Parameter Optimization for an H2 Problem with Multivariable Gain and Phase Margin Constraints

Acute robustness problems can arise when the standard Linear Quadratic Regulator/Loop Transfer Recovery (LQR/LTR) method is applied to H2 problems having frequency-dependent penalties on plant inputs. In this case, state augmentation results in a cross-state-input term in the cost functional which can destroy the good robustness properties of LQR-based designs. The LTR procedure can not, in general, recover sufficient robustness. This paper presents a parameter optimization approach that adopts a typical frequency-shaped Linear Quadratic Gaussian (LQG) control structure in which the feedback and observer gains are optimized simultaneously. Robustness is guaranteed in this parameter optimization approach by incorporating multivariable gain and phase margin constraints. Here, the undue conservatism of using singular values alone is alleviated since both gain and phase information are considered.