Uncertainty compensation for a flexible-link manipulator using nonlinear H control

In a flexible-link manipulator, in general the effect of some parameters such as payload, friction amplitude and damping coefficients cannot be exactly measured. One possibility is to consider the above as parameters with uncertainty. In this paper, constant as well as L2-bounded deviations of parameters from their nominal values are considered as uncertainties. These uncertainties make it difficult for a linear controller to achieve desired closed-loop performance. To remedy this problem, a nonlinear dynamical model of a flexible-link manipulator which has a constant input vector field (g in [xdot]=f(x) + g(x)u) is obtained. Based on recent results in nonlinear robust regulation with an H∞ constraint a nonlinear controller is designed for the flexible-link manipulator. The contribution of this paper is in demonstrating that the nonlinear controller has a larger domain of attraction than the linearized controller. In fact, for the single-link flexible manipulator considered in this paper, the linear H∞ controller results in instability for step changes in the desired output of greater than 3.6 rad, whereas the nonlinear H∞ controller yields desired step changes of 2π rad. Simulation results demonstrating the advantages and superiority of the nonlinear H∞ controller over the linear H∞controller are presented.