Optimal gain‐scheduling control of proton exchange membrane fuel cell: An LMI approach

Here, an optimal linear parameter varying (LPV) controller is developed for non‐linear proton exchange membrane fuel cell (PEMFC) systems. Two performance criteria are involved in the optimal controller, including the membrane pressure and the power of the PEMFC. The former should be minimized; and, the latter should be maximized. Since the goal is to derive sufficient conditions in terms of linear matrix inequality (LMI) constraints, both performances are re‐formulated and augmented in a unique convex optimization problem. Further, the non‐linear PEMFC with the equilibrium profile dependent on time‐varying parameters, that is, current and temperature, is represented by an LPV model. Using the LMI constraints and the obtained LPV model, the gains of the controller are derived. Comparing with the state‐of‐the‐art methods, the proposed approach offers an optimal control approach with a systematic design method, in which both practical issues are treated, simultaneously. To show the advantages of the developed approach, six typical controllers, including the proposed and existing approaches, are considered and several numerical simulation results are conducted.