A fuel control system of an engine includes a simulation module and a control module. The simulation module generates a simulated pre-catalyst exhaust gas oxygen (EGO) sensor signal based on a simulated oxygen concentration of an exhaust gas. The simulation module determines a simulated pre-catalyst equivalence ratio (EQR) for the exhaust gas based on the simulated pre-catalyst EGO sensor signal. The control module generates a desired pre-catalyst EGO sensor signal based on a desired oxygen concentration of the exhaust gas. The control module determines a desired pre-catalyst EQR based on the desired pre-catalyst EGO sensor signal. The control module determines a cost function based on the simulated pre-catalyst EQR and the desired pre-catalyst EQR. The fuel control system is calibrated based on the cost function.