Diss . ETH No . 19386 INDIVIDUAL CYLINDER AIR - FUEL RATIO CONTROL

The thesis presents a complete framework for the design of an individual cylinder air-fuel ratio (A/F) controller that aims to further reduce the exhaust emissions of modern automotive gasoline engines. It is well known that this type of controller relies on a correct estimation of the A/F of the individual cylinders. Otherwise, the control system can become unstable. Therefore, the conditions for its stability and robustness are studied in detail and the results are then used to improve the robustness of the controller. A control-oriented algebraic model is formulated in the frequency domain and a Fourier analysis of the A/F sensor signal is incorporated. The observability of the individual cylinders is evaluated analytically with the condition number and graphically with polar diagrams. The structure of the model and the computation of the Fourier coefficients using the Discrete Fourier Transform (DFT) lead to a periodic time-varying linear control system which is transformed by usage of the lifting technique to a linear time-invariant (LTI) system with an increased number of input and output signals. The lifted system allows to discuss the stability with tools available for LTI systems, specifically eigenvalue analysis and robustness analysis using a modeled uncertainty. In a first approach, the robustness is investigated using Monte-Carlo simulations. As a result, the domain of robust operation is defined by two newly introduced metrics. In a second approach, two uncertainty models of different complexity are incorporated for a discussion of robustness using the scaled small gain theorem. An engine test bench is available to validate the model, the controller, and the robustness of the control system. The controller has been successfully tested under the transient conditions of the federal test procedure (FTP) and criteria for robust operation have been developed. The robustness can be increased if changes in the operating point, the ambient air pressure, and the exhaust gas temperature are compensated. Further, in dependence of the number of cylinders on one engine bank, degrees of