Robust stabilization of closed-loop 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 with 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 this parametrization can be interpreted as a PID controller with an internal model and a free parameter. We call this controller the PID + Q controller. Moreover, we design a robust stabilizer for a closed-loop system implemented as a PID controller by selecting an appropriate free parameter.