Friction-attenuation control design for unstable nonminimum-phase systems

The dry friction in an unstable non-minimum-phase system can cause a self-sustained oscillation. The state feedback design can do nothing with such oscillations. If the non-minimum-phase is stabilized by output feedback, as is well known, an inner fast loop is generally needed to guarantee the robustness. It is pointed out that the friction can be attenuated by the fast loop with additional compensation design. A novel H_∞ design methodology is proposed for this two-loop system, in which the dynamics of the inner loop is treated as unmodeled dynamics, while the order of the controller can also be reduced. Such a design is a typical example of applying H_∞ control theory to multi-loop systems.