Robust control with stable proportional-integral-plus controllers

This paper considers robust control with a stable controller using proportional-integral-plus control techniques. A formulation of robust PIP controllers is proposed on the basis of parametric pole assignment. The robustness function in the frequency domain is minimised using the freedom provided by parametric pole assignment. It shows how to combine time-domain performance specifications provided by pole assignment and robust performance specifications in the frequency domain considered by H°° control to realise joint optimum robustness. This paper also builds upon the existing PIP design philosophy, introducing a design step which stabilises the PIP controller. This design strategy not only stabilises the controller, but also ensures that the equivalent closed-loop transfer function of the system remains identical to that of the original PIP closed-loop system.