Time-optimal control of flexible systems subject to friction

This paper presents a technique for the determination of time-optimal control profiles for rest-to-rest maneuvers of a mass-spring system, subject to Coulomb friction. A parameterization of the control input that accounts for the friction force, resulting in a linear analysis of the system is proposed. The optimality condition is examined for the control profile resulting from the parameter optimization problem. The development is illustrated on a single input system where the control input and the friction force act on the same body. The variation of the optimal control structure as a function of final displacement is also exemplified on the friction benchmark problem.