Ridge Regression and Data-Driven Tuning for Direct Design of FIR Type Feedback Controller

Ikezaki and Kaneko proposed Virtual Internal Model Tuning (VIMT). VIMT can tune a controller so that the closed-loop response closely matches the desired control response. However, VIMT might not achieve the desired closed-loop response if the orders of the feedback controller are unsuitable. When the feedback controller is a non-parametric controller, such as an FIR filter, there's no need to determine the desired orders of the feedback controller. But, over-learning can occur when the initial experimental data includes measured noise. In this study, we refine VIMT to prevent over-learning. We employ Ridge regression, a method designed for estimating the coefficients of multiple-regression models in situations where independent variables are highly correlated. The cost function of VIMT is minimized using a linear optimization method with 12 regularization. Over-learning is prevented by this 12 regularization. We demonstrate the effectiveness of the proposed method through experimental verification.