Tuning of dynamical controllers by a data-driven loop-shaping method for a single input plant

In this paper, a data-driven design method of a feedback gain for loop shaping is proposed for a single input plant. This method can be applied to the tuning of a static feedback gain and also that of the output matrix of a dynamical controller. Constraints on the feedback gain are represented by linear matrix inequalities based on the unfalsified concept using many responses obtained by filtering a plant response. The feedback gain is a solution of a linear matrix inequality problem, where the integral gain of the loop transfer function is maximized subject to the constraints. Numerical examples demonstrate the usefulness.