Figure 3 Instantaneous Model Validation, Honda Accord.
Related Figures (11)
Figure 1: Typical power vs. fuel consumption functional form Consequently, two power-based second-order polynomial models are proposed in this paper. These models are entitled the Virginia Tech Comprehensive Power-based Fuel Consumption Model-1 and -2 (VT-CPFM-1 and VT-CPFM-2). The use of a second-order mode with a positive second-order parameter is required in order to ensure that a bang-bang control does not result from the application of the model, as was described earlier in the paper. Additior of higher than second-order parameters would add to the complexity of the model and thus not allow for model calibration using the EPA city and highway cycles. Consequently, a second- order model provides a good compromise between model accuracy and applicability. The two VI-CPEM models are formulated as As was mentioned earlier, the first model does not require engine data to estimate vehicle fuel consumption rates. The idling fuel consumption rate for the VT-CPFM-1 model is estimated using Equation (7) and bounded using Equation (8) to ensure that the functional form is convex, as will be discussed later in the paper. The idling fuel consumption rate in Equation (7) is an average operating point method that was proposed by Guzzella and Sciarretta. It should be noted that in reality the idling fuel consumption rate constantly fluctuates, however the proposed mode assumes, for simplicity purposes, that the rate remains constant. Here Py. is the idling fuel mean pressure (400,000 Pa); ia is the idling engine speed (rpm); d is the engine displacement (liters); O is the fuel lower heating value (43,000,000 J/kg for gasoline fuel); N is the number of engine cylinders; Fin, and Fy, are the total fuel consumed for the EPA city and highway drive cycles (liters), respectively (computed using Equations (9) and (10), respectively); Tein, and Thwy are the durations of the city and highway cycles (1875s and 766s, respectively); Pein, and P’ cir, are computed as the sum of power and power squared exerted each second over the entire cycle (computed using Equations (11) and (12), respectively). Similarly, Pj, and Pinwy are estimated in the same manner for the highway cycle (computed using Equations (11) and (12), respectively). The ¢ term ensures that the second-order parameter (Q2) is greater than zero. Experimentation with the model revealed that a minimum value of 1E- 06 ensures that the optimum fuel economy cruising speed is in the 60 to 80 km/h range which is typical of light-duty vehicles. Table 1: List of Parameters Required for Model C alibration Figure 4: Instantaneous M odel Validation, City Cycle. Figure 6: Simulated Fuel Economy for Different Driving Cycles. 6. CONCLUSIONS
