Controller design for flexible systems with friction: linear programming approach

The design of a controller for a flexible system under the influence of friction is presented. A linear programming technique for finding an optimal control of linear flexible systems is extended to fractional systems. A floating oscillator is used in the development, where friction and control input forces are acting on the first mass. The result of the linear programming is a control profile for rest-to-rest maneuvers where the static and Coulomb friction is included in the system model. The positive pulse controller is also developed based on the available friction force. These controllers can be applied to precision positioning systems and servo applications where the friction and flexibility are significant.