On optimal control of the wastegate in a turbocharged SI engine

The project aims to improve positive torque transient response through more advanced wastegate controllers than what are used today. All controllers are developed for a standard General Motors turbocharged engine. In many turbocharged SI engines, a wastegate is used for preventing the turbine to overrun and to decrease the pumping loss. Today, the wastegate is controlled by a PI controller, which tries to fulfill a compromise between fuel consumption and torque response by regulating the wastegate position. A nonlinear Mean Value Engine Model (MVEM) of this engine, with 13 states and linearized in 45 different working points, is used. The original model, implemented in Matlab/Simulink, has been enriched with new features, like lambda and spark advance efficiencies and the related exhaust temperature correction. The project aims to do a theoretical analysis to find the optimal control of wastegate position, investigating also spark retard and fuel enrichment during a positive torque transient. First a solution for achieving optimal wastegate control is designed, based on Linear Quadratic (LQ) approach. Since the optimal control strategy is expected to vary quite much for different working points, a gain scheduling architecture has been investigated. An independent lambda controller has been developed, in order to maximize the lambda efficiency and quicken the torque response during transient. Since the system operates near a constraint boundary, another solution based on Model Predictive Control (MPC) of the wastegate has been investigated. The MPC design has been extended also to a MIMO formulation, adding the throttle and the air to fuel ratio as control inputs, and the trade off between fast torque response and fuel economy is analyzed. A complete realtime MPC implementation, with the capability for automatic code generation in the dSpace microAutobox environment, requires the model, now with 13 states, to be reduced to a minimum state space order. The extent of model reduction that is required and the possible performance deterioration have been investigated