Multivariable controller tuning based on closed-loop interaction using frequency responses

In this paper, a multivariable controller design method using frequency response data set is proposed. The proposed method evaluates closed-loop interaction by using H_∞ norm and designs a controller by solving an optimization problem that involves nonconvex quadratic matrix inequalities. Then, a performance index for closed-loop interaction is directly evaluated without an approximation. This optimization problem is represented as linear matrix inequalities (LMI) by introducing iterative LMI constrains. The controller achieving highly diagonal dominance in a closed-loop manner is designed by repeating an update of the optimization problem and the LMI optimization. This optimization algorithm guarantees monotonical convergence of an evaluation value with respect to the iteration. The experimental results show the effectiveness of the proposed method in comparison with the previous method.