Proportional–Integral Controller Design for Combustion-Timing Feedback, From n-Heptane to Iso-Octane in Compression–Ignition Engines

The problem of designing robust and noise-insensitive proportional–integral (PI) controllers for pressure-sensor-based combustion-timing control was studied through simulation. Different primary reference fuels (PRF) and operating conditions were studied. The simulations were done using a physics-based, control-oriented model with an empirical ignition-delay correlation. It was found that the controllable region in between the zero-gain region for early injection timings and the misfire region for late injection timings is strongly PRF dependent. As a result, it was necessary to adjust intake temperature to compensate for the difference in fuel reactivity prior to the controller design. With adjusted intake temperature, PRF-dependent negative-temperature coefficient (NTC) behavior gave different system characteristics for the different fuels. The PI controller design was accomplished by solving the optimization problem of maximizing disturbance rejection and tracking performance subject to constraints on robustness and measurement-noise sensitivity. Optimal controller gains were found to be limited by the high system gain at late combustion timings and high-load conditions; furthermore, the measurement-noise sensitivity was found to be higher at the low-load operating points where the ignition delay is more sensitive to variations in load and intake conditions. The controller-gain restrictions were found to vary for the different PRFs; the optimal gains for higher PRFs were lower due to a higher system gain, whereas the measurement-noise sensitivity was found to be higher for lower PRFs.