Abstract-A linear programming approach designed to eliminate the residual vibration of the two-mass harmonic system subject to friction and undergoing a point-to-point maneuver is implemented. Techniques for non-robust and robust open loop controller design are explored. It is shown that consistent results can be obtained from experiments and the robustness against frequency uncertainty results in reduction in residual vibration as well as steady-state error.

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A linear programming approach designed to eliminate the residual vibration of the two-mass harmonic system subject to friction and undergoing a point-to-point maneuver is proposed and implemented on an experimental test bed. Techniques for design of positive pulse control profiles for nonrobust and robust open loop controller design are explored, where the positive pulses initiate motion and the friction force brings the system to rest. It is shown that consistent results can be obtained from experiments and the robustness against frequency uncertainty results in the reduction in residual vibration as well as steady-state error.

This paper presents a technique for the determination of timeoptimal control profiles for a rest-to-rest maneuvering multiple spring-mass-damper system, subject to Coulomb friction. A parameterization of the control input which accounts for the friction force, resulting in a linear analysis of the system is proposed. Optimality condition are examined for the control profile resulting from the parameter optimization problem. The variation of the optimal control structure as a function of final displacement is exemplified on the friction benchmark problem.

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