Robust control of multivariable systems by PID+Q controller

The Youla parametrization of all stabilizing compensators consists of a full-order observer-based controller and free parameters in RH_∞. In this paper, we derive a parametrization of all stabilizing compensators, which has a static output feedback term in the central part, by state-space methods instead of coprime factorization methods. Using the parametrization obtained here, we give a parametrization of stabilizing compensators based on a PID controller and point out that our parametrization based on PID controller can be interpreted as a PID controller with an internal model and a free parameter. Moreover, we design a robustly stabilizer for a closed-loop system implemented a PID controller by selecting an appropriate free parameter