Study of robust control designs using the critical-direction method for ellipsoidal uncertainties

The robust stability of control systems containing a plant with ellipsoidal parametric uncertainties can be analyzed using the critical-direction technique. This paper presents a succinct review of the analysis technique, and proposes two methods for synthesizing robust controllers. A simple water-heating control system with a discrete PI controller is used for illustrating the analysis and synthesis methods. The uncertainty in the plant parameters is quantified in terms of an ellipsoid derived from the results of standard parameter estimation methods. The nominal plant parameters are used to tune three candidate PI controllers using standard techniques, and then the robustness of each controller is analyzed. It is verified that the controllers cannot be stabilized from knowledge of the nominal process alone. Finally, two alternative robust control designs are realized via numerical optimization and are compared.