A study of fixed-order mixed norm designs for a benchmark problem in structural control

This study investigates the use of H 2 , μ-synthesis, and mixed H 2 /μ methods to construct full-order controllers and optimized controllers of fixed dimensions. The benchmark problem definition is first extended to include uncertainty within the controller bandwidth in the form of parametric uncertainty representative of uncertainty in the natural frequencies of the design model. The sensitivity of H 2 design to unmodelled dynamics and parametric uncertainty is evaluated for a range of controller levels of authority. Next, μ-synthesis methods are applied to design full-order compensators that are robust to both unmodelled dynamics and to parametric uncertainty. Finally, a set of mixed H 2 /μ compensators are designed which are optimized for a fixed compensator dimension. These mixed norm designs recover the H 2 design performance levels while providing the same levels of robust stability as the μ designs. It is shown that designing with the mixed norm approach permits higher levels of controller authority for which the H 2 designs are destabilizing. The benchmark problem is that of an active tendon system. The controller designs are all based on the use of acceleration feedback.