Coldstart Modeling and Optimal Control Design for Automotive Si Engines

A large portion of the unburned hydrocarbon (HC) emissions in a typical drive cycle of an automotive SI engine is produced mainly in the initial 1-2 minutes of its operation. This period is commonly termed as "Coldstart." The minimization of the cumulative tailpipe emissions involves a trade-off between the engine-out raw emissions and efficiency of the catalytic converter. It is non-trivial to find an optimal solution. The focus of this dissertation is on developing optimal strategies to reduce coldstart emissions without adding extra hardware components to the engine. Initially, control oriented models of the engine and the catalyst were developed. Engine subsystems whose models exist in the literature such as the engine rotational model and the throttle model were adapted to the coldstart problem. An improved model for the fuel dynamics that describes the fuel film formation in the engine intake port for coldstart purposes was developed. New simplified control oriented models were developed for the exhaust temperature and the raw hydrocarbon emissions. A new energy conservation based model was developed for the engine catalyst, too and further improved using least squares adaptation. The complete engine-catalyst system model agreed well with the experimental data. In the next part of this study, controllers were developed for reduction of hydrocarbon emissions during the coldstart. The first controller design presented here was based on the principle of MIMO Dynamic Surface Control. The controller was designed to simultaneously track the profiles of two engine variables: desired raw hydrocarbon emissions and desired catalyst temperature. The trajectories could be set to achieve a fast catalyst light-off or to reduce the raw hydrocarbon emissions. These two objectives are at trade-off during the coldstart. The tracking controller was used to analyze the optimality of the various input-output profile combinations. Experimental results affirmed the effectiveness of the controller. Further, a stability analysis was added to determine the conditions on input saturation limits to guarantee convergence to a boundary layer. To further improve the controller performance, a hybrid controller was designed that switches between two hybrid modes, each favoring either of the two competing objectives. Reachability tools were used to analyze the stability of the controller. Further, an adaptive controller was designed to achieve robustness against model uncertainties. The parameters of the model were adapted using the online recursive least squares method, hence resulting in an indirect adaptive controller. Thereafter, a nonlinear Model Predictive Control (MPC) problem was formulated for optimal coldstart HC reduction. Mean value models of the engine and the catalyst were used for the purpose. Being a difficult problem to solve in its original form, a series of relaxations were employed to drive the problem to a solvable form. The objective was redefined and a convex relaxation of the model was employed to obtain a convex objective with box constraints. Redefining the objective involved choosing a parameter, for which a new iterative algorithm was proposed. A numerical example simulating the coldstart process has been presented to demonstrate the convergence and effectiveness of the algorithm.