Robust stability assessment of a 2-DOF manipulator based on μ-analysis

From a feedback control perspective two of the major concerns in manipulator-design are the dynamical couplings between the individual links, and the parameter-variations of the coefficients in the model as the manipulator is following a trajectory in the workspace. The first concern is basically related to the multivariable nature of the manipulator, and the second concern gives rise to robustness considerations-i.e. is the system stable along a class of trajectories? The latter concern is made more complicated by the existence of cross-coupling uncertainties. In the paper an approach to the analysis of such multivariable robustness issues is presented. The approach is based on structured singular value analysis (μ-analysis). This technique has been shown to be very powerful in analyzing the robustness of a number of industrial processes. However, no studies of μ-analysis of manipulator robustness have been presented. The paper addresses the modelling of the 2-DOF manipulator. Essentially this is a model of the upper and fore arm of an industrial robot (the Hitachi PW10)