Fuel cell (FC) systems are part of a prominent key enabling technology for achieving efficient and carbon-free electricity generation and, as such, their optimum operation is of great importance. This work presents the combination of two advanced model predictive control (MPC) methodologies to guarantee the optimal operation of a polymer electrolyte membrane (PEM) fuel cell system. More specifically, at the core of the proposed framework is a nonlinear model predictive control (NMPC) formulation that solves online a nonlinear programming (NLP) problem using a simultaneous direct transcription optimization method. The performance of the NLP solver is enhanced by a warm-start initialization and a search space reduction (SSR) technique. A piecewise affine (PWA) approximation of the variable's feasible space is used to define the boundaries of the search space computed offline, using a multiparametric quadratic programming (mpQP) method. The proposed unified framework is developed and deployed online to an industrial automation system. The response of the multivariable nonlinear controller is assessed through a set of experimental studies, illustrating that the control objectives are achieved and the fuel cell system operates in a stable environment, regardless of the varying operating conditions.