City-level traffic management remains a challenging problem. Model predictive perimeter control approaches employing macroscopic fundamental diagram (MFD) based models of large-scale urban road traffic represent a high-performance solution with substantial potential for practical implementation. In this paper we propose a model-based system identification method for computing the MFD parameters given measurements on historical trajectories of the traffic state and inflow demand. The method involves casting the problem of finding the MFD parameters yielding the best fit between measurements and model predictions as an optimization problem. A nonlinear model predictive perimeter control formulation is presented to serve as an application framework, in which the MFD parameters obtained by the proposed method are used by the controller for real-time traffic control purposes. Microsimulation-based case studies, considering an urban network with 1500 links, demonstrate the operation of the proposed method.