Nonlinear H_∞-tracking control of friction mechanical manipulators

Nonlinear H_∞-controller synthesis is developed for position tracking control of friction mechanical manipulators. To facilitate exposition, the friction model chosen for treatment is confined to the Dahl model augmented with viscous friction. A local solution is derived by means of a certain perturbation of the differential Riccati equations, appearing in solving the H_∞-control problem for the linearized system, when these unperturbed equations have bounded positive semidefinite solutions. Stabilizability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure obviates an extra work on verification of these properties. Performance issues of the nonlinear H_∞-tracking controller are illustrated in a simulation study made for a two degrees-of-freedom robot manipulator.