Inversion-based sliding control of a flexible-link manipulator

In this paper a control strategy based on nonlinear inversion is considered for a class of multi-link, structurally flexible manipulators to achieve small tip-position tracking errors while maintaining robust closed-loop performance. This is accomplished by defining new outputs near the end points of the arms. Motivated by the concept of a sliding surface in variable structure control (VSC), a robustifying term is developed to drive the nonlinear plant's error dynamics onto a sliding surface. On this surface the error dynamics are guaranteed to be independent of parametric uncertainties. In order to avoid over-excitation of higher frequency flexural modes due to control chattering, the discontinuous functions normally used in classical VSC are replaced by saturation nonlinearities at the outset. This also facilitates analysis by the standard Lyapunov techniques. The controller performance is demonstrated by simulation on a two-link manipulator with the second link flexible and with considerable parametric uncertainty. In the absence of the sliding controller, the inversion-based controller results in instability when subjected to parametric uncertainty.