Robustification of the generalized predictive law (GPC) by the implicit application of the H∞ method

In this paper, we propose a method of robustification of the initial polynomial form of the generalized predictive law (GPC) for a permanent magnet synchronous machine (PMSM). For this, the procedure consists of the following three steps: First, synthesis of an initial predictive controller to ensure a better follow-up of the properties of the closed-loop system. Secondly, a robust H∞ controller is synthesized by solving the mixed sensitivity problem by using the two Riccati equations to ensure a better dynamics in regulation. Third, the two previous controllers are combined, using Youla's parameterization to determine a robustified GPC controller. This controller should simultaneously satisfy the same better tracking dynamics of the initial GPC predictive controller. In addition, it should provide the same robustness of the robust H∞ controller. To validate the efficiency of this method, a permanent magnet synchronous machine (PMSM), which presents a real process, The dynamic behavior of the proposed process is modeled by an uncertain model. In our case the nominal model is used for the synthesis of the GPC controller with and without noise, thus used for the synthesis of the controller H∞. The system is controlled by the three previous controllers where their results are compared in the time and frequency domains.