A comparison of scaled Popov and maximum entropy controller synthesis for flexible structures

The scaled Popov criterion is used to derive an upper bound for the worst case ℋ₂ norm over a set of linear, time-invariant, norm-bounded, block-structured parameter perturbations. This upper bound provides the basis for scaled Popov controller synthesis, which minimizes the upper bound and guarantees asymptotic stability of the closed-loop system for all real parameter perturbations in the specified set. Numerical examples demonstrate the tradeoff between achievable ℋ₂ performance and guaranteed robustness to real parameter perturbations as well as the reduction in conservatism due to the scaling matrix. These results are then compared to robust controllers obtained from the maximum entropy design technique. Both approaches are shown to yield positive real controllers for colocated structures under high levels of uncertainty in the damped natural frequencies