Optimal Control of Direct Driven Feed Axes with Flexible Structural Components

In this paper we provide formulas for the controller gain for the velocity control of direct driven feed axes with flexible structural components. Our mathematical setting covers two general classes of structural flexibilities. For the first class we present a formula for the damping optimum, for the second a formula for the stability bound. Both formulas are algebraically exact. They are proved using the algebraic approach provided by Grobner bases. In addition, the formulas are shown to fit well to experimental data from the different drives of a machine tool manipulator.