated through simulations.