Research on Improved MPC-Based Control Strategies for PEMFC Under Low-Temperature and Normal Temperature Operating Conditions

In polar marine equipment, proton exchange membrane fuel cells (PEMFCs) are subject to two canonical regimes—low-temperature cold start and normal temperature load operation—under which standard model predictive control (MPC) manifests fundamentally distinct deficiencies. During cold start, the MPC reference trajectory fails to track the direction of maximum heat generation in real time; during normal temperature load operation, MPC rests on a deterministic prediction model and is therefore incapable of quantifying the prediction uncertainty arising from model mismatch. To overcome these limitations, we embedded two auxiliary mechanisms within the MPC architecture: an extremum-seeking control (ESC) algorithm that furnishes MPC with a maximum power reference trajectory under low-temperature conditions, and sparse variational Bayesian learning (SVB) that equips MPC with probabilistic prediction capability under normal temperature conditions. Crucially, both enhancements retain the receding-horizon optimization structure of the baseline MPC. A lumped-parameter PEMFC model was developed in MATLAB (R2025b) and validated against data taken from the literature for the low-temperature regime and against a 1 kW stack experiment for the normal temperature regime. The results demonstrate that, under the −10 °C cold start condition, ESC-MPC shortens the startup time to 19.8 s—a 24.5% reduction relative to standard MPC and a 44.4% reduction relative to optimal constant current density (CCD) control—while the peak ice volume fraction attains 61%, remaining below the safety threshold. Under the 25 °C load-step condition, SVB-MPC attenuates the voltage overshoot by 51.2% relative to PID and by 34.1% relative to standard MPC, achieves zero steady-state error in temperature regulation, and reduces the settling time by 34.7% compared with standard MPC. Collectively, these findings establish that configuring regime-specific auxiliary mechanisms within the MPC framework effectively compensates for the deficiencies of standard MPC under both operating regimes, thereby offering a viable pathway toward the reliable application of PEMFC in extreme polar environments and clean energy systems in coastal areas.