Exergy Based Optimal Controller Design of a Spark-Ignition Internal Combustion Engine

Internal combustion engine (ICE) control techniques have been developed with only the first law of thermodynamics in mind, e.g. improving thermal efficiency, tracking specific load requirements, etc. The first law of thermodynamics does not account for the losses in work potential that are caused due to the in-cylinder high temperature thermodynamic processes irreversibilities. For instance, up to 25% of fuel exergy or fuel availability may be lost to irreversibilities during the combustion process. The second law of thermodynamics states that not all energy in an energy source is available to do work; its application evaluates the maximum available energy in that source after accounting for the losses caused by the irreversibilities. Therefore, including the exergy in an optimal engine control algorithm may lead to improved ICE thermal efficiencies. In this work, a model predictive controller (MPC) is developed based on the first and second laws of thermodynamics to control a detailed eight-cylinder ICE model developed in GT-Power. To make the controller practically applicable for eventual hardware in the loop (HiL) investigations, the GT-Power model is approximated with a single layer feedforward neural network (SLFN) that was trained on engine maps developed from a design of experiments. Two algorithms are used to solve the MPC optimization problem: sequential quadratic programing (SQP) and the continuation/forward difference generalized method of residuals (C/FDGMRES) for the purpose of comparing solution time and performance. Incorporating the second law of thermodynamics into the MPC design results in fuel savings of 6.8% and 3.2% for SQP and C/FDGMRES, respectively, when compared to controller MPC controller designs without exergy considerations. Comparing average solution times between the two MPC algorithms found C/FDGMRES solved the control problem on average four times faster than SQP.