With the presence of distributed energy resources in microgrids, the problem of load-frequency control (LFC) becomes one of the most important concerns. Changes in the parameters of the microgrid components, as well as the disturbances forced on the grid, make it more difficult to design a suitable LFC. This paper discusses the design of a robust model predictive controller (RMPC) based on the linear matrix inequality as a secondary controller in LFC systems for controlling a microgrid on the shipboard. The main purpose of the proposed method is to improve the frequency stability of the microgrid in the presence of disturbances and the uncertainty of its parameters. The proposed controller is simulated and compared in several different scenarios considering the uncertainty of the microgrid parameters and the input disturbances. The main controllers are the fuzzy proportional-integral type 1 and 2, and multi-objective multi-purpose functions optimized with the MOFPI (MBBHA) and MOIT2FPI (MBHA) algorithms. The effectiveness of the proposed method in terms of increasing the response speed, reducing fluctuations, overcoming uncertainties of the parameters, and ensuring robustness to disturbances are discussed. The simulations are made in MATLAB software. The proposed method reduces the frequency oscillations caused by disturbances on the microgrid by 68% (68% improvement over other methods used in this field). Also, using this method, the damping speed of microgrid frequency fluctuations is increased by 53% (performance improvement).
