Time-optimal control of a single-DOF mechanical system with friction

This note presents the exact solution to the minimum-time optimal control problem of a single-degree-of-freedom (DOF) mechanical systems with friction. In particular, the optimal control input can be synthesized in feedback form. The effect of Coulomb friction, which has been ignored or precompensated in the prior works, is taken into full account. As a result, the admissible range of control input can be maximized so as to achieve faster responses. A practical example using a direct-driven single-DOF robotic manipulator is discussed to demonstrate the practical use of the optimal solution.