Part 2 detailed the power train Model-Based Design and simulation process used by the team.

Verification and validation
In order to ensure the simulation tools noted in Part 2 of this series were effective for Model-Based Design, verification and validation of the results obtained from these simulators was performed. The data shown below comes from the second year competition of Challenge X and individual experiments performed at the Center for Automotive Research (CAR) at The Ohio State University. At the present time, no verification of cX-TRAC has been accomplished as this simulator is still in the development stage.

cX-SIM
Using the data collected from competition, the acceleration performance and fuel economy predicted by cX-SIM is shown to yield a very reasonable match to reality.

Experimental testing at CAR led to the validation of the battery model used in cX-SIM as shown below. During an arbitrary driving cycle, voltage data from the battery is collected and then compared to the battery voltage reported by cX-SIM once the appropriate parameters are set.

In a similar fashion, the emissions model included in cX-SIM was validated and the results are shown below. The temperature of the lean-NOx trap and outlet NOx are of particular interest when using a diesel engine and are thus the primary metrics for validating the emissions predication of cX-SIM.

cX-Dyn
In a similar fashion to cX-SIM, the results of cX-Dyn are compared to results from actual vehicle testing for verification purposes. One of the competition events used accelerometers to evaluate drivability. Using the collected data from this event, the Ohio State team proved the accuracy of their dynamic simulator.

The plot below shows the vehicle speed as predicted by cX-Dyn (blue line) when the accelerator and brake pedal positions collected from the drive quality event are used as inputs. The actual vehicle speed collected from the same event is shown on the same plot as the red line.

The next plot shows the engine speed comparisons between the simulated results and acquired data from the event. Once again, a strong correlation between the prediction of cX-Dyn and reality was exhibited.

The plot below shows the simulated and collected engine speeds during an engine start. Once again, the simulation proved to be a useful and accurate tool for predicting engine start and stop behavior.

Control strategy development and implementation
A set of conditions determined by the control strategy enables the Normal Mode. A fuel minimization strategy is active in this mode along with additional controls that regulate the battery state of charge (SOC) and maintain acceptable vehicle drivability.

Regulation of the battery SOC is an inherent feature of the fuel minimization strategy. However, additional controls are occasionally required to achieve firmer constraints on battery SOC. Drivability control is mostly achieved by means of a torque demand constraint imposed on the fuel minimization strategy. Avoiding other conditions such as pedal sensitivity, response delays, and mode transition disturbances require additional controls.

The details of these control strategies follow:

Adaptive consumption control
The Ohio State team utilized an adaptive version of the Equivalent Consumption Minimization Strategy (ECMS) to optimize the power split among energy converters. ECMS operates based on the principle that all energy consumed by the vehicle ultimately comes from the fuel tank, so that energy extracted from, or put into, the battery equates to an equivalent fuel usage or savings, respectively. The goal of ECMS is to find (through static optimization) the set of power train component torque inputs that, at a given vehicle state, minimizes the instantaneous equivalent fuel usage:

Further, power flow to and from the electric machines (EMs) affects the SOC of the battery. This also has several limitations:

Another restriction arises from the responsibility to continuously meet the driver's instantaneous power request:

The equivalent fuel consumption terms for the electric machines can be expressed as:

ECMS has an inherent weighting factor (denoted as S in (1)) that determines the equivalency between the cost of electric power and that of the chemical fuel. The fuel equivalency factor is highly correlated with the battery SOC, and its optimal value is also driving cycle-dependent. This relationship is depicted below, showing that a different choice of the equivalence factor results in measurable changes in fuel economy for different driving cycles.

The Ohio State team used an adaptive algorithm that recognizes the past driving pattern in a short time window and modifies the equivalence factor appropriately. This algorithm computes statistical measures of past driving conditions (such as mean and peak vehicle velocity) and matches the estimated driving pattern to the optimal equivalence factor for that driving pattern. A slight increase in computational complexity brings significant fuel economy improvement when compared to a non-adaptive version of the ECMS.

To accelerate the computation of a relatively complex algorithm, the ECMS minimization problem of (1) is solved off-line and look-up tables are then generated. For the Normal Mode, the input/output relationships are described by 6-dimensional maps of actuator torques as a function of engine speed, rear electric machine speed, accelerator pedal position, engaged gear, battery SOC, and the equivalence factor. SOC estimation and control
In order to have an accurate control of the battery SOC, a reliable estimate of the SOC is needed. The Ohio State team has designed an adaptive SOC estimation strategy that is shown schematically here.

This routine uses experimental models of the NiMH battery pack along with direct current integration to estimate the battery SOC. The concept behind this adaptive algorithm is to use a weighted average of two estimates of the battery SOC. One estimate is obtained by current integration and the other (much less frequently) by using the battery voltage at rest. This algorithm can be expressed in mathematical form as:

At key-on, the SOC estimate is initialized. Once a sufficiently long resting period has elapsed, the SOC estimate is corrected using experimentally determined charging-discharging maps, which are based on battery temperature and voltage measurements. An adaptive weighting factor, w, is modified in real-time according to the slope of the battery maps at the current operating conditions. This weighting factor renders the estimation routine more stable and reliable for a wide range of battery operating conditions.

Proper tuning of the equivalence factor results in a charge-sustaining control strategy over most driving cycles; however, it is beneficial to employ stricter boundary constraints into the control strategy to absolutely guarantee a desirable battery state-of charge. To achieve this, the controller switches to a modified strategy to charge or discharge the battery more aggressively near the firm SOC boundaries by adjusting the torque commands to both electric machines.

Conclusion
Through modeling and experimentation, the Ohio State Challenge x team predicted that is hybrid vehicle outperforms the stock Chevy Equinox by having a higher fuel economy and a smoother vehicle start. The team made these predictions using models developed and refined over the first three years of the Challenge X competition. These models have been verified using experimental data. As additional components are being integrated into the vehicle, the team is further refining these models using in-vehicle experimental data.

Mike Arnett is the Ohio State University Challenge X team leader. He can be contacted at arnett.62@osu.edu

Read more in these exclusive first-hand accounts from other Challenge X student design teams
Design tools spur fuel cell development year round
Student engineers develop and test a hybrid power train: Part 1 - the model
Student engineers develop and test a hybrid power train: Part 2 - the controller

References
1. The Energy Information Administration of the U.S. Department of Energy, visited 11/28/2005
2. OSU Challenge X Team, "Validation of Design and Vehicle Capabilities," Ohio State University, 2007
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4. S. Midlam-Mohler. "Modeling, Control, and Diagnosis of a Diesel Lean NOx Trap Catalyst," Ohio State University, 2005
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14. OBD trouble codes