This dissertation studies the spark-ignition (SI) engine knock phenomenon, abnormal combustion due to the auto-ignition of end-gas ahead of the propagated flame front, resulting in the rapid chemical energy release with aggressive combustion, limiting the further improvement of thermal efficiency and even damaging the engine mechanically. A control-oriented combustion and pressure wave model with satisfactory accuracy and low computational effort is a necessity for the knock control strategy design. This dissertation develops a control-oriented knock predictive model that includes a two-zone reaction-based combustion model and a pressure wave model. This knock predictive model is capable of accurately describing the combustion process of a spark-ignited engine and predict the in-cylinder pressure oscillations under knocking combustion in real-time. Based on this model, a feedforward and feedback stochastic knock limit control strategy is developed to reduce the knock cyclic variability and control the knock mean-intensity below a desired up bound while keeping spark timing as close to engine maximum brake torque (MBT) timing as possible. A control-oriented two-zone reaction-based model to accurately describe the combustion process of a SI engine is first developed. Instead of using the conventional pre-determined Wiebe-based combustion model, a two-step chemical reaction model is utilized to predict the combustion process along with important thermodynamic parameters such as the mass-fraction-burned, in-cylinder pressure, temperatures and individual species mass changes in both zones. Sensitivities of model parameters are analyzed during the model calibration process. As a result, one set of calibration parameters are used to predict combustion characteristics over all engine operating conditions studied in this paper, which is the major advantage of the proposed method. Also, the proposed modeling approach is capable of modeling the combustion process for real-time simulations. As the by-product of the model, engine knock can also be predicted based on the Arrhenius integral in the unburned zone, which is valuable for model-based knock control. The proposed combustion model is intensively validated using the experimental data with a peak relative prediction error of 6.2% for the in-cylinder pressure. Based on this validated combustion model, a control-oriented pressure wave model for SI engines is further developed. This model is capable of predicting the in-cylinder pressure oscillations under knocking combustion in real-time and can be used for the model-based knock prediction and control. A pressure wave equation including the knock deadening behavior is proposed, simplified, and used to calculate the pressure perturbations generated by the knocking combustion. The boundary and initial conditions at knock onset are analyzed and the analytic solution of the pressure wave equation is obtained. The model is calibrated and validated over two different engine operating conditions at knock limit. The chemical kinetic-based Arrhenius integral (ARI) and the KI20 are used as the evaluation methods for knock onset and intensity prediction, and the knock frequency is studied with a fast Fourier transform of the filtered in-cylinder pressure oscillations. Especially, the knock characteristics associated with gas mixture properties at intake valve closing is analyzed based on the experimental data and their effect to knock cycle-to-cycle variation is also studied for the proposed model. In addition, this dissertation studies the correlation between in-cylinder mixture temperature at intake valve closing and the engine knock, along with knock cyclic variability based on the knock predictive model. A strong correlation between the intake temperature and knock intensity has been obtained and validated based on the simulation investigation and experiment data obtained at knock limit. Therefore, a model-based feedforward and feedback stochastic knock limit control strategy is developed to reduce the knock cycle-to-cycle variability and maintain the knock mean-intensity within a desired up bound by controlling the spark timing as close to MBT timing as possible. The control performance is validated with the simulation results to show the capability of the model-based feedforward and feedback stochastic knock limit control in significantly reducing the knock cyclic variability and improving the knock intensity distribution for the best fuel economy.
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