Optimal Air-to-Fuel Ratio Tracking Control With Adaptive Biofuel Content Estimation for LNT Regeneration

This paper presents an optimal control method of tracking the desired air-to-fuel ratio (AFR) based upon the adaptively estimated biofuel content for internal combustion engines equipped with the lean NOx trap (LNT) aftertreatment system. This biofuel content (or percentage of biofuel) is adaptively estimated based upon the exhaust oxygen AFR sensor signal under both the normal engine operations with lean combustion and the LNT regeneration operations with the closed-loop AFR control. The engine system is approximated by a third-order linear system in this paper. A linear quadratic optimal tracking controller is used to track the desired engine AFR during the LNT regeneration period. The robust stability of the closed-loop tracking control system with the adaptive biofuel content estimation is guaranteed over the entire biofuel range and engine speed between 600 and 5500 rpm by using the robust stability criteria for linear parameter variation systems, where the biofuel gain and engine speed are considered as the variable parameter. Several adaptive control schemes are studied through simulations, and then the selected control strategies are evaluated through dynamometer tests for a lean burn spark ignition engine. The best performance is achieved by the gain-scheduled adaptive scheme.