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This brief uses an air conditioning system to illustrate the benefits of iteratively combining first principles and system identification techniques to develop control-oriented models of complex systems. A transcritical vapor compression system is initially modeled with first principles and then verified with experimental data. Both single-input-single-output (SISO) and multi-input-multi-output (MIMO) system identification techniques are then used to construct locally linear models. Motivated by the ability to capture the salient dynamic characteristics with low-order identified models, the physical model is evaluated for essentially nonminimal dynamics. A singular perturbation model reduction approach is then applied to obtain a minimal representation of the dynamics more suitable for control design, and yielding insight to the underlying system dynamics previously unavailable in the literature. The results demonstrate that iteratively modeling a complex system with first principles and system identification techniques gives greater confidence in the first principles model, and better understanding of the underlying physical dynamics. Although this iterative process requires more time and effort, significant insight and model improvements can be realized.