An Air-to-Fuel ratio estimation strategy for turbocharged spark-ignition engines based on sparse binary HEGO sensor measures and hybrid linear observers

An effective Air-to-Fuel Ratio (AFR) control is paramount to ensure a good combustion and high catalyst efficiency. This work addresses the problem of determining continuous-time estimates of AFR in turbocharged Spark Ignition (SI) engines on the basis of binary sparse measurements of the exhaust gas Oxygen. The latter are provided by a HEGO (Heated Exhaust Gas Oxygen) sensor installed at the catalytic converter input in place of a more expensive linear UEGO (Universal Exhaust Gas Oxygen) sensor, as nowadays common in commercial cars. The HEGO sensor outputs two voltage values only, corresponding respectively to low or high concentration of the residual Oxygen in the exhaust gas (on/off behavior). In view of this, it can be classified as a binary sensor generating irregular and sparse measurements in that the useful information is only present at the instants of the on/off and off/on transitions. An estimation scheme based on the use of a recursive least-squares algorithm has been designed by resorting to the theory of linear hybrid observers with quantized inputs. A detailed convergence analysis of the state reconstruction error is also provided. The proposed hybrid observer scheme is employed in a PI control-loop designed to maintain the AFR close to a desired value. The effectiveness of the proposed method is demonstrated by several numerical simulations based on both synthetic and real data.