LPV-Based Air-Fuel Ratio Control of Spark Ignition Engines Using Two Gain Scheduling Parameters

The three way catalytic converter (TWC) is a critical component for the mitigation of tailpipe emissions of modern internal combustion (IC) engines. Because the TWC operates effectively only when the air-fuel ratio is very close to stoichiometric, accurate control of the air-fuel ratio is required. The dynamics of the IC engine can be modeled as a first order plus dead time for controller design purposes and vary with both engine speed and air flow. Traditional control schemes using time-invariant controllers have been successful in guaranteeing stability over the operating range of the engine but have introduced a degree of conservatism. To reduce the conservatism, a gain scheduling controller taking both engine speed and air flow as scheduling parameters is proposed. A linear parameter varying model of the plant is constructed and the controller design method is formulated in terms of linear matrix inequalities yielding a convex optimization problem. The resulting closed-loop system has guaranteed stability and performance over the designed operating range of the engine. Simulations are performed to validate and compare the controller with a time-invariant controller as well as a gain scheduling controller that takes only engine speed as a scheduling parameter.