Hybrid model predictive control of direct injection stratified charge engines

This paper illustrates the application of hybrid modeling and model predictive control techniques to the management of air-to-fuel ratio and torque in advanced technology gasoline direct-injection stratified-charge (DISC) engines. A DISC engine is an example of a constrained hybrid dynamical system, because it can operate in two distinct modes (stratified and homogeneous) and because the mode-dependent constraints on the air-to-fuel ratio and on the spark timing need to be enforced during its operation to avoid misfire, knock, and high combustion variability. In this paper, we approximate the DISC engine dynamics as a two-mode discrete-time switched affine system. Using this approximation, we tune a hybrid model predictive controller with integral action based on online mixed-integer quadratic optimization, and show the effectiveness of the approach through simulations. Then, using an offline multiparametric optimization procedure, we convert the controller into an equivalent explicit piecewise affine form that is easily implementable in an automotive microcontroller through a lookup table of linear gains.