Pachner, D., Beran, J., and Tigelaar, J., "Uncertainty Analysis of a Virtual Turbo Speed Sensor," SAE Technical Paper 2016-01-0096, 2016, doi:10.4271/2016-01-0096.
On downsized turbocharged engines, turbo speed is correlated with maximum engine airflow and therefore with maximum engine power. To ensure safe operation in the field, auto makers introduce significant engineering margins to the turbocharger maximum speed limit. Physical turbo speed sensors provide one way to reduce this engineering margin, but are not appropriate for some applications. An accurate mathematical estimation of turbocharger speed using virtual sensor can help reduce these margins, therefore increasing available power. This paper examines the best turbo speed estimation accuracy that can be achieved using a given set of production engine sensors. “Best” is defined in a minimax sense as the smallest turbo speed error interval achievable assuming the worst case combination of sensor and actuator errors and plant parameter mismatch. A combination of physical mean value engine modeling and linear optimization techniques are used to calculate the achievable turbo speed estimate accuracies in the steady-state. It is shown that close the maximum turbo speed limit, the turbo speed can be typically estimated with less than ±3% error provided the sensor set includes mass air flow (MAF) and intake manifold pressure (MAP).