In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon (HC) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe HC emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.

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More than three-fourths of the unburned hydrocarbon (HC) emissions in a typical drive cycle of an automotive engine are produced in the initial 2 minutes of operation, commonly known as the coldstart period. Catalyst light-off plays a very important role in reducing these emissions. Model-based paradigm is used to develop a control-oriented, thermodynamics based simple catalyst model for coldstart purposes. It is a modified version of an available model consisting of thermal dynamics and static efficiency maps, the critical modification being in the thermal sub-model. Oxygen storage phenomenon does not play a significant role during the warm-up of the engine. The catalyst is modeled as a second-order system consisting of catalyst brick temperature and temperature of the feedgas flowing through the catalyst as its states. Energy balance of an unsteady flow through a control volume is used to model the feedgas temperature, whereas energy balance of a closed system is used to model the catalyst brick temperature. Wiebe profiles are adopted to empirically model the HC emissions conversion properties of the catalyst as a function of the catalyst temperature and the air-fuel ratio. The static efficiency maps are further extended to include the effects of spatial velocity of the feedgas. Experimental results indicate good agreement with the model estimates for the catalyst warm-up. It is shown that the model represents the system more accurately as compared to the previous model on which it is based and offers a broader scope for analysis.

Automotive engine models vary in their complexity depending on the intended application. Pre-prototype performance prediction models can be very complex in order to make accurate predictions. Controller design models need to be as simple as possible since model-based controllers must operate in real time. This paper develops hybrid models for engine control that incorporate time and events in their formulation. The resulting hybrid controllers have the capability of switching between two alternative control modes. The first mode is designed to reduce the raw hydrocarbon (HC) emissions while the second mode tries to increase the temperature of the catalytic converter as rapidly as possible during the initial transient or ''cold start'' period. Reachability, as a tool for system analysis, is used to verify the properties of the closed loop system.

The initial 1-2 minutes of operation of an automotive spark-ignition engine, commonly called as the "coldstart" period, produces more than 75-80 % of the hydrocarbon (HC) emissions in a typical drive cycle. Model-based controller development requires accurate, yet simple, models that can run in realtime. Simple, intuitive models are developed to predict both tailpipe hydrocarbon (HC) emissions and exhaust temperature during coldstart. Each of the models is chosen to be sum of first order linear systems based on the experimental data and ease of parameter identification. Inputs to these models are AF R, spark timing and engine crankshaft speed. A reduced order thermodynamic model for the catalyst temperature is also developed. The parameters are identified using least squares technique. The model estimates for the coldstart are compared with the experimental results with good agreement.