An approach to the nonlinear control of flexible robot arms based on the differential geometric nonlinear control theory and the linear quadratic regulator (LQR) theory is considered using only the actuators at the joints. The control is separated into two parts: one derived by the differential geometric structure algorithm is a global external linearization and decoupling nonlinear feedback law for nominal trajectory tracking, and the other synthesized by combined LQR and servocompensator techniques is a robust linear time‐invariant stabilization and error correcting feedback control designed for active damping of elastic vibrations and for robustness to uncertainty in system parameters. By suitable selection of output variables, the suggested control design methodology can be used for either joint space control or task space control. For illustrations, a weightless three‐link PUMA type robot arm with a special flexible third link is tested via simulation.