Desensitized control of vibratory systems with friction: Linear programming approach

This paper presents a linear programming based approach for the design of controllers for rest-to-rest manoeuvres of vibratory systems subject to friction. A multiple spring mass system is considered in the development where friction and control input forces act on the same mass. The result of the linear programming is a control profile for rest-to-rest manoeuvres where the static and Coulomb friction is included in the system model. The positive pulse controller is also developed when the available frictional force brings the system to rest. These controllers can be applied to precision positioning systems and servo applications where the effect of friction and flexibility are significant.