Data-Driven Loewner Matrices-Based Modeling and Model Predictive Control of a Single Machine Infinite Bus Model

In this paper, we consider the problem of data-driven modelling and model predictive control (MPC) of a single machine infinite bus system (SMIB). When a linear state-space model of the plant is not available, a pair of Loewner matrices is constructed from a set of measured input-output data and a set of prescribed poles. We prove that the Loewner matrices are the solutions of two Sylvester equations. We compute the unique linear model of an order equal to the dimension of the data sets, that interpolates the input-output data and that has all the poles prescribed at the selected locations. As an application we perform MPC on both the original system and its approximant. The simulation show that the linear data-driven model is a good approximation of the SMIB and achieves good closed-loop MPC performance.