Automatic loop shaping of QFT robust controllers with multi-objective specifications via nonlinear quadratic inequalities

This paper introduces a new methodology to synthesize automatically robust controllers in the Quantitative Feedback Theory (QFT) framework. The method avoids the classical gridding of the controller's phase, and deals with multi-objective specifications and parametric uncertainty in the plant model. By tacking the required robust stability and robust performance specifications, and grouping them into two nonlinear quadratic inequalities, the method derives a nonlinear and frequency-dependent expression for the controller magnitude, which is independent of the controller phase. Then, by evaluating this expression for every frequency of interest, and using a least-square-type algorithm with phase constraints to find the parameters of an a priory fix order controller structure, the method finds automatically the most appropriate controller parameters to meet all the multi-objective specifications for all the plants within the uncertainty. The method is exemplified with a DC motor control application.