The surge in demand for hydrogen (H2) across diverse sectors, including clean energy transportation and chemical synthesis, underscores the need for a thorough investigation into H2 production dynamics and the development of effective controllers for industrial applications. This paper focuses on an electrically heated steam methane reforming (SMR) process for H2 production, offering advantages such as enhanced environmental sustainability, compactness, efficiency, and controllability compared to conventional reforming methods. Electric heating of the entire system allows for adjustments in current to control reactor temperature, thereby impacting hydrogen production rates. However, accurately modeling hydrogen production dynamics presents a formidable challenge, as complex models with high precision are computationally unsuitable for real-time control integration. Considering these factors, an accurate and efficient first-principles-based lumped-parameter model is developed to provide a dependable estimation of hydrogen production in an electrically-heated steam methane reformer. This model is validated experimentally and then utilized in a model predictive controller (MPC). To obtain the necessary state estimate information for the MPC, an extended Luenberger observer (ELO) method is employed to estimate state variables from limited, infrequent and delayed measurements of gas-phase reactor outlet stream and frequent measurements of the reactor temperature. Simulation comparisons with a proportional-integral (PI) controller reveal a much faster response in achieving the desired H2 production rate under the estimation-based MPC. Additionally, the simulations demonstrate the robustness of the controller to process variability such as a decrease in catalyst activation energy, commonly encountered in the SMR process, highlighting its effectiveness in maintaining stable operation under varying process conditions.