Optimal steady-state control for linear non-right-invertible systems

The output regulation problem for an LTI plant whose outputs to be regulated are more than the control inputs is considered. For the case of constant references, a two-degree-of-freedom control scheme that minimises a quadratic cost function is presented. This cost function weights the tracking error at steady state. The methodology is based on the singular value decomposition of the plant transfer matrix at s=0. It is then shown how, by introducing some stronger assumptions, it is possible to modify the controller so as to reduce the steady-state control effort at the cost of a higher tracking error. A detailed numerical design example is finally presented