Rest-to-Rest Motion of an Experimental Flexible Structure Subject to Friction: Linear Programming Approach

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.