Discrete-time cross-term forwarding design of robust controllers for HCCI engines

Abstract

This paper presents a model-based nonlinear feedback controller designed to regulate the crank angle at 50% fuel burned (θ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CA50</inf> ) for a gasoline homogeneous charge compression ignition (HCCI) engine with high dilution during load transitions and charge temperature variations. Discrete-time version of cross-term forwarding, which has not been presented in the literature to the best of the authors' knowledge, is developed in this example based on a positive definite Lyapunov function with set-point for the temperature at intake valve closing (IVC). The nonlinear feedback controller depends on measurement of the combustion timing θ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CA50</inf> and estimation of the temperature at IVC. Closed-loop simulation of the full order engine model shows that the nonlinear feedback controller, along with a nonlinear observer, is able to regulate the combustion timing θ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CA50</inf> by stabilizing the temperature dynamics during load transitions and intake temperature variations despite the existence of model uncertainties and measurement noise.