Performance and robustness trade-offs in PIR control of uncertain second-order systems with input disturbances

We investigate the robustness, disturbance attenuation and performance capabilities of a Proportional-Integral-Retarded (PIR) controller when controlling a class of uncertain second-order systems with input disturbances. The purpose of this paper is to provide insight into the trade-offs between these conflicting requirements. This is accomplished by introducing simple delay-dependent stability conditions, expressed in linear matrix inequality form, which are used to establish the trade-offs in PIR control. In light of the obtained stability conditions, we show that improving performance comes at the cost of reduced robustness and disturbance attenuation. To our knowledge, this problem has not been addressed before and these new results provide valuable insights and systematic guidelines for designing these controllers with trade-offs in mind, thereby completing our current understanding of the tuning mechanisms in PIR control. Inspired by the application field of fuel-cell systems, experiments are carried out on a proof-of-concept switching converter prototype to demonstrate the relevance of the obtained results.