Many chemical/petrochemical processes in industry are not completely modeled from a first-principles perspective because of the complexity of the underlying physico-chemical phenomena and the cost of obtaining more accurate, physically relevant models. System identification methods have been utilized successfully for developing empirical, though not necessarily physical, models for advanced model-based control designs such as model predictive control (MPC) for decades. However, a fairly recent development in MPC is economic model predictive control (EMPC), which is an MPC formulated with an economics-based objective function that may operate a process in a dynamic (i.e., off steady-state) fashion, in which case the details of the process model become important for obtaining sufficiently accurate state predictions away from the steady-state, and the physics and chemistry of the process become important for developing meaningful profit-based objective functions and safety-critical constraints. Therefore, methods must be developed for obtaining physically relevant models from data for EMPC design. While the literature regarding developing models from data has rapidly expanded in recent years, many new techniques require a model structure to be assumed a priori, to which the data is then fit. However, from the perspective of developing a physically meaningful model for a chemical process, it is often not obvious what structure to assume for the model, especially considering the often complex nonlinearities characteristic of chemical processes (e.g., in reaction rate laws). In this work, we suggest that the controller itself may facilitate the identification of physically relevant models online from process operating data by forcing the process state to nonroutine operating conditions