Contraction and Sum of Squares Analysis of Hcci Engines

By modulating engine valves to reinduct hot exhaust gas together with air and fuel, a clean and efficient form of autoignition can be created. Control of this combustion process, known as homogeneous charge compression ignition (HCCI), requires not only precise valve control but also a combustion control strategy that accounts for the cycle-to-cycle coupling through the exhaust. This paper outlines approaches for proving closed-loop stability of a valve controller and combustion controller using nonlinear analysis tools. Stability of the valve controller is shown using contraction analysis. Stability of the combustion controller is shown using sum of squares decomposition, convex optimization and the Positivstellensatz.