Double-integrator control for precision positioning in the presence of friction

In order to achieve good performance in precision positioning systems where friction is present, a straightforward approach is using single-integrator controllers to suppress the effect of friction. In this paper, double-integrator (DI) control, in which two integrators are involved, is proposed to enhance controller gain at lower frequencies. A new integral anti-windup scheme is developed for the DI control and is shown to be effective. Performance of a DI controller is compared with that of a proportional-integral-derivative controller (I-PD) and a pole-placement-with-integration controller (PPI) by experiment on a slide system driven by a dc motor. In the system, the dc motor has brushes that give rise to friction, and all other frictional contacts are removed by frictionless aerostatic support. Because of the unmodeled high frequency dynamics caused by aerostatic dynamics, closed-loop bandwidth with the I-PD controller is limited at a lower value than in the cases with the DI and PPI controllers. With the three controllers having parameters for similar closed-loop bandwidths, the DI controller gives uniform closed-loop responses to step inputs of different heights, while for the other two controllers the responses are obviously dependent on the height of the step inputs.