Turbo Speed Estimation Using Fixed-Point Iteration
In modern turbocharged engines the power output is strongly connected
to the turbocharger speed, through the flow characteristics of the
turbocharger. Turbo speed is therefore an important state for the
engine operation, but it is usually not measured or controlled
directly. Still the control system must ensure that the turbo speed
does not exceed its maximum allowed value to prevent damaging the
turbocharger. Having access to a turbo speed signal, preferably by a
cheap and reliable estimation instead of a sensor, could be beneficial
for over speed protection and supervision of the turbocharger.
This paper proposes a turbo speed observer that only utilizes the
conditions around the compressor and a model for the compressor
map. These conditions are either measured or can be more easily
estimated from available sensors compared the conditions on the
turbine side. The observer utilizes an ellipse model for the
compressor that outputs pressure ratio as a function of turbo speed
and compressor mass flow, alternatively mass flow as a function of
pressure ratio and turbo speed. The model is however hard to solve
analytically for the turbo speed, which is the state to be
estimated. To solve this problem a fixed-point iteration is proposed,
where the turbo speed estimation from the previous sample step
together with measured mass flow is used to estimate the pressure
ratio. The estimation is then compared to the measured pressure ratio
and the difference is used to update the turbo speed estimation for
the next iteration.
The observer is first validated in simulation showing that it
converges exactly when the model is perfect. Robustness to model
errors and noise is then shown using engine experiments where the
observer converges to track the measured turbo speed.
Andreas Thomasson, Xavier Llamas and Lars Eriksson
2017

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Last updated: 2021-11-10