Servo constraint control for mechanical systems: friction force depending on control design

In this paper, the problem of motion of controlled mechanical systems under a servo constraint is considered. The servo constraint which is prescribed by the designer is supposed to be non-ideal, that is, it does work in a virtual displacement. The second order form constraint is introduced to obtain a closed-form (i.e., analytical form) control input. The final servo control contains two parts: the first one generates the constraint force so that the constraint is exactly followed, while the second one can be designed by the designer for the facility, such as to compensate the effects of the friction force. After geometrical analysis applied to the Coulomb friction forces, we found that they actually depend on the control forces (i.e., the two are coupled). Application to a 3-DOF robot manipulator is made.