Data-driven controller design for loop-shaping using plant transient responses

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 derived based on the unfalsified control using the plant responses without assuming any mathematical model. A solution can be obtained by solving a linear matrix inequality, where the integral gain of the loop transfer function is maximized subject to the constraints. Numerical examples demonstrate the usefulness.