No-weight design of H2 controllers for square plants
In this study, a reduced complexity design procedure for H2 control problems of square plants is presented. First, all stabilising controllers are parameterised. Second, a modified inner–outer factorisation is defined for unstable plants and analytical formulas are developed. Third, the unique optimal controller is analytically derived by utilising the proposed parameterisation and the modified inner–outer factorisation. Finally, a simple tuning rule is developed for quantitative performance and robustness. The proposed procedure has three features: First, it is a no-weight design. The designer is not required to choose a weight. Second, this is an analytical design. The designer can directly use the developed design formulas and thus the design procedure is significantly simplified. Third, this is a quantitative design. The designer can design the controller for quantitative performance such as overshoot or stability margin. Numerical examples are given to illustrate the proposed method.
